<STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Let's Get Together</p></td></tr><tr><td bgcolor=#ffffff> <p><span class="cap">I</span>t's Saturday afternoon and Shanice and her friends want to get together and have some fun. In this project, you will use scientific ideas of velocity to help them meet up. As you work through this project, think about what velocity means to you.</p> <!-- BEGIN templated image --!> <BR> <CENTER><IMG SRC="http://wise.berkeley.edu/upload/14198/friends_hanging_out.gif"></CENTER><BR> <!-- END templated image --!> Evidence created 9/30/2004 by Jason Finley Updated 10/24/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. What does velocity mean to you and your partner? <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Hanging Out With Friends</p></td></tr><tr><td bgcolor=#ffffff> <br> <p>Shanice finishes with her Saturday Math and Science Academy classes around 12:45 pm. While she is waiting for a classmate to finish copying her notes, she uses her cell phone to text message her friends, Vijay, Isabel, and Antonio. </p> <table align=center width=90% border=1> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange.jpg"></td> <td><b>"Hey friends, where are you? What are you up to today?"</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_vijay.jpg"></td> <td><b>"I am across the street from the library. I was doing some research for my report due next week."</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_isabel.jpg"></td> <td><b>"I am at the park collecting soil samples for my science fair project."</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_antonio.jpg"></td> <td><b>"I am volunteering at the Police Station."</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_antonio.jpg"></td> <td><b>"Do you all want to see a $2 matinee movie?"</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_vijay.jpg"></td> <td><b>"Yes, the new movie with all the special effects is playing."</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_isabel.jpg"></td> <td><b>"A $2 movie! I'm down! The movie starts at 1:15 PM."</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange.jpg"></td> <td><b>"Let's all meet there at 1:10 PM. It’s 1:00 PM now."</b></td> </tr> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/cell_orange_all.jpg"></td> <td><b>"Cool, C-ya in 10 minutes!"</b></td> </tr> </table> </td></tr></table> Evidence created 9/30/2004 by Jason Finley Updated 10/10/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">City Map</p></td></tr><tr><td bgcolor=#ffffff> <p>The stars (<IMG SRC="http://wise.berkeley.edu/upload/18343/star.xbm">) on the City Map below show the location of the friends from the text message conversation. Use the City Map to figure out the distance and direction each friend needs to travel to the Movie Theater (Cinema). </p> <br> <p><b>Fill in Columns A and B in Table A in the "Hanging With Friends" Worksheet with the <i>distance</i> and <i>direction</i> each friend needs to travel to the Movie Theater.</b>.</p> <br> <p>Remember: <br> <ul><li>Vijay is across the street from the City Library.<br> <li>Antonio is at the Police Station.<br> <li>Isabel is at the Lake Park.<br> <li>Shanice is at City Middle School.</ul></p><br> <br> <center><IMG SRC="http://wise.berkeley.edu/upload/18343/introcitymap.gif"> </td></tr></table> Evidence created 9/30/2004 by Jason Finley Updated 10/10/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. How far and in what direction does Shanice have to travel to get to the Movie Theater? Stars on the map show you where to begin and end measuring distances. <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">"How do we get there?"</p></td></tr><tr><td bgcolor=#ffffff> <p>What type of transportation do you think each friend should use if they need to arrive at the Movie Theater in <u>exactly</u> 10 minutes?</p> <br> <p>Each friend has six choices for transportation. They can:</p> <ul> <p><li> ride a bike and travel at 4 meters per second. <br> <li> ride in a car (with a parent's permission) and travel at 12 meters per second.<br> <li> ride the bus and travel at 10 meters per second.<br> <li> rollerblade and travel at 3 meters per second.<br> <li> walk and travel at 2 meters per second.<br> <li> ride on a scooter with an adult and travel at 6 meters per second. </ul> </p> <p>Fill in Columns C and D in Table A with each friend's choice of transportation and the speed it travels.</p> </td></tr></table> Evidence created 9/30/2004 by Jason Finley Last updated 10/3/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. What type of transportation do you think each friend should use if they need to arrive at the theater in <u>exactly</u> 10 minutes? How did you figure out Vijay's mode of transportation? What was the most difficult part of solving this problem? <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Speed and Velocity</p></td></tr><tr><td bgcolor=#ffffff> <p>Scientists use speed and velocity to describe motion.</p> <br> <table align=center width=100% border=0><tr><td valign=top> <p><b>Speed</b> is the rate a person or object changes their position. </p> <br> <p><b>Velocity</b> has two components, magnitude, also called speed, and direction. Basically, <b>velocity is speed with direction</b>.</p> </td> <td><!-- BEGIN templated image --!> <BR> <IMG SRC="http://wise.berkeley.edu/upload/14198/speedlimitsigns.gif"> </td></tr></table> <p>By using speed and velocity to describe the motion of a person or object, you learn:</p> <ul> <li> How fast or slow a person or object moves. <br> <li> How far the person or object travels. <br> <li> The direction a person or object moves. <br> <li> The time it takes a person or object to travel. </ul> </td></tr> <tr><td> Image courtesy of Como Signs </td></tr></table> Evidence created 10/6/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. Pick one of the friends (Shanice, Isabel, Vijay or Antonio) and describe his or her speed and velocity. <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#ffffff> <p>In Activity 1, words were used to describe the motion of the four friends, Antonio, Vijay, Shanice, and Isabel. This is only one way to describe the friends' motion. What other ways can you think of to describe this problem?</p> <center><IMG SRC="http://wise.berkeley.edu/upload/14198/studygirls.jpg"></center> </td></tr></table> <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Visualize the Problem</p></td></tr><tr><td bgcolor=#ffffff> <p>Use the visual representation below to figure out which method of transportation each friend should use to travel to the Cinema and arrive in <u>exactly</u> 10 minutes.</p> <p><b>Instructions</b>: <ol><li>Decide what transportation each friend should use.</li> <li>Drag a picture of each friend's transportation to their location.</li> <li>To test if you chose the correct transportation for each friend, click the START button. The friends will move toward the cinema.</li> <li>Watch the time in the left hand corner to see what time each friend arrives the cinema.</li> <li>If all of the friends do not arrive at the Cinema in <u>exactly</u> 10 minutes, click the RESET button and start over.</li> <li>When all of the friends arrive at the Cinema in <u>exactly</u> 10 minutes, click the "Comparison notes" step.</li> </p> <!-- URL's used in the movie--> <!-- text used in the movie--> <!--Bike = 4 m/sWalk = 2 m/sCar = 13 m/sBus = 10 m/sNSE8000 m 2400 m 1200 m 6000 m CINEMAD = 200 mA B C go--><OBJECT codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,0,0" WIDTH="700" HEIGHT="700" id="vectors4" ALIGN=""> <PARAM NAME=movie VALUE="vectors4.swf"> <PARAM NAME=quality VALUE=high> <PARAM NAME=bgcolor VALUE=#FFFFFF> <EMBED src="http://svn.concord.org/svn/projects/trunk/common/java/otrunk/otrunk-examples/LOOPS-Pas/models/vectors4.swf" quality=high bgcolor=#FFFFFF WIDTH="700" HEIGHT="700" NAME="vectors4" ALIGN="" TYPE="application/x-shockwave-flash" PLUGINSPAGE="http://www.macromedia.com/go/getflashplayer"></EMBED> </OBJECT> <!-- BEGIN templated link --!> </tr></td></table> Evidence created 9/30/2004 by Jason Finley Updated 10/25/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. Does this Velocity Visualization help you understand the friends' velocity problem better than the word problem you tried to solve earlier? Why? <p></p><p></p> To refresh your memory, here are screenshots of the word problem and visualization:<p></p> <table width="340" border="0" cellspacing="0" cellpadding="0"> <tr> <td><div align="center">Velocity Word Problem</div></td> <td><div align="center">Velocity Visualization</div></td> </tr> <tr> <td><div align="center"><a href="http://wise.berkeley.edu/upload/16146/velocityverbal.gif" target="_new"><img src="http://wise.berkeley.edu/upload/16146/velocityverbal.gif" width="160" height="187" border="0"></a></div></td> <td><div align="center"><a href="http://wise.berkeley.edu/upload/16146/velocityvisual.gif" target="_new"><img src="http://wise.berkeley.edu/upload/16146/velocityvisual.gif" width="160" height="187" border="0"></a></div></td> </tr> </table> <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Interview with Isabel</p></td></tr><tr><td bgcolor=#ffffff> <p>Later in the day, Isabel heads back to the Movie Theater. Let's <i>interview</i> Isabel to find out her velocity as she traveled from the Lake Park to the Movie Theater. An interview is simply a conversation with someone about their experiences and knowledge. <br></p> <br> <p>In the interview below, we are the "Interviewers" who ask Isabel several questions. As you read, pay attention Isabel's answers. </p> <br> <table align=center width=100% border=1> <tr> <td><b>Interviewers</b></td> <td>"Isabel, where did you begin your trip?"</td> </tr><tr> <td><b>Isabel</b></td> <td>"I started my trip at Lake Park, the corner of 2nd Avenue and Main Street. This is referred to as my <font color=red><i>initial position</i></font>."</td> </tr><tr> <td><b>Interviewers</b></td> <td>"What time did you leave Lake Park?"</td> </tr><tr> <td><b>Isabel</b></td> <td>"I left the Lake Park at 5:00 pm, before it got dark. This is referred to as my <font color=red><i>initial time</i></font>." </td> </tr><tr> <td><b>Interviewers</b></td> <td>"Where did you end your trip?" </td> <tr></tr> <td><b>Isabel</b></td> <td>"I ended my trip at Movie Theatre at 3rd Avenue and Main Street. This is referred to as my <font color=red><i>final position</i></font>."</td> </tr><tr> <td><b>Interviewers</b></td> <td>"What time did you arrive at the Movie Theater?" </td> <tr></tr> <td><b>Isabel</b></td> <td>"I was running a bit late and almost didn’t get a seat. I arrived at the Movie Theatre at 5:05 pm. This is referred to as my <font color=red><i>final time</i></font>." </td> </tr><tr> <td><b>Interviewers</b></td> <td>What direction were you traveling in when you were going to the Movie Theater?" </td> </tr><tr> <td><b>Isabel<b></td> <td>"I was travelling West."</td> </tr><tr> <td><b>Interviewers</b></td> <td>"Wow! Thanks, Isabel for all this information! Let's write some of this down before we forget." </td> </tr></table> </td></tr></table> Evidence created 10/7/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. Record data from the interview which will help you calculate Isabel's velocity. Why do you need this information? How would you use this data to calculate Isabel's velocity? <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Calculating Isabel's Velocity </p></td></tr><tr><td bgcolor=#ffffff> <p>To calculate velocity, we use the following formula:</p> <br> <table align = center width=100% border=0 bgcolor=66CCCC> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>Final Position - Initial Position</b> </center> </td> <td> <br> </td> <td> <center> <b>Change in Position</b></center> </td> </tr> <tr> <td> <center> <b> Velocity </b></center></td> <td> <center> <b> = </b> </center> </td> <td> <center> <b> ---------------------------------- </center> </b></td> <td> <b> = </b></td> <td> <center> <b> ----------------------------------------- </b> </center> </td> </tr> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>Final Time - Initial Time </b></center> </td> <td> <br> </td> <td> <center><b> Change in Time</b> </center> </td> </tr> </table> <br> <p> Let's use this formula to calculate Isabel's velocity! Let's start with the "<font color=FF000>change in position</font>."</p> <table border="0" cellspacing="3" cellpadding="3"> <tr> <td width="382"><p>Isabel's Initial Position:</p> <p><img src="http://wise.berkeley.edu/upload/16146/isabel_initial_pos.jpg"></p> <p>Isabel's Final Position:</p> <p><img src="http://wise.berkeley.edu/upload/16146/isabel_final_pos.jpg"></p> <p>Isabel's Change in Position:</p> <p><img src="http://wise.berkeley.edu/upload/18343/isabel_change_pos1.jpg"></p></td> <td width="248"><IMG SRC="http://wise.berkeley.edu/upload/18343/compass.gif"></td> </tr> </table> <br> <p>&nbsp;</p> <p>Now, let's update our velocity formula with what we know:</p> <table align = center width=100% border=0 bgcolor=66CCC> <tr> <td> <br> </td> <td> <br> </td> <td><center><font color="FF000"><b>3600 meters - 0 meters </b> </font></center> </td> <td> <br> </td> <td> <center> <font color="FF000"> <b>3600 meters West </b></font></center></td> <td> <br> </td> <td> <center> <b><font color="FF000">Change in Position</font> </b></center> </td> </tr> <tr> <td> <center> <b> Velocity </b></center></td> <td> <center> <b> = </b> </center> </td> <td> <center> <b> ------------------------- </center> </b></td> <td> <b> = </b></td> <td> <center> <b> ---------------------------------</b> </center> </td> <td> <b> = </b></td> <td><b><center>-------------------------------</b></center> </td> </tr> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>Final Time - Initial Time </b></center></td> <td> <br> </td> <td> <center> <b>Final Time - Initial Time </b></center></td> <td> <br> </td> <td> <center><b> Change in Time </b> </center> </td> </tr> </table> </td></tr></table> Evidence created 9/30/2004 by Jason Finley Updated 10/17/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Calculating Isabel's Velocity </p></td></tr><tr><td bgcolor=#ffffff> <p>Now we know Isabel's "change in position." </p> <br> <table align = center width=100% border=0 bgcolor=66CCC> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>3600 meters West</b></center> </td> <td> <br> </td> <td> <center> <b>Change in Position </b></center> </td> </tr> <tr> <td> <center> <b> Velocity </b></center></td> <td> <center> <b> = </b> </center> </td> <td> <center> <b> ---------------------------- </center> </b></td> <td> <b> = </b></td> <td> <center> <b> -------------------------------------------- </b> </center> </td> </tr> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>Final Time - Initial Time </b></center> <td> <br> </td> <td> <center><b> Change in Time</b> </center> </td></td> </tr> </table> <br> <p> Let's figure out her "<font color="FF000">change in time</font>."</p><br> <p>Isabel's Initial Time:</p><p><img src="http://wise.berkeley.edu/upload/16146/isabel_initial_time.jpg"></p> <p>Isabel's Final Time:</p><p><img src="http://wise.berkeley.edu/upload/16146/isabel_final_time.jpg">&nbsp;&nbsp;&nbsp;&nbsp;<img src="http://wise.berkeley.edu/upload/18343/compass.gif"></p> <p>Isabel's Change in Time:</p><p><IMG SRC="http://wise.berkeley.edu/upload/18343/isabel_change_time1.jpg"></p> <br> <table align = center width=100% border=0 bgcolor=66CCC> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>3600 meters West</b></center> </td> <td> <br> </td> <td> <center> <b>3600 meters West</b></center> </td> <td> <br> </td> <td> <center> <b>Change in Position </b></center> </td> </tr> <tr> <td> <center> <b> Velocity </b></center></td> <td> <center> <b> = </b> </center> </td> <td> <center> <b> ---------------------------- </center> </b></td> <td> <b> = </b></td> <td> <center> <b> -------------------------------------------- </b> </center> </td> <td> <b> = </b></td> <td> <b> <center>---------------</center></b></td> </tr> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <font color="FF000"> <b> 5:05 PM - 5:00 PM </b></font></center> </td> <td><br></td> <td> <font color="FF000"><center> <b> 5 minutes </b> </font></center></td> <td> <br> </td> <td> <center><b> <font color="FF000">Change in Time</font></b> </center> </td> </tr> </table> <br> <p>Before we complete this calculation, let's look closer at the "change in time." Our change in time is 5 minutes. We need time in seconds. Using the fact that there are 60 seconds in 1 minute, we will convert 5 minutes to <font color="FF000">300 seconds</font>. Let's plug this value into our equation:</p> <br> <table align = center width=100% border=0 bgcolor=66CCC> <tr> <td> <br> </td> <td> <br> </td> <td> <center> <b>3600 meters West</b></center> </td> <td> <br> </td> <td> <center> <b>3600 meters West</b></center> </td> <td> <br> </td> <td> <center> <b>12 meters West</b></center> </td> </tr> <tr> <td> <center> <b>Velocity</b></center></td> <td> <center> <b> = </b> </center> </td> <td> <center> <b> ---------------------------- </center> </b></td> <td> <b> = </b></td> <td> <center> <b> -------------------------------------------- </b> </center> </td> <td> <b> = </b></td> <td> <b> <center>---------------</center></b></td> </tr> <tr> <td> <br> </td> <td> <br> </td> <td> <center><b>5 minutes </b></center> </td> <td><br></td> <td> <font color="FF000"><center> <b>300 seconds</b> </font></center></td> <td> <br> </td> <td> <center><b>seconds</b> </center> </td> </tr> </table> <br> <p>Using information about Isabel's trip, we calculated Isabel's velocity as she traveled to the Movie Theater: </p> <br> <table align=center width=100% border=0 bgcolor=66CCC> <tr> <td> <center> <b> Isabel's Velocity </b></center></td> <td> <center> <b> = </b> </center> </td> <td> <center> <b> 12 meters/second (m/s) in the Westward direction </b> </center> </td> </tr> </table> </td></tr></table> Evidence created 10/9/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. Does the Friends' Calculation Visualization help you understand velocity better than the Velocity Visualization you worked with earlier? Why? <p></p><p></p> To refresh your memory, here are screenshots of the visualizations:<p></p> <table width="340" border="0" cellspacing="0" cellpadding="0"> <tr> <td><div align="center">Friends' Calculation Visualization</div></td> <td><div align="center">Velocity Visualization</div></td> </tr> <tr> <td><div align="center"><a href="http://wise.berkeley.edu/upload/16146/velcalcmodel.gif" target="_new"><img src="http://wise.berkeley.edu/upload/16146/velcalcmodel.gif" width="160" height="187" border="0"></a></div></td> <td><div align="center"><a href="http://wise.berkeley.edu/upload/16146/velocityvisual.gif" target="_new"><img src="http://wise.berkeley.edu/upload/16146/velocityvisual.gif" width="160" height="187" border="0"></a></div></td> </tr> </table> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#ffffff><center><b> Use the graphs below to answer questions 1 and 2.</b></center> <table align=center width=90% border=0><tr> <td><center><IMG SRC="http://wise.berkeley.edu/upload/14198/shanicegraph.jpg"> </center></td> <td> <br> </td> <td><center><IMG SRC="http://wise.berkeley.edu/upload/14198/isabelgraph.jpg"> </center></td></tr> <tr> <td> <center><b>Graph A</b></center> </td> <td> <br> </td> <td> <center><b>Graph B</b></center> </td> </tr> </tr></table> </td></tr></table> <br> <p align=left><b>1. </b>Carefully study Graph A and Graph B. Compare and contrast the two graphs.</p> <p><b>2. </b>Remember the "Friends' Velocity Calculation Visualization" you worked with Activity 3. These are graphs of Shanice's and Isabel's motion.</p> <p>Use the information you recorded in <b>Table B</b> on the worksheet to help you figure which graph matches Shanice's motion. <b>Explain your answer</b>.</p> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta name="generator" content="HTML Tidy for Java (vers. 26 Sep 2004), see www.w3.org" /> <title></title> </head> <body> <center> <table align="center" width="90%" border="1" bgcolor="E9FDEB" cellspacing="5" cellpadding="12"> <tr> <td bgcolor="#D1F3FE"> <center> <p class="h3">Let's Ride with Antonio!</p> </center> </td> </tr> <tr> <td bgcolor="#ffffff"> <table align="center" width="100%" border="0"> <tr> <td> <p>To help us understand more about graphs, we need Antonio. In this activity, you will observe Antonio as he rides his bicycle.</p> <br /> <p>Click on <b>Launch</b> button below to begin running the Antonio's Ride visualization.</p> <br /> <p><b>WARNING</b>: It may take a few minutes to load. Patience is a virtue! While you wait, think about what you have learned about graphs in your science and math classes. Discuss with your partner.</p> </td> <td><img src="http://wise.berkeley.edu/upload/14198/bike.JPG" /></td> </tr> </table> </td> </tr> </table> </center> </body> </html> <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Let's Ride with Antonio!</p></td></tr><tr><td bgcolor=#ffffff> <p>Let's review Antonio's bike rides. Below are the graphs of Antonio's rides that you observed in the last activity. </p> <table align=center width=90% border=0> <tr><td><IMG SRC="http://wise.berkeley.edu/upload/14198/antoniopos.jpg"></td> <td><IMG SRC="http://wise.berkeley.edu/upload/14198/antonioneg.jpg"> </td> <td><IMG SRC="http://wise.berkeley.edu/upload/18343/compass.gif"></td> </tr> <tr><td> <center><b>Antonio's Bike Ride to the East</center></b></td> <td> <center><b>Antonio's Bike Ride to the West</center></b></td> </tr></table> <br> <p>Let's compare and contrast these two graphs. This means we will discuss the similarities and differences between these two graphs.</p> <br> <table align=center border=1 width=100%> <tr><td valign=top><p><font color="FF000"><b>Similarity:</b>Both graphs are <i>position vs. time graphs</i>.</font> </p> <p><b>Evidence:</b>The axes determine the type of graph. The horizontal axis displays the time during Antonio's rides. The vertical axis displays Antonio's position during his rides.</p></tr></td> <tr><td><p><font color="FF000"><b>Similarity:</b>Both graphs show the same speed (magnitude of velocity) for Antonio's rides.</font> </p> <p><b>Evidence:</b> Look at the <i>slope</i> or slant of the line to determine speed. Use the postion and time values to calculate his speed. Rule of thumb: The steeper the slope, the higher the speed.</p></tr></td> <tr><td valign=top><p><font color="FF000"><b>Similarity:</b> Both graphs show that Antonio traveled at a <i>constant velocity</i>.</font> That means he rode at the same speed and in the same direction his entire trip.</p> <p><b>Evidence:</b>On a position versus time graph, constant velocity is represented with a straight line.</p></td></tr> <tr><td><p><font color="FF000"><b>Difference:</b>Each graph represents the different directions that Antonio rode his bike.</font></p> <p><b>Evidence:</b> Look at the slope of the line to figure out direction. Calculate the <i>change in position</i> (final position - initial position). If the number is positive, then the graph of Antonio's ride has a positive slope. See Antonio's Ride to the East graph. If the number is negative, then the graph of Antonio's ride has a negative slope. See Antonio's Ride to the West graph.</p> </td> </tr> </table> </td></tr></table> Evidence created 10/15/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#ffffff><b><p> You have just learned more about graphs. Use this new information to study Graph A and Graph B again. Use the graphs below to answer question 1.</b></p><br> <table align=center width=90% border=0><tr> <td><center><IMG SRC="http://wise.berkeley.edu/upload/14198/shanicegraph.jpg"> </center></td> <td> <br> </td> <td><center><IMG SRC="http://wise.berkeley.edu/upload/14198/isabelgraph.jpg"> </center></td></tr> <tr> <td> <center><b>Graph A</b></center> </td> <td> <br> </td> <td> <center><b>Graph B</b></center> </td> </tr> </tr></table> </td></tr></table> <br> <p align=left><b>1. </b>Compare and contrast the two graphs.</p> Does the Antonio's Ride Visualization help you understand velocity better than the Friends' Calculation Visualization you worked with earlier? Why? <p></p><p></p> To refresh your memory, here are screenshots of the visualizations:<p></p> <table width="340" border="0" cellspacing="0" cellpadding="0"> <tr> <td><div align="center">Antonio's Ride Visualization</div></td> <td><div align="center">Friends' Calculation Visualization</div></td> </tr> <tr> <td><div align="center"><a href="http://wise.berkeley.edu/upload/16146/antridemodel.gif" target="_new"><img src="http://wise.berkeley.edu/upload/16146/antridemodel.gif" width="160" height="187" border="0"></a></div></td> <td><div align="center"><a href="http://wise.berkeley.edu/upload/16146/velcalcmodel.gif" target="_new"><img src="http://wise.berkeley.edu/upload/16146/velcalcmodel.gif" width="160" height="187" border="0"></a></div></td> </tr> </table> <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">The Race</p></td></tr><tr><td bgcolor=#ffffff> <p>Vijay challenges Wei-Lynn to a 50 meter race. They do not start in the same position. Vijay starts 50 meters North of the finish line and Wei-Lynn starts 50 meters South of the finish line. The graph below shows the first 30 meters of Vijay's run and the first 30 meters of Wei-Lynn's run. They each still have to run 20 more meters to reach the finish line.</p></td></tr> <tr><td><center><p><IMG SRC="http://wise.berkeley.edu/upload/18343/revised_racegraph.jpg"></p></td></tr> </table> Evidence created 10/18/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. Who do you predict to win the race, Wei-Lynn or Vijay? Why? By how many seconds will the winner of the race cross the finish line before the 2nd place finisher? <STYLE TYPE="text/css"> acronym { color: green; } P {font-family:Arial, Helvetica;font-size:14pt;color:#330000;margin:6px 3px} P.block {font-family:arial, Helvetica;font-size:12pt;color:#330000;margin:6px 3px} SPAN.cap {font-size:20pt} SPAN.em {color:#993300} P.h1 {font-family:Arial, Helvetica;font-size:28pt;font-weight:bold;color:#993300;text-align:center;margin:2px} P.h2 {font-family:Arial, Helvetica;font-size:18pt;color:#1C1B35;text-align:center;margin:2px} P.h3 {font-family:Arial, Helvetica;font-size:28pt;color:#96071F;text-align:center;margin:2px} P.h4 {font-family:Arial;color:#000033;font-size:12pt;margin:2px} SPAN.earth {font-family:Arial, Helvetica;font-size:18pt;color:#230B33;text-align:center;margin:2px} P.photo {margin:0px 8px 2px;font-size:10pt;font-style:italic} P.someGrim {font-size:16pt;font-weight:bold;color:#CCEEFF} P.stat {font-family:Arial, Helvetica;font-size:14pt;font-weight:bold;margin:8px 4px;color:#993300} P.toRead {font-family:Times;font-size:12pt;margin:8px 8px 2px} P.outLink {font-family:times;font-size:18pt;text-alin:center;margin:2px 8px 8px} </STYLE> <CENTER><TABLE ALIGN=CENTER WIDTH=90% BORDER=1 bgcolor=E9FDEB CELLSPACING=5 CELLPADDING=12> <tr><td bgcolor=#D1F3FE><center><p class="h3">Where Will They Meet?<p></td></tr><tr><td bgcolor=#ffffff> <table align=center width=100% border=1> <tr><td bgcolor=D1F3FE> <p>After the movies, Shanice text messages her friend Wei-Lynn so they can meet and walk around town. Your job is to figure out when and where they will meet. The stars (<IMG SRC="http://wise.berkeley.edu/upload/18343/star.xbm">) show where Wei-Lynn and Shanice are located.</p> <br> <p>It is 3:30 pm and Wei-Lynn just got on the bus at the Main Street Bus Station and heads toward the Movie Theater (Cinema). She travels at the constant velocity of 8 meters per second East.</p> <br> <p>Shanice leaves the Movie Theater (Cinema) and begins to walk toward the Main Street Bus Station at 3:30 pm. She travels at the constant velocity of 2 meters per second West.</p> <br> <p>Wei-Lynn asks the bus driver to stop the bus as soon as she and Shanice are in the same place. In the next step, draw a graph that shows Shanice's movement.</p> </td></tr> <tr><td> </b> </ul></p> <br> <br> <p><center><IMG SRC="http://wise.berkeley.edu/upload/18343/finalcitymap.gif"> </center></p> </td></tr> </td></tr></table> Evidence created 9/30/2004 by Jason Finley Updated 11/4/2004 by Erika Tate Modified 2/7/2008 by Ken Bell. What time do Wei-Lynn and Shanice meet? Where on Main Street do Wei-Lynn and Shanice meet?