ࡱ>  Mbjbj jjHl"""""""64.d6'.'0'0'0'0'0'0'${) +T'-"]"T'""':"".'.'( #""J% Ё !6 *v$J%'0'$c,c,J%66""""Lesson 1 - Average Speed as a Weighted Average Average Speed as a Weighted Average explores the difference between the instantaneous and average speed of an object by varying the speed of a car on an elliptical track.  Prerequisites Students should be familiar with the definition of average speed as the ratio of distance traveled over time elapsed. Learning Outcomes Students will be able to use the concept of time-weighted average of speed to calculate the average speed. Instructions Students should understand the applet functions that are described in Help and ShowMe. The applet should be open. The step-by-step instructions in this lesson are to be carried out in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.  Contents  HYPERLINK "\\FILEDEV\sped\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\" \l "1" The Average of Two Speeds  HYPERLINK "\\FILEDEV\sped\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\" \l "2" Average Speed as a Time-Weighted Average 1. The Average of Two Speeds Suppose a car goes around an oval track at a speed of 20m/s. Upon completing the first round, the car increases its speed very quickly (let's assume instantaneously to make the calculation easier) to 40m/s and then goes around the track the second time at 40m/s. What is the car's average speed over the two rounds? It may be tempting to say 30m/s. After all, the average would be (20m/s + 40m/s) / 2 = 30m/s. However, that would not be the right answer because average speed is not defined as an arithmetic mean of multiple speeds. Average Speed is equal to the distance traveled divided by the time elapsed.Expressed as an equation,  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation1.gif" \* MERGEFORMATINET (1) Quantity Symbol SI Unit average speed vav m/s distance d m time interval t s Before we use equation (1) we will use the applet to determine the average speed "experimentally".  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise1.gif" \* MERGEFORMATINET  Simulate the car's motion with the applet by setting the speed to 20m/s, letting the car complete one round, pausing the motion, resetting the speed to 40m/s, and letting the car complete the second round and pausing the motion again. You may not be able to pause the motion exactly after the car has completed a round, which will introduce a slight error. Sketch the car's average speed vs. time after the car has completed the second round by selecting the Speed vs. Time checkbox. Observe that the average speed changes continually during the second round, but that at no time during that round it is equal to 30m/s. The average speed is always less than 30m/s, and you should find that upon completion of the second round it is around ____________m/s. Record the total accumulated time from the data table (click  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\control_icon_png\\data.png" \* MERGEFORMATINET ). total time: ___________s Average Speed vs. time  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\graph_paper.gif" \* MERGEFORMATINET  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise2.gif" \* MERGEFORMATINET  Reset the applet. Set the car's speed to 20m/s and pause the motion after it has completed one round. Display the data table and record the accumulated time from Bin 9 in the Data table. time = _______s Sketch the graph of speed vs. time graph and calculate the area under the graph for the first round. The area of a rectangle is equal to height x base. area = ____________ units of the area = ___________ 20m/s Speed vs. time  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\graph_paper.gif" \* MERGEFORMATINET  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise3.gif" \* MERGEFORMATINET  Reset the applet. Set the car's speed to 40m/s and pause the motion after it has completed one round. Display the data table and record the accumulated time from Bin 9 in the data table. time = _______s Sketch the graph of speed vs. time. Again, determine the area (notice that the rectangle is twice as high, but only half as wide). area = ____________ units of the area = ___________ 40m/s Speed vs. Time  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\graph_paper.gif" \* MERGEFORMATINET  Is the area of the second graph equal to the area of the first? If so, what does this mean? INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise4.gif" \* MERGEFORMATINET  Verify that the area under the average speed graph from Exercise 1 is equal to the distance traveled by the car when going around the oval twice. Thus, the average speed line is drawn at a level such that the definition above for average speed is satisfied. area (distance) of average speed graph = _____________m (re: use the total time and average speed recorded in Exercise 1) area of 20m/s speed graph + area of 40m/s speed graph = ____________m (re: Exercise 2 + Exercise 3) Compare the two distances - they should be nearly identical. Example problem: Calculate the average speed for the two rounds assuming a speed of 20m/s was maintained for exactly one round and a speed of 40m/s for the second round. The distance (d) around the oval is not given because it is not needed. Work with the symbol (d) for this distance in your calculation. (If you find this difficult, use d = 500m. The value of the average speed should not depend on what value for d you assume.) Solution: We need the total distance traveled and the total time elapsed. The total distance traveled is 2d. The time elapsed during the first round is t = d/(20m/s). The time elapsed during the second round is t = d/(40 m/s). Thus, the total time T elapsed is:  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation8.gif" \* MERGEFORMATINET This gives for the average speed:  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation9.gif" \* MERGEFORMATINET  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise5.gif" \* MERGEFORMATINET  Calculate the average speed for the two rounds assuming a speed of 15m/s was maintained for exactly one round and a speed of 45m/s for the second round. Verify your answer using the applet. 2. Average Speed as a Time-Weighted Average In the previous section, you calculated the average speed for a motion where two different speeds were maintained over equal distances. What if the distances are not equal? A more general expression for the average speed will now be derived that applies in all cases where a motion is performed at two different speeds. Let the two speeds be denoted by v1 and v2, the distances traveled at these speeds by d1 and d2, and the times elapsed while these speeds are maintained by t1 and t2 respectively. The total distance traveled is d1 + d2 and the total time T elapsed is t1 + t2. With that, the definition of average speed gives equation (2).  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation2.gif" \* MERGEFORMATINET (2)In equation (2) for the average speed, each speed is multiplied by a factor equal to the fraction of the total time during which the speed is maintained. This factor is a called a weighting factor and this kind of an average is called a time-weighted average. Equation (2) requires the times and speeds to be known. If instead of the times, the distances are known, equation (2) becomes:  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation3.gif" \* MERGEFORMATINET (3)  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise6.gif" \* MERGEFORMATINET  Is it ever true that the average speed over a motion that consists of two different speeds v1 and v2 is equal to the arithmetic mean (v1 + v2) / 2? If so, under what special condition would this be true? Only when the factors (t1/T) and (t2/T) in equation (2) are both equal to 1/2, the arithmetic mean will give the average speed. This is the case when the times t1 and t2 elapsed during which the two speeds are maintained are equal. This is not the case when the two speeds are maintained over equal distances, as was the case in Exercise 1. The times taken to cover the same distance will be different when the car is moving at different speeds. Example problem: A car travels around an oval track at a speed of 20m/s and then a second time at 40m/s. Calculate the car's average speed for the two rounds using equation (2).Solution: Since the car goes twice as fast the second time around, its travel time for the second round is half that for the first round. Therefore,  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation4.gif" \* MERGEFORMATINET Substituting the time factors into equation (2) gives:  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation5.gif" \* MERGEFORMATINET  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise7.gif" \* MERGEFORMATINET  Reset the applet. Set the car's speed to 15.0m/s. Make sure both the Speed vs. Time graph and the Accumulated Time vs. Speed graph are not displayed. Do display the Data box, and scroll its display so that Bins 7 and 14 are simultaneously on display. These bins display the times associated with the speeds 15m/s and 30m/s. Play the car's motion, and Pause it when the Accumulated Time in Bin 7 is 10.0s or close to it. Then set the car's speed to 30.0m/s. Play the car's motion, and Pause it when the Accumulated Time in Bin 14 is 30.0s or close to it. Use equation (2) to calculate the average speed for the actual times elapsed in your experiment, which will be close to 10s and 30s for the two speeds. Compare your result to the "Average Speed (exact value)" at the bottom of the Data box. Sample calculation. Figure 1 below shows values similar to those that you might obtain. With t1 = 10.02s , t2 = 30.18s , and the total time T elapsed equal to 10.02 + 30.18 = 40.20s , equation (2) gives:  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation6.gif" \* MERGEFORMATINET  This is the value shown at the bottom of the Data box in Figure 1.  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\AverageSpeedDataBox.gif" \* MERGEFORMATINET  Figure 1 Show your times and calculations here. t1 = _______s t2 = _______s T = t1 + t2 = __________s Bin Speed Average: In addition to the exact value of the average speed (26.26m/s), the applet also calculates a bin speed average, which in this case comes out to 25.51m/s. This value is obtained as follows. The applet divides the available speed range from 0 to 50m/s into bins of equal size. At present, with the number of bins equal to 25, each bin has a width of 50/25 = 2m/s. The bins are numbered 0 to 24. Bin 7 covers the interval (14.0,16.0]m/s. This interval is open at the left and therefore does not include 14.0m/s, but is closed on the right and does include 16.0m/s. The bin speed, the speed at the midpoint of a bin, is representative for all speeds in that bin. Bin 7 has 15m/s at its midpoint, so 15m/s is the bin speed. Bin 14 covers the interval (28.0,30.0]m/s and has the bin speed 29.0m/s. The bin speed average is the time-weighted average bin speed calculated according to equation (2). In the present case, the bin speed average is  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\equation7.gif" \* MERGEFORMATINET  Continuing from Exercise 7, if you display the Accumulated Time vs. Speed graph it will look similar to Figure 2.  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\avg_speed_weighted_avg\\applethelp\\images\\AccumulatedTimeSpeedGraph.gif" \* MERGEFORMATINET  Figure 2 The bin speed of 15.0m/s is shown with an accumulated time of 10s and the bin speed of 29.0m/s with an accumulated time of 30s. The bin speed average of 25.51m/s is displayed below the speed axis. The two columns in Figure 2 are proportional to the time weightings given to the two bin speeds shown in the calculation above. The bin speed average is a kind of "center of weight" for the two bin speeds that are contributing to the average. Note that the bin speed average is quite a bit closer to the bin speed with the larger time weighting. It is not in the middle between the two speeds. Why Bins and Bin Speeds? We need to sort speeds into finite-sized bins in order to be able to define a time-weighted average of speed for continuously variable speed. If only discrete speeds are involved in a situation, as in the examples dealt with here, we can work with only these speeds and do not need bins. However, if the speed is varying continuously, i.e., not jumping by discrete amounts, sums like those in equation (2) need to be replaced by an integral. An integral is the limit of a calculation that uses bins and where one lets the bin size approach zero. Finite bins introduce an error. In Examples 2 and 3, the actual speed of 30.0m/s is replaced by the bin speed of 29.0 m/s. However, making the bins smaller will tend to make this kind of error smaller as well. The error vanishes in the limit of zero bin size.  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise8.gif" \* MERGEFORMATINET  Reset the applet. Set the car's speed to 18.0m/s. Make sure both the Speed vs. Time graph and the Accumulated Time vs. Speed graph are not displayed. Do display the Data box, and scroll its display so that Bins 8 and 11 are simultaneously on display. These bins display the times associated with the speeds 17m/s and 23m/s. Play the car's motion, and Pause it when the Accumulated Time in Bin 8 is 10.0s or close to it. Then set the car's speed to 23.0m/s. Play the car's motion, and Pause it when the Accumulated Time in Bin 11 is 30.0s or close to it. Use equation (2) to calculate the average speed for the actual times elapsed in your experiment, which will be close to 10s and 30s for the two speeds. Compare your result to the "Average Speed (exact value)" at the bottom of the Data box. Now use equation (2) to calculate the average bin speed in your experiment. Compare your result to the "Bin Speed Average" at the bottom of the Data box.  INCLUDEPICTURE "N:\\LearnAlberta.Ca\\Travis Whyte\\science\\physics2030\\physique_20-30\\physique_20-30_0.01\\HTML\\java\\libraries\\exercise\\exercise9.gif" \* MERGEFORMATINET  Suppose a motion involves three different speeds. Write down an expression for the average speed as a time-weighted average of the three speeds analogous to equation (2) for the time-weighted average of two speeds. Summary If you need to calculate the value of the average speed, you cannot go wrong if you use the definition of average speed as distance traveled divided by time elapsed. Then why should one know about time-weighted averages and equations like equation (2) at all? Knowing how to calculate an average speed as a time-weighted average of speed provides a deeper understanding of the concept of average speed. Equation (2) makes it clear what kind of an average is involved in calculating an average speed, while the ratio of distance traveled over time elapsed does not. Moreover, the concept of time-weighted average of a quantity is a general concept that does not apply only to speed. For example, one is often interested in the average temperature over some time period, say, one month. This is a time-weighted average of temperature, and this average cannot be calculated as the ratio of the change in some quantity divided by the time elapsed. One has to use the basic definition of a time-weighted average to calculate average temperature, i.e., to split the possible temperature range into equal-sized bins, measure the amount of time during which the value of the temperature was in each bin, etc.  Physics 20-30 v1.0 HYPERLINK "\\FILEDEV\sped\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\" \l "top"  2004 Alberta Learning ( HYPERLINK "http://www.learnalberta.ca" www.learnalberta.ca) Last Updated: June 16, 2004 %&  @ A B ] ^ N P R T \ l n z |   )-jSOJQJU H*OJQJj8OJQJUCJaJOJPJQJ^J5OJQJ\ 0JOJQJjOJQJUOJQJjOJQJUF0cu%  A B 5$$IfF  634a$If & Fdd[$\$[$\$MB ] \ n | O\$K$L$IfTKFg Vj7^ 0 6    34Kab  $$IfK$a$$IfK$ $$Ifa$$If f8^fP^$IfK$$K$L$IfTKFg Vj7^ 0 6    34Kab  $$IfK$a$   qk5,[$\$5$$IfF  634a$If$K$L$IfTKFg Vj7^ 0 6    34Kab  K? 5$$IfF  634a $$Ifa$$If$If[$\$-GHIJJKL$4.0y{OJPJQJ^J6OJQJ]5OJQJ\j:OJQJUj1OJQJUj*OJQJUj!OJQJUjOJQJUCJaJjOJQJUj OJQJUjOJQJUOJQJ:?QuJK$$If[$\$5$$IfF  634a $$Ifa$$If !!!Y"#`kki`[$\$H$$IfK0| H 634Ka$If $$Ifa$$If5$$IfK| 634Ka BCpu !!!!!!!U"V"W"X"#G#$$$$$$$$$$$$$%%%&%+%,%-%[%\%]%`%a%b%v%w%%%%%%%%%&&&&jxVOJQJU H*OJQJjNOJQJUjHOJQJUCJaJjBOJQJUjOJQJU6OJQJ]OJQJ5OJQJ\F##G#$%&&'"(()v*w*6,,$If $[$\$a$5$$IfK| 634Ka $$Ifa$$If[$\$&&&Q'a'''"(#((((((())))*** * **0*1*2*5*6*7***********+++++ +g+j+++6,G,,,,,--K.L.M.N.O.Q...R/S/j`kOJQJUOJPJQJ^J5OJQJ\ H*OJQJjcOJQJUj^OJQJUjOJQJU6OJQJ]CJaJOJQJD,,-O.P.Q..V/W/X/0W1ɘkki`[$\$H$$IfK04| z 634Ka$If $$Ifa$$If5$$IfK| 634Ka S/T/U/V/X/Y/ 0 0 000063H3333333334444445555555555&6(66686J6L6O6P6a6s66688+:,::::::::o;p;I<J< <OJQJj;OJQJUjOJQJUjOJQJU H*OJQJ6OJQJ]5OJQJ\j3xOJQJUCJaJOJQJjOJQJUjfpOJQJU@W111C26334455555%656E6_6a6475$$IfF  634a $$Ifa$$If$If[$\$ & Fdd[$\$478+::::o;M<W<Z<%=>>>@y5$$IfF  634a5$$IfF  634a $$Ifa$$If[$\$J<K<L<M<U<Y=h=>>>>>AABBBB4C7C5D:DDDxFyF+G,G-G.G HHLLLLLMMMMMMMMMMMM 0JOJQJ jCJOJQJUmHnHujŴOJQJUjXOJQJUjԥOJQJUCJaJ6OJQJ]5OJQJ\OJQJjOJQJUjǞOJQJU0@ABCVD}DDEuF/GH HHIHJLLMMM & Fdd[$\$ & Fd[$ & Fdd[$\$[$\$ 1h/ =!"#$%nnb\%}&kPDPNG  IHDR v"PLTE3fɛovbKGDH cmPPJCmp0712OmIDAT(ϥ=j0` Ck L^CP6O4J* -91 j{xRO, tRNSq6bKGDH cmPPJCmp0712HsIDATHKVn@L4*!-TZ/P\m_0םA0Rd2i^Rްl9xM %''瘮}R%So7~B~f;صR`=a+OU} hV gKYC_MWE04/5\ɞmu^^ p}ڶQtD mfW&8oF <@ّ14kS%DҐj) %Iysnop!mQ]vQd`_|:r Y09 ݟkMNQ) Wjݛ*. XbDRTk^'"JE C|E(_Z%4o=wl7o>i_xoj{Ct6"Pϻ$"#^]=UIENDB`DdV  S 2A  N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\control_icon_png\data.pngDatab8V/33]F6)9 n V/33]F6)9PNG  IHDRagAMA|Q cHRMz%u0`:oIDATxb1gd``Pb% ~ρ/;\ Pl <@ Yd@Q b^ / 3 @, eK2b(& bMՁ?q(  PCg P9> ^y@  @\ uk ΂TJ{@0 t  _?P@  Dz@|g o 1 ^adA#66Hw oB] @ @| ə0֫P`9f s0`?3h "P1@b+ BDDDDp\S`PF-IENDB`Dd+  S ^A4 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\graph_paper.gifimageb%"|NwbS«Ϻn"|NwbS«ϺPNG  IHDR%aQPLTE𠠤XbKGDH cmPPJCmp0712Hs~IDATx^nP DX wV"@IJɮ\z5-z{.O[^ܾum|zk,+?-۷n><ֽ_[gs_-+ҷOc՗t-=vi}S5N:NW :N8W_v 1/#tYK˵TYt#9T pIJ&lڦɦJs{[VY/ɗ>bNܛ{:TisoėܛPBK]uL&QBI%$_/զSt.J(͹|IĽK5 ބJ]cL4Js'9.ė|I& K2RroB . t1U&D %hs)9~RN3(wzLrA-ҹ[]׽pRZPE %D(ԥ:;$J5JWg]/7NjLIENDB`|Dd'\  S 8AN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise2.gifexercise 2bjXCB&37MCnjXCB&37MCPNG  IHDRigPLTE $(48IM!!!!))))111199BBJJJJRRZZcckkss{{Änjǔ˔ӥӭ׭׵۵߽𠠤z+m@tRNS{DbKGDH cmPPJCmp0712HsIDATHKVn08GElRT, 44$_uV{@RiYyGj':m,t:,|JLqC`00]4M0EvrTWa[m#mch4YL=SuC6>`-|GGYz}E2ulwcLCh'51W1(W|-YA{3mm X(n4O+ӑzE cL\hWf`c4_\Tʥ$J,3h,1؟"Z\ XHԝ-qfL*ll@B^ʩlplʚ/GDRSUg8tscdz4_{LL2?FFn%,?VUHWon-do,Cng$!dvbL |d }12IENDB`Dd+  S ^A4 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\graph_paper.gifimageb%"|NwbS«Ϻ]!n"|NwbS«ϺPNG  IHDR%aQPLTE𠠤XbKGDH cmPPJCmp0712Hs~IDATx^nP DX wV"@IJɮ\z5-z{.O[^ܾum|zk,+?-۷n><ֽ_[gs_-+ҷOc՗t-=vi}S5N:NW :N8W_v 1/#tYK˵TYt#9T pIJ&lڦɦJs{[VY/ɗ>bNܛ{:TisoėܛPBK]uL&QBI%$_/զSt.J(͹|IĽK5 ބJ]cL4Js'9.ė|I& K2RroB . t1U&D %hs)9~RN3(wzLrA-ҹ[]׽pRZPE %D(ԥ:;$J5JWg]/7NjLIENDB`zDd\   S 8AN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise3.gifexercise 3b'4jb`6tWX*n'4jb`6tWPNG  IHDRhl(YPLTE $(48!!!!))))111199BBJJJJRRZZcckkss{{Änjǔ˔ӥӭ׭׵۵߽𠠤 ;>tRNSq6bKGDH cmPPJCmp0712HsIDATHKVn0 x@@U21.XE;o͎8e"ķ$hiKx0 BTԊ*fS1L(a3uNP{NU:Ϙc! ^eǮ7i=n)䅐"ΰx5qMV#7/-S$#;Eآ=`D?͸ċUHճSn>}.md abGE2^8~kz2a /'wOhzIENDB`Dd+   S ^A4 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\graph_paper.gifimage b%"|NwbS«Ϻ1n"|NwbS«ϺPNG  IHDR%aQPLTE𠠤XbKGDH cmPPJCmp0712Hs~IDATx^nP DX wV"@IJɮ\z5-z{.O[^ܾum|zk,+?-۷n><ֽ_[gs_-+ҷOc՗t-=vi}S5N:NW :N8W_v 1/#tYK˵TYt#9T pIJ&lڦɦJs{[VY/ɗ>bNܛ{:TisoėܛPBK]uL&QBI%$_/զSt.J(͹|IĽK5 ބJ]cL4Js'9.ė|I& K2RroB . t1U&D %hs)9~RN3(wzLrA-ҹ[]׽pRZPE %D(ԥ:;$J5JWg]/7NjLIENDB`Dd \   S 8AN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise4.gifexercise 4 b_d#X2w{C:n_d#X2w{CPNG  IHDRgVaqPLTE $(8I!!!!))111199BBBBJJJJRRZZcckkss{{{{njˌǔ˔ӥ׭׵۵۽߽𠠤AtRNS0UbKGDH cmPPJCmp0712HsIDATHKVn0 xF .Fuhl\Z'.{!Gn۱irJb}Oy%["^ii$ٶJT缚ur|&G>f~^G֭ҦҼ2[w4o Km2C-2mq/m|BN*އ:ϑ^!Zjkx}:JO,/=Daݚq[ߴ}CHHul6L8fG/h LyGnN )PAʯ+~3?hnKB++E0: | 4 TDT>v-B %:ȷHU| ]SY}!Tx8(}4vꃏi.JxP>c|kب+ב@x~,wncF]d_\n*ޫ_촳2oiHIENDB`Dd ~   S ZA0 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation8.gifimage bu4ZZ LBnu4ZZ PNG  IHDRBׯbKGD݊ cmPPJCmp0712Om IDATH=n0pwiǎT!'a7C-] in4dА!h!E|%-Yc,qI'#$z_=~iyràW+˿W.-?~57G;WR=뿎XV__s#}A>o$j70jWlN'j ])* vi7uz_GUr̺2L>kvϵ>t8|+>!]ڕ^d0}zYs~~D{ko}5zӧU}Q.Ar#~3'ϓcXS x"%pLp]qzev"ylH|ΖigIFxMathType001DSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/!D/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  T==d 120m/s++ 140m/s[]T==d 60800m/s[]T== 3d40m/sIggIFxMathType002B IENDB`LDd~   S ZA 0 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation9.gifimage bzRRkT-?ʱ?VHnNRRkT-?ʱ?PNG  IHDRvWbKGD݊ cmPPJCmp0712OmIDATHMN11 DvK s  0+( oHיN}"$D]M_.8owg#bp@̉!AoIÞ3;&* ̸ [/A)Y+hB=zV9Dq, o{[q->|/GYO1#~~>رϞw7bzcdw YjR[U}ԇ8:g'qZlϫLs¤w-:w/qGyLDq7-VQm땃O#? E[.2k13}Z*I/0°f0$y疡Ƀb7ydy2㌛<2 6y6нzE׈gIFxMathType001DSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/!D/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  v av == 2d 3d40m/s[]v av == 80m/s3v av ==26.7m/scgIFxMathType002)nG(IENDB`}Dd'\  S 8A N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise5.gifexercise 5 b 1]OH2(?On 1]OH2(PNG  IHDRigPLTE $(48IM!!!!))))111199BBJJJJRRZZcckkss{{Änjǔ˔ӥӭ׭׵۵߽𠠤z+m@tRNS{DbKGDH cmPPJCmp0712HsIDATHKVYo0 xF .81 A;,|]I iRWK,a5Zy2>K/0@\:82T4l˔/qY״ݬ=mQϱ{d κų;dnG``g#g: vgDbOZi(ϛ:fCYSj77g8g!:?ࠒ,tL<F z/bSO@%grH8Ds֊?ZFϋp~&2UKucg ş|_Ǣ+Iۥ-@n:FͺxTpBEK#*Nٕ59;(ןz `lAn t=F8)Suvb`It?^EL%MMI<ن;ڏh^U4M_bL>#x]6{2Fkodxv[IENDB`vDd~ ~  S ZA 0 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation2.gifimageb8prFPlҼVnx8prFPlҼPNG  IHDRZbKGD݊ cmPPJCmp0712OmIDATXMn@pGYtq ؠ*Ҽ!r8@Sg e bL cgys<_jbAɮ8'01ҜEӧ&Px@e'XVf%| KVDz']T[!һ6y|XWCЋmµI]wJ3i"а+u*yZXev;VR{:|}IR#TP ԍ ֵ<9#҉ jѩM,Խz6?0󁍏Ol\uuͣdhu4?ې!oCކ|Mm=qbhcf\|?QWՓgIFxMathType001DSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/!D/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  t 1 == d 1 v 1 t 2 == d 2 v 2'gIFxMathType002mS[IENDB`DdE\  S 8A N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise6.gifexercise 6b cPBpm"dn cPBpmPNG  IHDRkRZPLTE $(48!!!!))))111199BBJJJJRRZZcckkss{{Änjǔ˔ӥӭ׭׵۵߽𠠤 ;>tRNSq6bKGDH cmPPJCmp0712HsIDATHKVmo@ &~&|sDQZ_y9r֖!0)uڦit] V}<ֺIY.&'Zf.M_/ /_s4[d4~KYڻ:#aѝr8zw7@.JUPnRj7ᰯڭtg|r 7 +0z: D m^p^%ţesjFej@ j, iG\%{IHSкm-?6ER]mcxe<&5flE!JnDpXOf8k}sZ _ \{2vO_|ȩ&IENDB`Ddv~  S ZA0 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation4.gifimageb4hZ.t6\WlknhZ.t6\WlPNG  IHDR*gbKGD݊ cmPPJCmp0712OmIDAT8˥ѱ 0ЀC7,'?N~B -6.w V,4m^r.6iCLLjX+y6{JZLvϒɶʗV˃+l7zvr gB׹/ʛi/ 0 XHzWb]-#K|GYf&:z5d|pbI_8Z2+Ͳ%6BpBZѴ*ϻyz=-u(]WxgIFxMathType001DSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/!D/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   t 1 T== 23and t 2 T== 13}YOgIFxMathType002MMIENDB`Dd ~  S ZA0 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation5.gifimageb|[?u62pn|[?u62PNG  IHDRxcbbKGD݊ cmPPJCmp0712OmIDATH1n0`wT:HWx0 fV_ޢ<6ILBMGR6))DP?QH'ijs-7BfnbP>*BxH\9ܦpgXyxpP9CrA{!A.d "X'? \pi&DhXA>dƑjd&A-H<+:R|bt|r2!B${C˧æ'i+;B{^9XiOn::XI8׊,BMCXqIAz5*`3\ Cŧ< m$mA3v/k`y+-|i-$ f>`̢["93UtSGĦ6o!#acGU0[[gԾf"K59]޺QxX{Yڼ; nvf_{.Vޜ ~#GM m|< 5LH)Mq_L*X fb6I2  Bi~TNCgR#tZ}1Fq>DpgIFxMathType001DSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/!D/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  v av ==v 1  t 1 T()++v 2  t 2 T()v av ==20m/s 23()++40m/s 13()v av ==26.7m/s&egIFxMathType002,>D֛IENDB`uDd\  S 8AN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise7.gifexercise 7bA B́XwxnA B́XPNG  IHDRhl(YPLTE $(48IM!!!!))))111199BBJJJJRRZZcckkss{{Änjǔ˔ӥӭ׭׵۵߽𠠤z+m@tRNS{DbKGDH cmPPJCmp0712HsIDATHKVN@mx&VI PD.Vlʹng1<ɺ'ӝ۞ݨ:M^qeFPs\ ]dFf]r9FzveHuQ_Dn9pNpFϼlϽQR NcjP}c8tlubLC UWYQ*|-Y'C ڢ ۏsMHi&Q@/1Hqc3xT8\*`xmwR.|nWď{}Wfޝ zKgoESdcU7M͉cݜm'$8c|O1i2cQпz =*o* 6_p>l 34M_BȒ r9岛Mx'P{Ӭ?hIENDB` Dd&~  S ZA0 N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation6.gifimagebDc:=}Ljgc? nc:=}Ljgc?PNG  IHDR2zbKGD݊ cmPPJCmp0712Om^IDATXn0pz 6dVSG^`S{ݪ T[QOVWa*T?;$dTi>d~> ?uC,ļpPzCy^)wZT:ENĥ? S7nUjw^V{שlq2u5]\(8ՎsxDRD o,u0No=PSq8&HǍv~5#qY<13AwphXo(u5v ޏO7dc8Q殻J:{wY瞹j|n}n/˥.3Ӭ[>/?1|7K&f 0ɹ9'x 0r˻vj W4NеS>EN8uIB'2QY;QX7^gjU^ NحWn&'&?9f-B]*?i]9~XW]Y9겋ÑwqK9:攬zǜ9xH;꺤[wkEΥaI3.Ӂux"uxOѭW$}i<7>~wX]7Iq#>N ˸_]wݸ:C~&nwl?El#y:]DU\}Tf#E'W^*po͛s*X=-i~boݮLV>^kv9ibN> ~Q^\Sv.{ J=ǧ>>7:`*c};{>zT: J'[\LRAM~Oe[Ft{ yMWk\NƤ!gIFxMathType001DSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/!D/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  v av ==v 1  t 1 T()++v 2  t 2 T()v av ==15m/s 10.02s40.2s()++30m/s 30.18s40.2s()v av ==26.26m/spgIFxMathType002->IENDB`} Dd  S nAD N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\AverageSpeedDataBox.gifimageb $8*rEs nk $8*rEPNG  IHDRHjq PLTEbb;evbKGDH cmPPJCmp0712Om IDATx[4iJ£!D*dFylC䞪]guh* WxoUoMUROL7cUA*H(2^>e5 zHUIr#HZ\!O= jNLr1 sPz2DF֛`9`@oTq\ǒՋ@QXO7!w#0X|B | 4pu !$>e ȭ>dnj!Oy`e:`!@2ȧD`b _Ne-Z@L- +7>lo[6}2>Rk@@(}hFiC#(eҦ(ǁ(e`hafL=wIhS,-Xs9dBQY1gmO)@OB} @;NԪaM@>İ 6Kg"^ )fZvK1ۇ= RVs 9K wC;|i~5`6O<9hz2(K2f+-V1dP /OYm|&Dcy^]i3ްyTy{C .jYS>dP婚!.~p/OK{3害)>oXvAbN( D8ĝP٫Ox gfc`2m Nyc hh|hrq*ЮfZB#g.3ƷG,i0$,ި\Ϣ:!ps>l ')K0]_´]I|}FbiS)k b(Or'.nZ؁¦&VOgI'pTW7TFzZ8 j$䉻Eyayi%˓@o%`@` c}t-JyTƊ{++K@s TZ(~807RzKCgLڇ{}(=-=L]dGC5&Gqפ11ǀi\ds]ï33[zo 7o?2bT@enuPW[7d r7H 2|8JX$TAu3y.j: X@bk9F_NAb/un!NbRaC(UҳDT_qMZHhU.l>$`;aS ^܇i FiniJ~G+yLaB^ ^vHӝ0WC'=v<P){;lNb?)' |I'c)' XIyrӕ0R'i&/䱞IyBlC4/Lمz'A2J[a.u9(!w+6麌M8$=O&$c@sqސZ\0I: e;-'x*˳bښ@Gin\mƅo$-l#x.QT]Lȅ')L $B镈J)/z}=۔!aAPMT{(̓B}ʸMEH OtYK R1 8q ;_BMG0-+ OaoTX`d s_@A'Ϙ @  @ dCta$/ {{ _۔|Tس^g QaU @ l&, Kp^ @."sxNX7&?Bp#jUM H^ hW3N#򿦨>&%#D #,m05>yvCAGwGᜅexǽTXJljUcCHHny: % mGpV^jęxYB!et L'RQxxԍltrt9~9tcwE =SR0z{uMS\ $6/ P#/Q:[h>ɣ#lx2;F[Mv)8=ʟw;_& o~qC6|=0qW'cq/\uU_h*RIENDB`mDdw\  S 8AN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise9.gifexercise 9b~ېm<{wdԆQ] _)c<Zx1|ki.g`?p"*t2xLd#Nj`3 Myt{*z #8Wf"nxnaRt4]S.$KbSO{@ 5 ETfxm[8DlCUɗ"EFoOltK lutg|o:;r jzU%[uw@ibVMs~f?\fp |i4⭍UE1E - Mu؇P8f Ib GG} dx i~DQЗM\Kx;}=k- lIENDB`Dd!<P  3 3"(( i8@8 NormalCJ_HaJmH sH tH Z`Z Heading 1dd@&[$\$"5CJKH$OJPJQJ\^JaJN`"N Heading 2dd@&[$\$5OJPJQJ\^JV`2V Heading 3dd@&[$\$5CJOJPJQJ\^JaJ<A@< Default Paragraph FontJ^`J Normal (Web)dd[$\$OJPJQJ^J.U`. Hyperlink >*B*phH 0cu%AB].7>FGUY]^giklz}  K?QuJK$YG !!""##$v%w%6'''(O)P)Q))V*W*X*+W,,,C-6..//00000%151E1_1a1423+5555o6M7W7Z7%8999;<=>V?}??@uA/BC CCDHEGGHHH0000(000(000c(00000 0 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0 0 000000000000000000000000000000000 0 0 0 0 00000000000 0-&S/J<MKRUWY\B ?#,W147@MLNOPQSTVXZ[]MM%]') GIKUW !!"####$$(K)M))R*T*X* + +///000+555o6I7K7<==xA+B-BGHHHHHHXXCCCCCCCCCCCCCCCCCCCCCCCCXXl,b$b\%}&kPDv"q@F(    hA$N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\buttons\top.gifback to topyK top#" B S  ?HHT=CUXz|HHGNUXYZ^fghijlp}~  ?C ..%1'151717CH33333333333333333333333Alberta LearningN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\Translations\wordDocs\missing\avg_speed_weighted_avg.doc.docj3J\@ +l1VNB0YV.p8$7^`CJOJQJo(^`CJOJQJo(opp^p`CJOJQJo(@ @ ^@ `CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(PP^P`CJOJQJo(^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.^`CJOJQJo(^`CJOJQJo(opp^p`CJOJQJo(@ @ ^@ `CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(PP^P`CJOJQJo(88^8`ph() ^`OJQJo(pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.0Y ~ \@j3+l1V.pб P V}wWPv.4Vpƺ ^$84(BLL|n ԢĦHz6600UnFdhURxOFxJIH1` ڶInG*JgtF2aD/AB.7>FGUY]^giklz} JK$!!6'''O)P)Q)V*W*X*6.00355599H@HH]HH( H@ @UnknownGz Times New Roman5Symbol3& z Arial7&  VerdanaI& ??Arial Unicode MS?5 z Courier New;Wingdings"1h¡F¡F ,<!0IuA2Q/Lesson 1 - Average Speed as a Weighted Average Alberta LearningAlberta LearningOh+'0$ @L h t 0Lesson 1 - Average Speed as a Weighted Average essAlberta Learninge Slbelbe Normal.dotrAlberta Learninge S1beMicrosoft Word 9.0S@F#@ !@p ! ,<՜.+,D՜.+,l( hp  Alberta LearningtI 0Lesson 1 - Average Speed as a Weighted Average Title% 8@ _PID_HLINKSA%4zQhttp://www.learnalberta.ca/qN\FILEDEVspedLearnAlberta.CaTravis Whytesciencephysics2030physique_20-30physique_20-30_0.01HTMLjavaavg_speed_weighted_avgapplethelp" l q\FILEDEVspedLearnAlberta.CaTravis Whytesciencephysics2030physique_20-30physique_20-30_0.01HTMLjavaavg_speed_weighted_avgapplethelp" l q\FILEDEVspedLearnAlberta.CaTravis Whytesciencephysics2030physique_20-30physique_20-30_0.01HTMLjavaavg_speed_weighted_avgapplethelp" l ZP N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation1.gif5cN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise1.gifN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\control_icon_png\data.png|[N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\graph_paper.gif6cHN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise2.gif|[N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\graph_paper.gif7c N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise3.gif|[ N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\graph_paper.gif0c N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise4.gifS  N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation8.gifR! N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation9.gif1cV"N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise5.gifY&N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation2.gifX(N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation3.gif2c)N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise6.gif_L.N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation4.gif^S/N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation5.gif3c 0N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise7.gif]4N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation6.gif|5N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\AverageSpeedDataBox.gif\:N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\equation7.gif J<N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\avg_speed_weighted_avg\applethelp\images\AccumulatedTimeSpeedGraph.gif<cBN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise8.gif=c,GN:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\exercise\exercise9.giftotopna{N:\LearnAlberta.Ca\Travis Whyte\science\physics2030\physique_20-30\physique_20-30_0.01\HTML\java\libraries\buttons\top.gif  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^`abcdefghijklmnopqrstuvwxyz{|}~Root Entry F< !Data _a1Tablec,WordDocumentSummaryInformation(DocumentSummaryInformation8H'CompObjjObjectPool< !< !  FMicrosoft Word Document MSWordDocWord.Document.89q