大學物理-平均速度－yffuhxy的部落格

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大學物理:平均速度

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題目:In reaching her destination,a backpacker walks with an average velocity of 1.34m/s, due west. This average velocity results because she hikes for 6.44km with an average velocity of2.68m/s, due west, turns around, and hikes with an average velocity of 0.447 m/s, due east. How far east did she walk?題意看不懂!... 顯示更多題目:In reaching her destination,a backpacker walks with an average velocity of 1.34m/s, due west. This average velocity results because she hikes for 6.44km with an average velocity of2.68m/s, due west, turns around, and hikes with an average velocity of 0.447 m/s, due east. How far east did she walk? 題意看不懂! 幫解答最好有中文

最佳解答:

This is a tricky question, because it uses Average Velocity, not Average Speed. Velocity is a vector, so it has direction, speed is a scalar and has no direction. Assume the backpacker walks X seconds due east, and also assume to the east is positive. Average velocity = Average Displacement / Total Time. Average Displacement (in meter) = 0.447 X - 6440 (negative sign in front of 6440 is because of due west) Total Time (in second) = X + 6440/2.68 Average Velocity = (0.447X - 6440) / (X + 6440/2.68) = -1.34 (negative sign in front of 1.34 is because of due west) Solve for X: 0.447X -6440 = -1.34 (X + 6440/2.68) ==> 0.447X -6440 = -1.34X - 3220 ==> 0.447X + 1.34X = 6440 - 3220 ==> 1.787X = 3220 ==> X = 1801.90 seconds How far did she walk to the east? Displacement = Velocity x Time = 0.447 (m/s) x 1801.90 (s) = 805.45 meters Therefore, she walks 805.45 meters to the east 2012-10-04 02:53:35 補充： If this question use "average speed", then in the solving process, where there is a negative sign changes to positive. You will get answer for using "average speed". 2012-10-04 02:54:00 補充： I am sorry that I am not able to type Chinese !!! 2012-10-05 01:36:11 補充： Therefore, she walks 805.45 meters to the east 這題答案是-0.81km 有-號你這樣好像是+的 The reason it has "-" is because when the person solve the problem, he or she assume to the west is positive !!! 2012-10-05 02:33:40 補充： typo! he or she assume ... ==> he or she assumes ... 2012-10-05 02:34:54 補充： In my solution, I assume "to the east" as the positive direction. 2012-10-05 06:50:42 補充： Anyway, I like to bring to your attention: displacement, velocity, acceleration are all vectors, so they all have direction. distance and speed are scalars. 2012-10-05 06:51:58 補充： therefore, if you walk 5 km to the east, then turn around walk another 5 km to the west, your displacement is ZERO, but distance is 10km.

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