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The running event known as the 100 m100 \mathrm{~m} dash consists of three stages. In the first, the runner accelerates to the maximum speed, which usually occurs at the 50 m50 \mathrm{~m} to 70 m70 \mathrm{~m} mark. That speed is then maintained until the last 10 m10 \mathrm{~m}, when the runner slows. Consider three parts of the record-setting run by Usain Bolt in the 20082008 Olympics: (a)(a) from 10 m10 \mathrm{~m} to 20 m20 \mathrm{~m}, elapsed time of 1.02 s1.02 \mathrm{~s}, (b)(b) from 50 m50 \mathrm{~m} to 60 m60 \mathrm{~m}, elapsed time of 0.82 s0.82 \mathrm{~s}, and (c)(c) from 90 m90 \mathrm{~m} to 100 m100 \mathrm{~m}, elapsed time of 0.90 s0.90 \mathrm{~s}. What was the average velocity for each part?

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Answered 1 year ago
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Givens

  • xa=xb=xc=x=10 mx_a=x_b=x_c=x=10\ \text{m} - the distances travelled in each part of the race
  • ta=1.02 st_a=1.02\ \text{s} - the time it takes in part a)
  • tb=0.82 st_b=0.82\ \text{s} - the time it takes in part b)
  • tc=0.9 st_c=0.9\ \text{s} - the time it takes in part c)

Required

  • vav_a, vbv_b, vcv_c - the average velocities in parts a), b) and c), respectively

How can we use the definition of the average velocity in order to solve this problem?

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