(7%) Problem 9: The velocity as a function of time for a world-class track sprin

Question

(7%) Problem 9: The velocity as a function of time for a world-class track sprinter in a 100 m race is shown in the figure. The sprinter accelerates for the first 4.0 seconds, and then runs at a constant velocity until the end of the race Sprinter Velocity vs Time 15 ime (s 0.0 2.0 4.0 6.0 8.0 10.0 eloci 12 0.0 6.0 12 12 12 12 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Time (s) ©theexpertta.com 25% Part (a) What is his average velocity for the first 4.0 s, in meters per second? 25% Part (b) What is his instantaneous velocity, in meters per second, at t = 5.0 s? 25% Part (c) What is his average acceleration, in meters per square second, during the first 4.0 seconds of the race? G 25% Part (d) What is his time for the race in seconds? Grade Summary Deductions Potential 0% 100%

Explanation / Answer

part A)

average velocity = total displacement/total time taken

average velocity = (0.50 * 4 * 12)/4

average velocity = 6 m/s

part B)

at t = 5

velocity = 12 m/s

part C)

acceleration =change in velocity/time

acceleration = (12 - 0)/4

acceleration = 3 m/s^2

d)

for race time

let the time is t

100 = 12 * (t - 4) + 0.50 * 12 * 4

solving for t

t = 10.3 s

the race time is 10.3 s  

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