In a bicycle race on a straight road, the leader is 72.0 m from the finish line

Question

In a bicycle race on a straight road, the leader is 72.0 m from the finish line and continues to travel to the finish line with a constant speed of 12 m/s. When the leader is 72.0 m from the finish line, the second-place rider is 5.0 m behind him and traveling with a speed of 11.0 m/s when she decides to accelerate, keeping a constant acceleration for the rest of the race. The two riders end up crossing the finish line at exactly the same time.

(a) Calculate the value of the second rider?s constant acceleration that allows her to cross the finish line at exactly the same time as the first rider.
m/s2

(b) What is the speed of the second rider as she crosses the finish line?
m/s

(c) What is the second rider's average speed over the final 77 m of the race?
m/s

Explanation / Answer

a) time taken for leader to finish the race : 72/12 = 6 seconds
distance of second place to finish line = 72+5 = 77m
using the formula : 2d / t = at + 2Vinitial

2(77)/6 = a(6) + 2(11)

6a = 3.67

a = 0.611 m/s2

b) v = u + at

v = 11 + 0.611(6) = 14.67 m/s

c) average speed = distance / time

speed = 77/6 = 12.83 m/s

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