A bicycle racer sprints at the end of a race to clinch a victory. The racer has

Question

A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial

velocity of 11.5 m/s and accelerates at the rate of 0.500 m/s2 for 7.00 s.

(a) What is his final velocity?

(b) The racer continues at this velocity to the finish line. If he was 300 m from the finish

line when he started to accelerate, how much time did he save by accelerating?

(c) One other racer was 5.00 m ahead when the winner started to accelerate, but was

unable to accelerate and traveled 11.8 m/s until the finish line. How far ahead of him (in

meters and in seconds) did the winner finish?

Explanation / Answer

a) v = 11.5+ 0.5*7 = 15m/s

b)normally time taken = 300/11.5 = 20.086 secs

if accelerates time taken = t

v = sqrt(v^2) = sqrt(11.5^2 + 2*0.5*300) = 20.79 m/s

so t = 20.79-11.5/0.5 = 18.58 secs

so time saved = 20.086 - 18.58 = 1.5 secs

c)time taken for other guy = 295/11.8 = 25sec

so at the end of 18.58 secs he travels 18.58*11.8 = 219.244m

so he is 295 - 219.244 m behind winner = 75.76m

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