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 12.0 m/s and accelerates at the rate of 0.650 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?(c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate and traveled at 12.2 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish? distance

Explanation / Answer

1a.) v = u + at
v = 12 + 0.65*7 = 16.55 m/s

1b.) v^2 = u^2 + 2as
16.55^2 = 12^2 + 2*0.65*s
s = 99.925 metres

So he travels 99.925 metres before reaching 16.55 m/s

He travels the last 200.08 metres at 16.55 m/s:
time = distance / speed =12.08 seconds

The acceleration period took 7 seconds so the total time is 19.08 seconds with the acceleration.

time = distance / speed = 300 / 12 = 25seconds

So he saves 5.92 seconds.

c.) time = distance / speed = 295 / 12.2 = 24.18 seconds

So he finishes 5.1 seconds behind the winner.

distance = speed*time = 12.2*19.08 = 232.77metres

So he finishes 67.224 metres behind the winner.

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