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 0.350 m/s2 for 7.00 s.

(a)What is his final velocity (in m/s)?

(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 (in s) 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 12.1 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?

Explanation / Answer

(a) v = u+a*t

v = 12 + 0.350*7

   = 14.45 m/s

(b) case 1: no acceleration

s = vt

300 =12 * t

t = 25 s

case 2 : with acceleration

v = 14.45 m/ sec

dstance covered = 12 * 7 + 1/2 * 0.350 * 7^2

                         = 92.575

remaining distance = 300 - 92.575 = 207.425

remaining time taken = 207.425 /14.45

                               = 14.355

total time in case 2 = 7 + 14.355 = 21.355

so time saved = 3.64 s

(c) time, t = d/v

here, d = 300 - 5 = 295 m

so , t = 295 / 12.1

t = 24.4 s

the winner racer wins from other racer with a time difference of

T = 24.4 - 21.355

T = 3.03 s

distance , d = 3.03 * 14.45

                  = 43.71 m

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