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 13.0 m/s and accelerates at the rate of 0.350 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 13.3 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?

distance

time

Explanation / Answer

(a) v=u+a*t

v = 13 + 0.350*7

= 15.45 m/s

(b) case 1: no acceleration

s=vt

300 =13 * t

t = 23.07 s

case 2 : with acceleration

v=15.45 m/ sec

dstance covered = 13 * 7 + 1/2 * .350 * 7^2

= 99.575

remaining distance = 300 - 99.575 =200.425

remaining time taken = 200.425 /15.45 =12.972

total time in case 2 = 7 + 12.972 = 19.972

so time saved = 3.104 s

(c) first racer :

time taken to complete = 19.972 from above prob

second racer :

distance travelled when 1 racer completed = 19.972 *13.3 =265.62 m

distance 1 racer is ahead = 300 - 265.62 -5

= 299.38 m

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