A bicycle racer sprints near the end of a race to clinch a victory. The racer ha

Question

A bicycle racer sprints near the end of a race to clinch a victory. The racer has an initial velocity of 11.3 m/s and accelerates at the rate of 0.490 m/s2 for 7.97 s. What is his final velocity?
15.2 m/s

The racer continues at this velocity to the finish line. If he was 291 m from the finish line when he started to accelerate, how much time did he save by accelerating?
5.59 s

One other racer was 4.70 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at a constant speed of 13.5 m/s until the finish line. How far behind (in meters) is he from the winner when the winner crosses the finish line?

How many more seconds did the other racer takes to cross the finish line

Explanation / Answer

b)

here

t = d / v = 291 / 11.3

t = 25.75 sec

291 = 0.5 * ( 11.3 + 15.2 ) * 7.97 + 15.2 * t

t = 12.19 sec

t2 = 12.19 + 7.97 = 20.16

therefore he saved the time = 25.75 - 20.16 = 5.59 sec

c)

d = v * t = 13.5 * 20.16 = 272.16 m

then the distance behind is

291 - 272.16 - 4.70 = 14.14 m

then the time

t = d / v = 14.14 / 13.5 = 1.047 sec

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