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 10.5 m/s and accelerates at the rate of 0.650 m/s2 for 5.75 s. What is his final velocity? The racer continues at this velocity to the finish line. If he was 320 m from the finish line when he started to accelerate, how much less time did it take him to finish had he not accelerated? One other racer was 9.5 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 the loser will the winner be in meters when the loser finishes?

Explanation / Answer

vf = v0 + a t

v = (10.5) + (0.650 x 5.75)

v = 14.2 m/s . ........Ans

when not accelerated, t1 = 320 / 10.5 = 30.5 sec

when accelerated:

distance travelled in 5.75 sec, d1 = (10.5 x 5.75) + (0.650 x 5.75^2 / 2)

d1 = 71.1 m

d = 320 - d1 = 248.9 m

t' = 248.9 / 14.2 = 17.5 sec

time taken = 5.75 + 17.5 = 23.3 sec

time differecne = 30.5 - 23.3 = 7.22 sec ..........Ans

distance travelled by other race in 23.3 sec = 23.3 x 12.2 = 284.26 m

and he was 9.5 m ahead.

so position of his when accelerated racer compeleted his race.

d = 9.5 + 284.26 = 293.8 m

distance between them = 320 - 293.8 = 26.2 m .........Ans

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