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 10.8 m/s and accelerates at the rate of 0.65 m/s^2 foe 6.25 s to accomplish this. What is his final velocity. in meters per second, after this period of acceleration? The racer continues at us the f,rush line If he was 349 m from the finish line when he stalled to accelerate how much less lime did it latte turn to finish then if had had run acccler One other racer was 7 J m ahead when the w ,wr siarvd u. accelerate. hul was loo tired lo speed up and traveled at 11.7m/s until the finish line. If the winner continues u. cycle at the same speed alter crossing celebrate his victory ), how far ahead of Ihc loser will the winner be. in meters, when the loser finishes'

Explanation / Answer

(a)

V = u + a*t = 10.8 + (0.65*6.25) = 14.8625 m

(b)

with acceleration

x = v*t1 + 0.5*a*t1^2

340 = (14.8625*t1) + (0.5*0.65*t1^2)

t1 = 16.7 s

without acceleration

x = v*t2

340 = 14.8625*t2

t2 = 22.9 s

time saved = 22.9-14.6 = 8.3 s

+++++++

(c)

time taken for looser to finsh the race

340-7.5 = 11.7*t

t = 28.42 s

for winner

speed after reaching finish line = v = 14.8625 + (0.65*14.6) = 24.3525 m/s

distance travelled

x = 24.3525*(28.42-14.6) = 336.55 m

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