##### A bicycle racer sprints at the end of a race to clinch a victory. The racer has

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A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 12.5 m/s and accelerates at the rate of 0.550 m/s2 for 7.00 s.

(a) What is his final velocity?
m/s
(c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate and traveled at 12.7 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?
distance
m
Sep 8th, 2015

Hello!

(a) the velocity of the first racer is v0+a*t. Here it is 12.5+0.550*7 = 16.35 (m/s).

(c) the distance for the first racer from the point where he started to accelerate is

d1(t)=v0*t+a*t^2/2,

for the second

d2(t)=5+12.7*t.

As I understand, finish for the first racer is after 7 seconds. Then the distance in question is

d1(7)-d2(7)=12.5*7+0.55*7^2/2-5-12.7*7=-0.2*7-5+0.55*49/2=

-6.4+13.475=7.075(m).

The time for the second racer to finish after that is this distance/his speed=7.075/12.7=approx. 0.557(s).

Please ask if something is unclear.
Sep 8th, 2015

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Sep 8th, 2015
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Sep 8th, 2015
Sep 26th, 2017
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