Two cars are traveling along a straight-line in the same direction, the lead car

Question

Two cars are traveling along a straight-line in the same direction, the lead car at 25.0 m/s and the other car at 35.0 m/s. At the moment the cars are 40.0 m apart, the lead driver applies the brakes, causing his car to have an acceleration of -1.80 m/s2.

(a) How long does it take for the lead car to stop?
s
(b) Assuming that the chasing car brakes at the same time as the lead car, what must be the chasing car's minimum negative acceleration so as not to hit the lead car?
m/s2
(c) How long does it take for the chasing car to stop?
s

Explanation / Answer

a)
t=-v0/a

=25/1.8

=13.89 s

b)

lead car stops in s=-v0^2/2a=625/3.6 = 173.6 m
chasing car has d= (40+173.6) m = 213.6 m to stop so he needs
at least
a=-v0^2/2d

=-1225/427

= -2.868 m/s^2

c) and it takes t=-v0/a

=35/2.868= 12.2 s

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