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 33 m/s and
the other car at 46 m/s. At the moment the
cars are 40 m apart, the lead driver applies the
brakes, causing the car to have a deceleration
of 1.5 m/s2.
How long does it take for the lead car to stop?
Answer in units of s.

Assume that the driver of the chasing car
applies the brakes at the same time as the
driver of the lead car.
What must the chasing car’s minimum neg-
ative acceleration be to avoid hitting the lead
car?
Answer in units of m/s2.

How long does it take the chasing car to
stop?
Answer in units of s.

Explanation / Answer

vf=0=vi+a(Delta)t and
(Delta)t=vi/a 33/1.5= 22s
B) We need to use d = v(Delta)t + (1/2)a(?t)2 (33)(22) + 1/2(-1.5)(22)2=363
d = v(Delta)t + (1/2)a(?t)2 363+40=403m Then we need to use vf2 - vi2 =2a(Delta)s (0-(462))/2(403)=-2.62m/s C) (Delta)t = -v/a -46/(-2.62)=17.55s
vf2 - vi2 =2a(Delta)s (0-(462))/2(403)=-2.62m/s C) (Delta)t = -v/a (Delta)t = -v/a -46/(-2.62)=17.55s

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