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

Question

Two cars arc traveling along a straight line in the same direction, the lead car at 24.1 m/s and the other car at 29.0m/s. At the moment the cars are 41.1m apart, the lead driver applies the brakes, causing her car to have an acceleration of -2.09m/s^2. How long does it take for the lead car to stop? What is the distance it travels during this time? 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? How long does it take for the chasing car to stop?

Explanation / Answer

for lead car:

u = 24.1 m/s

a = - 2.09 m/s^2

v = 0

Applying , v = u + at

0 = 24.1 - 2.09t

t = 11.53 sec

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d = u t + a t^2 /2

d = (24.1 x 11.53) - (2.09 x 11.53^2 / 2) = 138.92 m

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other car have to stop within 138.92 m from initial speed of 29 m/s

aplying v^2 - u^2 = 2 a d

0^2 - 29^2 = 2(a)(138.92)

a = - 3.03 m/s^2

---------------------

v = u + a t

0 = 29 - 3.03t

t = 9.57 sec

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