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 24.1m/s and the other car at 30.7m/s. At the moment the cars are 40.6m apart, the lead driver applies the brakes, causing her car to have an acceleration of -2.05m/s2. 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

let lead car velocity be u1 and other cars be u2 (u1=24.0m/s and u2=29.3m/s)
distance between them = 38.3 m
lead car:
a=-1.93 (since this is retardation)
final vel = 0
v=u+at so,0=24-1.93t,
t=12.43s (answer to 1)
s=ut+1/2at;s=24*12.43-.965*12.432

so,s=149.09m (answer to 2)

chasing car:

chasing car hitting the 1st car means it covers the s=149.09 m and the additional 38.3 m between them

so,

it must cover 187.39m

when it stops its final vel must be zero so,

v=u+at 0=29.3-at

so 29.3 = at ( remember this )

s=ut-1/2 at2

187.39=29.3*t-1/2(at)*t

since at = 29.3 so ,

187.39=29.3t-14.65t so, 187.39=14.65 t so ;

t=12.79 sec (answer to 4)

so , a= -2.29 m/s2 (this is retardation so there must be a negative sign ) (answer to 3)

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