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 36.0 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 Assuming that the chasing car brakes at the same time as the lead car m/s^2, 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? =?s

Explanation / Answer

here,

Va = 25m/s
Vb = 36 m/s

ab = -1.80 m/s
d = 40 m

Part A:

By using first equation of motion we have
v=u+at
where v is the final velocity
u is the initail velocity
a is the acceleration
t is the time

0 = 36 - 1.80t
t = 20 s

Time taken by lead car to stop by this deacceleration is 20s

Part B:
Solving for the distance travelled by lead car to stop,
v^2 - u^2 = 2as
-36^2 = -1.80^2 * 2 * s
s = 360 m

total distance travelled by two cars :
D = 360 +40 = 400 m

Now the minimum acceleration of other car will be :
v^2 - ^2 = 2 * a * s
0 -25^2 = 2 * a *400
a = -0.78 m/s

the chasing car's minimum negative acceleration so as not to hit the lead car is -0.78 m/s

Part C:
by using V = u + at

t = u /a
t = 25 / 0.78

t = 32.05 s

The chasing car will require 32.05s to stop in this process

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