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?

(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?

(c) How long does it take for the chasing car to stop?

Explanation / Answer

a) Using the formula:

v=u+at

where v is the final velocity ( 0 m/s)

u is the initail velocity ( 25m/s)

a is the acceleration ( -1.80m/s^2)

t is the time (unknown)

v=u+at

0 = 25 + (-1.80)(t)

t = 13.89s

b)

First use this formula to find the the distance the lead car travels before it comes to a stop:

v^2 = u^2 + 2aS

0^2 = 25^2 +2(-1.80)S

-625 = -3.6S

S= 173.61m

Second, find the total distance between the two cars, i.e.,

173.61m+40m = 213.61m

Lastly, find the minimum negative acceleration of the other car by the formula:

v^2 = u^2 + 2aS

0^2 = 36^2 +2(a)(213.61)

a = -3.03 m/s^2

(c) Use the formula:

v=u+at

0 = 36 + (-3.03)(t)

-36 = -3.03t

t = 11.88s

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