The brakes applied to a car produce an acceleration of $8 m / s^{2}$ in the opposite direction to the motion. If the car takes 3 seconds to stop after applying the brake, the distance it travels during the time will be?

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answer is B.

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Detailed Solution

The brakes applied to a car produce an acceleration of

8 m / s^{2}

in the opposite direction to the motion. If the car takes 3 seconds to stop after applying the brake, the distance it travels during the time will be

36 m

.
Time taken to come to rest,

t = 3 s

Final velocity,

v = 0 m / s

Acceleration,

a = - 8 m / s^{2}

(Negative sign represents retardation)
From first equation of uniformly accelerated motion,

v = u + at

0 = u - 8 (3)

Initial velocity,

u = 24 m / s^{2} .

By second equation of uniformly accelerated motion,

s = ut + \frac{1}{2} a t^{2}

= 24 (3) + \frac{1}{2} (- 8) \times 9

= 72 - 36

Displacement,

s = 36 m .

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