A train is moving with a velocity of 90 km h-1. It is brought to stop by applying the brakes which produce a retardation of 0.5 m s-2. Find (i) the velocity after 10 s, and (ii) the time taken by the train to come to rest.

As we know, according to the equation of motion,

v = u + at

Given,

u = 90 km h^-1 or 25 m s^-1

v = 0 (as the train stops on application of brakes)

t = 10 s

retardation = -a = -0.5 m s^-2

Substituting the values in the formula above we get,

v = 25 + (-0.5) × 10 = 20 ms^-1

Hence, the velocity after 10 s = 20 m s^-1.

(ii) As we know, according to the equation of motion,

v = u + at

Substituting the values in the formula above, to get the time taken by the train to come to rest.

0 = 25 + (-0.5 × t)

or, 0 = 25 – 0.5t

or, 0.5t = 25

or, t = 25/0.5 = 50 s

Hence, the time taken by the train to come to rest = 50 s.