Question

A train starts moving with a uniform velocity u, along a straight horizontal track, at t = 0. Brakes are applied to it, at t = 100 s, and these produce a uniform retardation ‘a’, on the train, for the next 10 s. 

The displacement (relative to the train, of a small object, kept on a smooth long (horizontal top table), as a function of time, would be represented by the graph, labelled as graph

Answer 1

Correct option is (A)

There is no force acting on the object as long as the train is moving with a uniform velocity. The object, in this inertial frame of reference, does not move, relative to the train, from (t = 0) to (t = 100 s). 

When the brakes are applied, the train experiences a backward force that produces a uniform retardation. The object would, therefore, experience a forward force that would give it a forward acceleration (=a). The displacement, of the object, relative to the train, from (t = 100 s) to (t = 110 s) would then be represented by

s = ut + 1/2 at²

(Where t would now take the values from 0 to 10). 

The graph, showing the displacement of the object, relative to the train, from (t = 0 s) to (t = 110 s), would, therefore, have the form shown in graph A.