A body is at rest at ` x =0 ` . At ` t = 0`, it starts moving in the positive `x - direction` with a constant acceleration . At the same instant another body passes through ` x= 0 ` moving in the positive ` x - direction ` with a constant speed . The position of the first body is given by `x_(1)(t)` after time 't', and that of the second body by ` x_(2)(t)` after the same time interval . which of the following graphs correctly describes `(x_(1) - x_(2))` as a function of time 't' ?

Options

A.
B.
C.
D.

Answer

C

Explanation

As ` u= 0`, for body ` 1, v_1 = at` and for bodt `2, v_2 =a` constant. Initially both are at ` x= 0`. Relative velocity of body ` 1` w.r.t. body ` 2 = vec -1 - vec _2`. At first, the velocity ` v_1` is less than ` vec _2`. The distance travelled by body `1 i.e. x-1 = 1/2 at^2 - v_2 t. This shows that the graph between 9x_1 -x_2) and (t) is a parabola before crossing (x0 axis as well as after crossing x-axis. the curve (c ) satisfies this.