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

B

Explanation

As `x_(1) (t) = (1)/(2) at ^(2)`
and `x_(2) (t) = vt`
`:. X_(1) - x_(2) = (1)/(2) a t^(2) - vt` (Parabola)
Clearly, graph (2) represents it correctly.