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

For the body starting starting from rest
` x_(1) = 0 + (1)/(2) at^(2) rArr x_(1) = (1)/(2) at^(2) `
For the body moving with constant speed
`x_(2) = vt`
`:. x_(1) - x_(2) = 1/2at^(2) - vt rArr (d(x_(1) - x_(2))/ (dt) = at - v`
At `t = 0` , `x_(1) - x_(2) = 0 `
For ` t lt (v)/(a)` , the slope is negative
For ` t lt (v)/(a)` , the slope is zero
For ` t lt (v)/(a)` , the slope is positive
These characteristics are represented by graph `(b)` .