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)` (r) after time t and that of the second body by `x_(2)` (r) 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

A

Explanation

For 1st body, `x_(1)(t)=1/2at^(2)`
For second body, `x_(2)=v_(2)t`
`:.x_(2)=1/2at^(2)-vt`
When `vt>1/2at^(2)` then `x_(1)-x_(2)` is -ve and when
`1/2at^(2)>vt` then `x_(1)-x_(2)` Is +ve.