A body starts from rest and moves with constant acceleration for t s. It travels a distance `x_(1)` in first half of time and `x_(2)` in next half of time, then

Options

A. `x_(2)=3x_(1)`
B. `x_(2)=x_(1)`
C. `x_(2)=4x_(1)`
D. `x_(2)=2x_(1)`

Answer

A

Explanation

As the body starts from rest,
`:.u=0`
Let a be constant acceleration of the body. Distance travelled by the body in `(t//2)` s is
`x_(1)1/2 a (t/2)^(2)=1/8at^(2)` ...(i)
Distance travelled by the body in t s is
`x_(1)+x_(2)= 1/2 at^(2)=4x_(1)` (Using (i))
`:.x_(2)=4x_(1)-x_(1)=3x_(1)`