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

Answer

D

Explanation

a = constant
Let A be the original point
From equation of motion,
`x=ut+(1)/(2)at^(2)=(1)/(2)at^(2) " " (therefore u=0)`
Here, x is the position of the particle.
For point C, `x_(1)=(1)/(2)a(t//2)^(2)rArr x_(1)=(1)/(8)at^(2)` ...(i)
For ppoint B, `x_(2)=(1)/(2)a(t)^(2)` ....(ii)
From Eqs. (i) and (ii), we get
`2x_(2)=8x_(1)rArr x_(2)=4x_(1)`