A particle starts its motion from rest under the action of a constant force. If the distance covered in first `10 s` is `s_1` and the covered in the first `20 s` is `s_2`, then.

Options

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

Answer

b

Explanation

Initial speed u=0
Given constant force, F=m a
Acceleration acting in the particle `a=(F)/(m)=` constant
The acceleration acting remains constant on the particle
`S_(1)=0+(1)/(2)at^(2)`
`S_(1)=(1)/(2)a(10)^(2)=50a`
`S_(2)=0+(1)/(2)a(20)^(2)=200a`
`S_(1)=0+(1)/(2)at^(2)`
`S_(1)=(1)/(2)a(10)^(2)=50a`
`S_(2)=0+(1)/(2)a(20)^(2)-200a`
`(S_(1))/(S_(2))=(50a)/(200a)=(1)/(4)`
`S_(2)=4S_(1)`