A body moves for a total of nine second starting from rest with uniform acceleration and then with uniform retardation, which is twice the value of acceleration and then stop. The duration of uniform acceleration is

Options

A. 3s
B. 4.5s
C. 5s
D. 6s

Answer

D

Explanation

Let acceleration is a and retardation is -2a Then for acceleration motion
`t_(1)=(upsilon)/(a)` ….(i)
For retarding motion
Given `t_(1)+t_(2)=9 rArr (upsilon)/(a)+(upsilon)/(2a)=9`
`rArr (3upsilon)/(2a)=9 rArr (upsilon)/(a)=6`
Hence, duration of acceleration, `t_(1)=(upsilon)/(a)=6 s`.