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

Options

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

Answer

d

Explanation

Applying v=u+at
For first part `v=0+at_(1)`
or `t_1=(v)/(a)`
For second part `0=v-2at_(2)`
or `t_(2)=(v)/(2a)`
Total time t=9 s=`t_1 +t_2 =(v)/(a)+(v)/(2a)`
`9=(2v+v)/(2a)=(3)/(2)(v)/(a)`
`(v)/(a)=6`
Now `t_1=(v)/(a)=6s`