Question

A body moves for a total of 9 seconds starting from rest with uniform acceleration and uniform retardation which is twice the value of acceleration amd then stops. the duration of uniform acceleration is

Answer 1

Let acceleration of body is $\alpha$ and retardation is $\beta$

A/C to question,
retardation is twice that acceleration. e.g.,$\beta=2\alpha$

case 1 :- body moves with acceleration $\alpha$ for $t_1$ sec.
use formula, v = u + at
$v=0+\alpha t_1$...........(1)

case 2 :- body retards with $2\alpha$ for time $t_2$ sec and then body becomes rest. use formula., v = u + at,
here, u = $\alpha t_1$
v = 0 and a = $-2\alpha$
so, $0=\alpha t_1-2\alpha t_2$
so, $t_1=2t_2$

as $t_1+t_2=9sec$

then, $t_1=3sec$ and $t_2=6sec$

hence, 3 sec body moves with uniform acceleration.

Answer 2

Answer: 3m/s or 6m/s

Explanation: