Question

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 stops. The duration of uniform acceleration

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

Answer 1

Answer: (A)

$3s$

Consider the acceleration of the is $\alpha$ and retardation is $\beta$

and according to question retardation is twice that acceleration then

$\beta =2a$

Body moves with acceleration $\alpha$ for $t_1$ sec

$v=u+at$

$v=0+\alpha t_1$ $.....\left(1\right)$

Body retards with $2\alpha$ for time $t_2$ sec and then body becomes rest .

$v=u+at$

Here,

$\begin{array}{c}u=\alpha t_1\\ v=0\\ a=-2\alpha \end{array}$

$\begin{array}{c}0=\alpha t_1-2\alpha t_2\\ t_1=2t_2\end{array}$

As

$t_1+t_2=9\sec$

Then,

$t_1=3\sec$

$t_2=6\sec$

Therefore, $3sec$ body moves with uniform acceleration.

Hence, Option $A$ is the correct answer.