Question

A car starts from rest acquires a velocity v, with uniform acceleration $2m/s^2$. Then it comes to stop with uniform retardation $4m/s^2$. If the total time for which it remains in motion is 3 s, the total distance travelled is ?

• A. $2m$
• B. $3m$
• C. $4m$
• D. $6m$

Answer 1

Answer: (D)

$6m$

Let time of acceleration be $t_1$ amd retardation be $t_2$,

Given,

$t_1+t_2=3$

$v=2t_1$

$0-v=-4t_2$

$v=2t_1=4(3-t_1)$

$t_1=2,t_2=1$

$v=4$

Let $s_1$ be accelrated journey and $s_2$ be deceleration journey.

And, $v^2-u^2=2as$

$4^2-0=2\times 2\times s_1$

$0-4^2=2\times 4\times s_2$

$s_1=4$

$s_2=2$

$s=s_1+s_2=6m$

Option $\text{D}$ is the correct answer