Question

A car accelerates from rest at constant rate of $2m/s^2$ for some time. Then its retards at a constant rate of $4m/s^2$ and comes to rest. if it remains in motion for $3$ seconds, then the maximum speed attained by the car is:-

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

Answer 1

The correct option is C $4m/s$

Let $v,t_1,t_2$ be the maximum velocity attained, time for which car accelerated and the time for which car retarded respectively

$\Rightarrow t_1=(v-u)/a=(v-0)/2=v/2$

$\Rightarrow t_2=(v-u)/a=(0-v)/(-4)=v/4$

Now it is given that,

$\Rightarrow t_1+t_2=3$

$\Rightarrow v/2+v/4=3$

$\Rightarrow v=4m/s$

Hence correct answer is option $C$