Question

A body starts from rest at time $t=0$, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be

• A. $65\text{m/s}$
• B. $55\text{m/s}$
• C. $45\text{m/s}$
• D. $35\text{m/s}$

Answer 1

The correct option is B $55\text{m/s}$

Body is starting from rest. So, $u=0$.
Velocity will be maximum when,
$\frac{dv}{dt}=0$
$\Rightarrow a=0$
At $t=11\text{s}$, maximum velocity is attained as $a=0$.
Area under the $a-t$ curve gives change in velocity.
Or, $v_f-v_i=\frac{1}{2}\times 10\times 11=55$
$\Rightarrow v_{max}-0=55$
$\therefore v_{max}=55\text{m/s}$

Why this question? Tips: Velocity increases as long as acceleration is positive.