Question

A particle is moving rectilinearly so that its acceleration is given as $a\left(m/s^2\right)=3t^2+1$ Its initial velocity is zero then the velocity of the particle at $t=1$ s will be

• A. $2\text{m/s}$
• B. $5\text{m/s}$
• C. $3\text{m/s}$
• D. $4\text{m/s}$

Answer 1

The correct option is A $2\text{m/s}$

As acceleration is given as, $a=3t^2+1$
$\Rightarrow \frac{dv}{dt}=3t^2+1$
$\underset{0}{\overset{v}{\int }}dv=\underset{0}{\overset{t}{\int }}(3t^2+1)dt$
$v=(t^3+t+c{)}_0^t$
$\Rightarrow v=t^3+t$ ($\therefore v=0$ at $t=0$)
At $t=1\text{s}$,
$v=1+1=2\text{m/s}$