Question

The rate of change of velocity gives acceleration. If the acceleration of a particle is $a=3t^2{ms}^{-2}$ and velocity of particle at $t=0$ is $1{ms}^{-1}$, then velocity of the particle at $t=2s$ will be

• A. $12{ms}^{-1}$
• B. $13{ms}^{-1}$
• C. $11{ms}^{-1}$
• D. $9{ms}^{-1}$

Answer 1

The correct option is D $9{ms}^{-1}$

Acceleration is given as $a=3t^2$

Using $a=\frac{dV}{dt}$

Or ${\int }_1^{V_f}dV={\int }_o^{2}adt$

Or ${\int }_1^{V_f}dV={\int }_o^{2}3t^{2}dt$

Or $V{|}_1^{V_f}=t^3{|}_o^2$

Or $V_f-1=2^3-0$

$⟹V_f=9m/s$