Question

If $a=(3t^2+2t+1)m/s^2$ is the expression according to which the acceleration of a particle moving along a straight line varies, then the expression for instantaneous velocity at any time $t$ will be (if the particle was initially at rest)

• A. $t^3+2t+1$
• B. $t^3+t+1$
• C. $t^3+t^2+t$
• D. $t^3+t^2+t+1$

Answer 1

The correct option is C $t^3+t^2+t$

$a=(3t^2+2t+1)$
${\int }_0^{v}dv={\int }_0^t(3t^2+2t+1dt)(\because a=\frac{dv}{dt})$
$v=t^3+t^2+t$