Question

The acceleration of a particles in $m{s}^{-2}$ is given by $a=3t^2+2t+2$, where time $t$ is in second. If the particle starts with a velocity $v=2$ $m{s}^{-1}$ at $t=0$, then find the velocity at the end of $2$ $s$

Answer 1

$a=3t^2+2t+2$
$v={\int }_0^{t}adt+c$
$v\left(t\right)={[t^3+t^2+2t]}_0^t+c$
$v\left(t\right)=t^3+t^2+2t+2[c=2m/satt=0]$
$v\left(2\right)=8+4+4+2=18$ $m/s$