1. Tardigrade
  2. Question
  3. Physics
  4. The acceleration ' a in m / s 2 of a particle is given by a =3 t 2+2 t +2 where t is the time. If the particle starts out with a velocity u=2 m / s at t =0, then the velocity at the end of v second is

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Q. The acceleration ' a in $m / s ^2$ of a particle is given by $a =3 t ^2+2 t +2$ where $t$ is the time. If the particle starts out with a velocity $u=2 m / s$ at $t =0$, then the velocity at the end of $v$ second is

Motion in a Straight Line

Solution:

$ a=3 t^2+2 t+2 $
$dv = adt$
$ v=\frac{3 t^3}{3}+\frac{2 t^2}{2}+2 t $
$ v=t^3+t^2+2 t $
at $t =0, u =2$
att $=2$
$ v=t^3+t^2+2 t+2 $
$ =8+4+2 \times 2+2 $
$ =8+4+4+2 $
$ =18 m / s $