The acceleration $a$ in $m/s^2$ of a particle is given by $a = 3t^2 + 2t + 2$,where $t$ is the time. If the particle starts with an initial velocity $u = 2\,m/s$ at $t = 0$,then the velocity at the end of $2\,s$ is:

An object moves in a straight line with deceleration whose magnitude varies with velocity as $3 v^{2/3}$. If at an initial point, the velocity is $8 \,m/s$, then the distance travelled by the object before it stops is (in $\,m$)

Give examples of a one-dimensional motion where:
$(a)$ The particle moving along positive $x$-direction comes to rest periodically and moves forward.
$(b)$ The particle moving along positive $x$-direction comes to rest periodically and moves backward.

Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.

$A$ particle is moving with constant acceleration $a$. The following graph shows the $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is $...... \text{m/s}^{2}$.

$A$ car moving at a speed $V$ is stopped in a certain distance $s$ when the brakes produce a deceleration $a$. If the speed of the car is $nV$,what must be the deceleration of the car to stop it in the same distance $s$ and in the same time $t$?