The same retarding force is applied to stop a train. The train stops after $80 \ m$. If the speed is doubled,then the stopping distance will be

$A$ moving body is covering distances which are proportional to the square of the time. Then the acceleration of the body is

$A$ bullet fired into a target loses one-third of its velocity after travelling a distance $x$ meters into the target. If the bullet comes to rest by travelling a further distance $x^{\prime}$, then the ratio $\frac{x^{\prime}}{x}$ is

In some appropriate units,the time $(t)$ and position $(x)$ relation of a moving particle is given by $t = x^2 + x$. The acceleration of the particle is

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.

If a body starts from rest and travels $120 \,cm$ in the $6^{th}$ second,what is the acceleration in $m/s^2$?