$A$ car moving along a straight highway with a speed of $126 \; km/h$ is brought to a stop within a distance of $200 \; m$. What is the retardation of the car (assumed uniform in $m/s^2$)?

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.

The velocity $v$ of a particle moving along the $x$-axis varies with its position $x$ as $v = \alpha \sqrt{x}$,where $\alpha$ is a constant. Which of the following graphs represents the variation of its acceleration $a$ with time $t$?

The velocity $u$ and displacement $r$ of a body are related as $u^2 = kr$,where $k$ is a constant. What will be the velocity after $1 \, s$? (Given that the displacement is zero at $t = 0$)

$A$ particle is moving along the $X$-axis with velocity $v = e^{-\beta x}$. At time $t = 0$,the particle is located at $x = 0$. The displacement of the particle as a function of time is

$A$ particle experiences a constant acceleration for $20 \,s$ after starting from rest. If it travels a distance ${S_1}$ in the first $10 \,s$ and a distance ${S_2}$ in the next $10 \,s$,then: