At time $t=0$,a car moving along a straight line has a velocity of $16 \; m/s$. It slows down with an acceleration of $a = -0.5t \; m/s^2$,where $t$ is in seconds. Mark the correct statement$(s)$.

For any arbitrary motion in space,which of the following relations are true?
$(a)$ $v_{\text{average}} = (1/2) (v(t_1) + v(t_2))$
$(b)$ $v_{\text{average}} = [r(t_2) - r(t_1)] / (t_2 - t_1)$
$(c)$ $v(t) = v(0) + at$
$(d)$ $r(t) = r(0) + v(0)t + (1/2)at^2$
$(e)$ $a_{\text{average}} = [v(t_2) - v(t_1)] / (t_2 - t_1)$
(The 'average' stands for the average of the quantity over the time interval $t_1$ to $t_2$.)

For the velocity-time graph shown in the figure,in a time interval from $t=0$ to $t=6\,s$,match the following columns.

Column $I$	Column $II$
$(A)$ Change in velocity	$(p)$ $-5/3\,SI \text{ unit}$
$(B)$ Average acceleration	$(q)$ $-20\,SI \text{ unit}$
$(C)$ Total displacement	$(r)$ $-10\,SI \text{ unit}$
$(D)$ Acceleration at $t=3\,s$	$(s)$ $-5\,SI \text{ unit}$

$A$ ball moves one-fourth of a circle of radius $R$ in time $T$. Let $v_1$ and $v_2$ be the magnitudes of mean speed and mean velocity vector. The ratio $\frac{v_1}{v_2}$ will be

In what different ways can the velocity of an object be changed?

The relation between time $t$ and distance $x$ is given by $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The retardation of the particle is: