Fill in the blanks:
$(a)$ If the distance covered by a particle is zero,then its displacement is ....... .
$(b)$ For an object moving with uniform acceleration $a$,the change in velocity during a time interval $\Delta t$ is ......... .
$(c)$ The time rate of change of position of an object is called .......... .

The displacement of a particle moving in a straight line depends on time as $x = \alpha t^3 + \beta t^2 + \gamma t + \delta$. The ratio of initial acceleration to its initial velocity depends on:

The driver of a bus moving with a velocity of $72 \ km/h$ observes a boy walking across the road at a distance of $50 \ m$ in front of the bus and decelerates the bus at $5 \ m/s^2$ by applying brakes and is just able to avoid an accident. The reaction time of the driver is (in $s$)

$A$ drunkard walking in a narrow lane takes $5$ steps forward and $3$ steps backward,followed again by $5$ steps forward and $3$ steps backward,and so on. Each step is $1\; m$ long and requires $1\; s$. Plot the $x-t$ graph of his motion. How long (in $s$) does the drunkard take to fall into a pit $13\; m$ away from the start?

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 $t=3\,s$	$(s)$ $-5\,SI \text{ unit}$

$A$ charged object is launched inside a time-varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$,its position vector $\vec{r}$,velocity $\vec{v}$,and acceleration $\vec{a}$ are measured. $A$ student watches the video at a later time but mistakenly plays the tape in the reverse direction. What are the position,velocity,and acceleration of the object at moment $A$ observed by the student,respectively?