The relation between time $t$ and distance $x$ is $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The relation between acceleration $a$ and velocity $v$ is:

$A$ motorbike starts from rest, attains a velocity of $10 \,m/s$ with an acceleration of $0.5 \,m/s^2$, travels $10 \,km$ with this uniform velocity, and then comes to a halt with a uniform deceleration of $0.2 \,m/s^2$. The total time of travel is: (in $\,s$)

$A$ train starts from rest from a station with acceleration $0.2 \, m/s^2$ on a straight track and then comes to rest after attaining maximum speed at another station due to retardation $0.4 \, m/s^2$. If the total time spent is half an hour,then the distance between the two stations is [Neglect the length of the train]. (in $, km$)

$A$ man moves in an open field such that after moving $10 \, m$ on a straight line,he makes a sharp turn of $60^{\circ}$ to his left. The total displacement just at the start of the $8^{\text{th}}$ turn is equal to ........ $m$.

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

State whether the following statements are true or false:
$(a)$ An object can have acceleration even when its velocity is zero.
$(b)$ If the acceleration of a moving object is constant,the direction of its velocity must remain the same.
$(c)$ The speed of an object can never be zero.