$A$ particle has an initial velocity of $10 \, m/s$. It moves due to a constant retarding force along the line of motion,which produces a retardation of $5 \, m/s^2$. Then:

State whether the following statements are true or false:
$(a)$ If the motion is not along a straight line,then path length = magnitude of displacement.
$(b)$ Stopping distance is directly proportional to the initial velocity.
$(c)$ The average speed of an object moving with different speeds is the average of those speeds.
$(d)$ The area under the position-time graph represents the displacement of the moving object.

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

Which of the following statements are true for a moving body?

$A$ particle moves along a straight line such that its retardation is proportional to its displacement. The loss in its kinetic energy for any displacement $x$ is proportional to:

$A$ 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 $\,s$)