Which of the following curves possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below.

The figure shows the velocity $(v)$ of a particle plotted against time $(t)$.

$A$ 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:

The speed-time graph for a body moving along a straight line is shown in the figure. The average acceleration of the body may be .......... $m/s^2$.

$A$ car starts from rest and moves with a constant acceleration of $5 \,m/s^2$ for $10 \,s$ before the driver applies the brake. It then decelerates for $5 \,s$ before coming to rest. The average speed of the car over the entire journey is: (in $\,m/s$)

$A$ man in a car at location $Q$ on a straight highway is moving with speed $v$. He decides to reach a point $P$ in a field at a distance $d$ from the highway (point $M$) as shown in the figure. The speed of the car in the field is half of that on the highway. What should be the distance $RM$ so that the time taken to reach $P$ is minimum?