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

$A$ 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 $\,s$)

$A$ 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?

Two masses of $3.4 \text{ kg}$ and $2.5 \text{ kg}$ are accelerated from an initial speed of $5 \text{ m/s}$ and $12 \text{ m/s}$, respectively. The distances traversed by the masses in the $5^{th}$ second are $104 \text{ m}$ and $129 \text{ m}$, respectively. The ratio of their momenta after $10 \text{ s}$ is $\frac{x}{8}$. The value of $x$ is . . . . . . .

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.

State whether the following statements are true or false:
$(a)$ Velocity can change without a change in speed.
$(b)$ The total distance covered by a freely falling body in a given time is directly proportional to the time.
$(c)$ $A$ particle is a point object that possesses dimensions.