$A$ person of height $1.6 \ m$ is walking away from a lamp post of height $4 \ m$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60 \ cm \ s^{-1}$,the speed of the tip of the person's shadow on the ground with respect to the person is . . . $cm \ s^{-1}$.

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.

Statement $(I)$: An object subjected to velocities $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ has a resultant velocity with magnitude $|\vec{v}| = |\overrightarrow{v_1}| + |\overrightarrow{v_2}|$.
Statement $(II)$: The magnitude of displacement is either less than or equal to the path length of an object between two points.
Statement $(III)$: The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?

$A$ metro train starts from rest and in $5 \, s$ achieves $108 \, km/h$. After that,it moves with constant velocity and comes to rest after travelling $45 \, m$ with uniform retardation. If the total distance travelled is $395 \, m$,then the total time of travelling is ....... $s$.

$A$ body is at rest at $x=0$. At $t=0$,it starts moving in the positive $x-$direction with a constant acceleration. At the same instant,another body passes through $x=0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $x_{1}(t)$ after time $t$ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1}-x_{2})$ as a function of time $t$?

$A$ man walks on a straight road from his home to a market $2.5 \; km$ away with a speed of $5 \; km \; h^{-1}$. Finding the market closed,he instantly turns and walks back home with a speed of $7.5 \; km \; h^{-1}$. What is the average speed of the man over the interval of time $0$ to $40 \; min$?