Assertion $(A)$: The angle between acceleration and velocity of a body in one-dimensional motion is always zero. Reason $(R)$: One-dimensional motion is along a straight line.

$A$ 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 $40 \; min$?

$A$ particle moves along a straight line such that its displacement $x$ varies with time $t$ as $x = \alpha t^3 + \beta t^2 + \gamma$, where $\alpha, \beta, \gamma$ are constants. $V_1$ is the average velocity of the particle during its journey between $t = 1 \ s$ and $t = 3 \ s$. $V_2$ is the instantaneous velocity of the particle at $t = 3 \ s$. The ratio $\frac{V_1}{V_2}$ is

Fill in the blanks:
$(a)$ Average velocity ....... average speed.
$(b)$ $A$ particle moves in a straight line with an initial velocity $v_0$ and constant acceleration $a$. The formula for the distance covered in the $n^{th}$ second is ............ .
$(c)$ When two objects are moving in the same direction with velocities $v_A$ and $v_B$,the formula for the velocity of $A$ relative to $B$ is .......... .

If a car covers $2/5^{th}$ of the total distance with speed $v_1$ and $3/5^{th}$ of the total distance with speed $v_2$,then the average speed is:

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 .......... $m/s^2$.