$A$ car moves from $A$ to $B$ with a speed of $30 \ km/h$ and from $B$ to $A$ with a speed of $20 \ km/h$. What is the average speed of the car (in $km/h$)?

$A$ particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2$. Its average speed during the complete journey is

$A$ car moves a distance of $200 \; m$. It covers the first half of the distance at a speed of $40 \; km/h$ and the second half of the distance at a speed of $v$. If the average speed is $48 \; km/h$,the value of $v$ is: (in $; km/h$)

The ratio of the numerical values of the average velocity and average speed of a body is always

If a person moving along a straight line path covers the first half distance with velocity $V_1$ and the next half distance with velocity $V_2$,then the average velocity of the person is

Explain clearly, with examples, the distinction between
$(a)$ magnitude of displacement over an interval of time, and the total length of path covered by a particle over the same interval.
$(b)$ magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval].
Show in both $(a)$ and $(b)$ that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only].