$A$ car travels a distance of $x$ with speed $v_1$ and then the same distance $x$ with speed $v_2$ in the same direction. The average speed of the car is

Write the relation between speed and the magnitude of velocity.

The position $(x)$-time $(t)$ graph for a particle moving along a straight line is shown in the figure. The average speed of the particle in the time interval $t=0$ to $t=8 \, s$ is .......... $m/s$.

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].

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

$A$ car covers the first half of the distance between two places at $40 \text{ km/h}$ and the second half at $50 \text{ km/h}$. The average speed of the car is (in $text{ km/h}$)