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

$A$ bus travels the first one-third distance at a speed of $10\; km/h$,the next one-third at $20\; km/h$,and the last one-third at $60\; km/h$. The average speed of the bus is ........ $km/h$.

Consider a particle moving along a straight line, whose position as a function of time is given by $s(t) = \alpha t^2 - \beta t + \gamma$, where $\alpha = 1 \text{ ms}^{-2}$, $\beta = 6 \text{ ms}^{-1}$ and $\gamma = 5 \text{ m}$. The average speed of the particle, in $\text{ms}^{-1}$, from $t = 0$ to $t = 6 \text{ s}$ 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].

$A$ motorcyclist travels a certain distance with a uniform speed of $30\, m/s$ and immediately turns back and returns to the starting point with a uniform speed of $20\, m/s$. Then the average speed of the motorcycle is ..........$m/s$ :-

$A$ body covers half of its distance with speed $u$ and the other half with a speed $v$,the average speed of the body is