Figure gives the $x-t$ plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least ? Give the sign of average velocity for each interval.

Explain clearly, with examples, the distinction between 

$(a)$ magnitude of displacement (somettmes called distance) 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 car goes from $A$ to $B$ (without changing direction), during first part of journey its average speed is $V_1$ and for second part of journey average speed is $V_2$ . The ratio path length of second part to the path length of first part is $\sqrt {\frac{{{V_2}}}{{{V_1}}}} $ . In that case the average speed of total path is ……. of average speeds of both parts. Choose correct option of fill. 

If magnitude of average speed and average velocity over a time interval are same, then

One car moving on a straight road covers one third of the distance with $20 \,km/hr $ and the rest with $60\, km/hr$. The average speed is……….$km/hr$