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 person travels along a straight road for the first half time with a velocity ${v_1}$ and the next half time with a velocity ${v_2}$ . The mean velocity $V$ of the man is

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

Which informations cannot be drawn from average velocity ?

A body has speed $V, 2V$ and $3V$ in first $1/3$ of distance $S$, seconds $1/3$ of $S$ and third $1/3$ of $S$ respectively. Its average speed will be