An object moves with speed $v_1, v_2$, and $v_3$ along a line segment $A B, B C$ and $C D$ respectively as shown in figure. Where $AB = BC$ and $AD =3 AB$, then average speed of the object will be :

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

A particle moves along a semicircle of radius $10\,m$ in $5$ seconds. The average velocity of the particle is………..$ms^{-1}$

A man walks on a straight road from his home to a market $2.5\; km$ away with a speed of $5 \;km h ^{-1} .$ Finding the market closed, he instantly turns and walks back home with a speed of $7.5 \;km h ^{-1} .$ What is the magnitude of average velocity in $m/s$?

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].