Five particles have speeds $1, 2, 3, 4, 5 \, m/s$. The average velocity of the particles is (in $m/s$):

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].

$A$ vehicle travels $4\,km$ with a speed of $3\,km/h$ and another $4\,km$ with a speed of $5\,km/h$. What is its average speed in $km/h$?

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

Explain average velocity and average speed.

$A$ car travels half the distance with a constant velocity of $40 \, km/h$ and the remaining half with a constant velocity of $60 \, km/h$. The average velocity of the car in $km/h$ is