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

$A$ balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $h_{1}$,a girl standing at a distance $d$ (point $B$) from $A$ sees it at an angle $45^{\circ}$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$,it is seen at an angle $60^{\circ}$ with respect to the vertical if the girl moves further by a distance $2.464d$ (point $C$). Then the height $h_{2}$ is (given $\tan 30^{\circ} = 0.5774$):

When is an object said to be a particle?

In which of the following examples of motion can the body be considered approximately a point object:
$(a)$ $A$ railway carriage moving without jerks between two stations.
$(b)$ $A$ monkey sitting on top of a man cycling smoothly on a circular track.
$(c)$ $A$ spinning cricket ball that turns sharply on hitting the ground.
$(d)$ $A$ tumbling beaker that has slipped off the edge of a table.

Why is a frame of reference required?

The position vector of a particle is given by the expression $\vec{r} = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$. The distance traversed in the first $10 \, s$ is ......... $m$.