Name the physical quantity which corresponds to the rate of change of momentum.

The following table shows the position of Renu, while she is going to her school. Draw a distance-time graph for her motion.

Time	Distance from her home $(km)$
$06:45 \, am$	$0$
$07:00 \, am$	$8$
$01:30 \, pm$	$8$
$01:45 \, pm$	$0$

$(a)$ Differentiate between distance and displacement.
$(b)$ Under what conditions is the magnitude of average velocity of an object equal to its average speed?

Prove that if a body is thrown vertically upward,the time of ascent is equal to the time of descent.

$A$ car travels $100\, km$ east and then $100\, km$ south. Finally,it comes back to the starting point by the south-east route. Throughout the journey the speed is constant at $60\, km\, h^{-1}$. The average velocity for the whole journey if the time taken is $3.3\, h$ is

The diagram shows a velocity-time graph for a car starting from rest. The graph has three sections $AB$,$BC$,and $CD$.
$(i)$ From a study of this graph,state how the distance travelled in any section is determined.
$(ii)$ Compare the distance travelled in section $BC$ with the distance travelled in section $AB$.
$(iii)$ In which section does the car have zero acceleration?
$(iv)$ Is the magnitude of acceleration higher or lower than that of retardation? Give a reason.