Using the following data,draw a time-displacement graph for a moving object:

Time $(s)$	$0, 2, 4, 6, 8, 10, 12, 14, 16$
Displacement $(m)$	$0, 2, 4, 4, 4, 6, 4, 2, 0$

Use this graph to find the average velocity for the first $4 \, s$,for the next $4 \, s$,and for the last $6 \, s$.

$(a)$ Draw velocity-time graphs for the following cases:
$(i)$ When the object is at rest.
$(ii)$ When the object is thrown vertically upwards.
$(b)$ $A$ motorcyclist riding motorcycle $A$ who is travelling at $36 \, km \, h^{-1}$ applies the brakes and stops the motorcycle in $10 \, s$. Another motorcyclist of motorcycle $B$ who is travelling at $18 \, km \, h^{-1}$ applies the brakes and stops the motorcycle in $20 \, s$. Plot the speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it came to a stop?

The following table shows the position of three persons between $8.00\, am$ to $8.20\, am$.

Time	Position of Person $A$ $(km)$	Position of Person $B$ $(km)$	Position of Person $C$ $(km)$
$8.00\, am$	$0$	$0$	$0$
$8.05\, am$	$4$	$5$	$10$
$8.10\, am$	$13$	$10$	$19$
$8.15\, am$	$20$	$15$	$24$
$8.20\, am$	$25$	$20$	$27$

$(i)$ Who is moving with constant speed?
$(ii)$ Who has travelled the maximum distance between $8.00\, am$ to $8.05\, am$?
$(iii)$ Calculate the average speed of person $A$ in $km\, h^{-1}$.

$A$ body moves with a velocity of $2\, m s^{-1}$ for $5\, s$,then its velocity increases uniformly to $10\, m s^{-1}$ in the next $5\, s$. Thereafter,its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$.
$(i)$ Plot a velocity-time graph for the motion of the body.
$(ii)$ From the graph,find the total distance covered by the body after $2\, s$ and $12\, s$.

Draw velocity-time graphs for the following situations:
$(i)$ When a body is moving with uniform velocity.
$(ii)$ When a body is moving with variable velocity,but uniform acceleration.
$(iii)$ When a body is moving with variable velocity,but uniform retardation.
$(iv)$ When a body is moving with variable velocity and variable acceleration.

All buses and cars these days are fitted with a speedometer,which shows the velocity of the vehicle. $A$ device called odometer records the distance moved by the vehicle. If the reading on the odometer of a vehicle in the beginning of a trip and after $40 \text{ minutes}$ were $1048 \text{ km}$ and $1096 \text{ km}$ respectively,calculate its average velocity. Will the reading on the speedometer show this velocity when the vehicle is moving? Support your answer with reason.