The slope of a velocity-time graph gives:

$A$ girl walks along a straight path to drop a letter in the letterbox and comes back to her initial position. Her displacement-time graph is shown in the figure. Plot a velocity-time graph for the same.

The area under a velocity$-$time graph is equal to the

$(a)$ Derive graphically the equation for velocity$-$time relation.
$(b)$ Name the device used to measure distance travelled by a vehicle.
$(c)$ Can displacement of a moving object be zero? Give reason.

The $v-t$ graph of cars $A$ and $B$ which start from the same place and move along a straight road in the same direction is shown. Calculate:
$(i)$ The acceleration of car $A$ between $0$ and $8\, s$.
$(ii)$ The acceleration of car $B$ between $2\, s$ and $4\, s$.
$(iii)$ The points of time at which both the cars have the same velocity.
$(iv)$ Which of the two cars is ahead after $8\, s$ and by how much?

The graph given below is the distance-time graph of an object.
$(i)$ Find the speed of the object during the first four seconds of its journey.
(ii) How long was it stationary?
(iii) Does it represent a real-life situation? Justify your answer.