Question

Show the shape of the distance-time graph for the motion in the following cases:
(i) A car moving with a constant speed.
(ii) A car parked on a side road.

Answer 1

The answer is in the above picture...
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Answer 2

(i) A car moving with a constant speed.

let speed of car = v (constant )

as we know, rate of change of distance with respect to time is known as speed.

so, v = dx/dt

⇒v∫dt = ∫dx

⇒vt = x

hence, distance is directly proportional time. so, distance time graph will be straight line with slope v as shown in figure.

(ii) A car parked on a side of road.

speed of car = 0 ( car is in rest )

so, dx/dt = 0

⇒∫dx = 0∫dt

⇒x = k (constant)

means, distance remains constant.

hence, distance-time graph will be straight line parallel to time axis (i.e., x-axis)