The motion of an object can be represented by motion graphs. Common motion graphs include displacement-time graph, velocity-time graph and acceleration-time graph.

 Fig. 5-1

Displacement-time graph

A displacement-time graph shows the positions of a moving object at different times. Fig. 5-1 shows the displacement-time graph of a car. From time to , the car moves forwards, and at it has a displacement of 60 m. Then it remains stationary there for 5 s, and finally moves back to its starting position in another 5 s.

The velocity of motion can be determined from the slope of the displacement-time graph. The velocity of the car is from to , it is zero (the car is at rest) from to and is from to . The negative slope in the last 5 s indicates that the car is moving backwards. Note that the slope of the graph in each of the time intervals is a constant, showing that the car is in a uniform motion (constant velocity) in each interval.

Flash animation: Displacement-time graph

 Fig. 5-2

Example

Fig. 5-2 shows the displacement-time graph of a car during parking. Describe the motion of the car and find the velocity in each time interval.

Solution

Stage 1: The car moves forwards from the origin to in the first 5 s.

(forwards)

Stage 2: The car moves backwards, passes the origin, to in the next 5 s.

(backwards)

Stage 3: The car remains at rest in the last 5 s.

Flash animation: Displacement-time graph

 Fig. 5-3

Exercise

Fig. 5-3 is the displacement-time graph for a car encountering a traffic light. Describe the motion of the car at each stage qualitatively.

Answer: Stage 1: moving with constant velocity; stage 2: decelerating; stage 3: at rest; stage 4: accelerating; stage 5: moving with the same constant velocity as in stage 1.

Note: In stage 2 the slope of the curve is decreasing, while in stage 4 the slope is increasing. This indicates that the car is decelerating in stage 2 and accelerating in stage 4.

 Fig. 5-4

Exercise

A boy walks at a velocity of along a street for 50 s, suddenly he remembers that he has to buy something in a shop that he has passed by, so he turns around and walks at a velocity of for 10 s. He then stops for 30 s at the shop, and finally walks forward again at for another 20 s. Plot a displacement-time graph for the motion of the boy.

Answer: See Fig. 5-4.