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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.
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| Fig. 5-1 |
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
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| 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
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| 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.
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| 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.
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