The velocity-time graph of an object is shown below. Find the displacement of object in 10 second and
acceleration of object for time intervals 0 to 5 s and 5 s to 10 s. Also draw the acceleration time graph of
object.
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Answer:
Figure (i) represents a velocity-time graph when the body starts from rest, and its velocity increases at a uniform rate.
The slope of the graph AC. i.e.,
BC
AB
gives the acceleration of body.
∴Acceleration=
Total time
change in velocity
=
5s
(16−0)ms
−1
=3.2ms
−2
The area of triangle ABC, gives the displacement.
Thus, displacement in 5 s
2
1
×AB×BC=
2
1
×16ms
−1
×5s
=40m
Figure (ii) represents velocity - time graph, where the body is initially not at rest.
The slope of graph AC, i.e., (
BC
AB
) gives the acceleration.
∴Acceleration=
BC
AB
4s
(25−5)ms
−1
=
4
20
ms
−2
=5ms
−2
The distance covered by the body in specified direction is area of trapezium ECAD.
∴Displacement=
2
1
(CE+AD)×ED
=
2
1
(5+25)ms
−1
×4s=60m
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