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Question
Figure (a) shows the velocity-time graph for the motion of a body. Use it to find the displacement of the body at t = 1 s, 2 s, 3 s and 4 s, then draw on Figure (b), the displacement-time graph for it.
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| (a) | (b) |
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Solution
Let displacements at t = 1 s, 2 s, 3 s, 4 s be S1, S2, S3, S4 respectively.
At t = 1 s, displacement S1 = `1/2 xx 1 xx 1` = 0.5 m
At t = 2 s, displacement S2 = `1/2 xx 2 xx 2` = 2 m
At t = 3 s, displacement S3 = `1/2 xx 3 xx 3` = 4.5 m
At t = 4 s, displacement S4 = `1/2 xx 4 xx 4` = 8 m
The table below gives the displacement of body at different instants.
| Time (in s) | 1 | 2 | 3 | 4 |
| Displacement (in m) | 0.5 | 2 | 4.5 | 8 |
The displacement time graph is shown below
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