Question

Figure 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 the displacement-time graph for it on figure (b).
velocity-time-graph-motion-body-find-displacement

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Answer

As we know, the displacement of body at any instant can be obtained by finding the area enclosed by the straight line with the time axis up to that instant.

Let displacements at t = 1 s, 2 s, 3 s, and 4 s be S1, S2, S3, and S4 respectively.

At t = 1 s,

S1 = 1\over 2 × 1 × 1 =  0.5 m

At t = 2 s,

S2 = 1\over 2 × 2 × 2 =  2 m

At t = 3 s,

S3 = 1\over 2 × 3 × 3 =  4.5 m

At t = 4 s,

S4 = 1\over 2 × 4 × 4 =  8 m

The table below gives the displacement of the 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

displacement-time-graph-motion-body-find-displacement-1029x677

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