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).

Category: Motion in One Dimension ICSE

February 22, 2024

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

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PrevPrevious QuestionA body at rest is made to fall from the top of a tower. Its displacement at different instants is given in the following table Draw a displacement-time graph and state whether the motion is uniform or non-uniform.

Time (in s)	0.1	0.2	0.3	0.4	0.5	0.6
Displacement (in m)	0.05	0.20	0.45	0.80	1.25	1.80

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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).

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