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Question

The velocity-time graph for an object is given below. Find the total displacement for the duration of 16 s?


A
100 m
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B
120 m
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C
80 m
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D
90 m
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Solution

The correct option is A 100 m

We know, the area under the velocity - time graph gives displacement.
Let the total displacement d=d1+d2+d3+d4 where,
d1 is the displacement from 0 s to 2 s.
d2 is the displacement from 2 s to 10 s.
d3 is the displacement from 10 s to 12 s.
d4 is the displacement from 12 s to 16 s.

From the graph, displacement from 0 s to 2 s,
d1= Area of triangle
d1=12×2×8=8 m
From the graph, displacement from 2 s to 10 s,
d2= Area of square
d2=8×8=64 m
From the graph, displacement from 10 s to 12 s,
d3= Area of triangle + Area of rectangle
d3=(12×4×2)+(4×2)
=4+8=12 m
From the graph, displacement from 12 s to 16 s,
d4= Area of square
d4=4×4=16 m

Total displacement:
d=d1+d2+d3+d4
d=8+64+12+16=100 m

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