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Question

A particle moves along the x-axis. Its velocity-time graph is given below.
The distance travelled by the particle in 0 to 3 s

A
Zero
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B
4 m
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C
8 m
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D
12 m
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Solution

The correct option is C 8 m
As the curve is parabolic let us assume a second order equation for velocity to fit in this curve
Let v=at2+bt+c(1)
Apply boundary condition to above equation to find a,b and c
At t=0 s, v=0 ms2
0=(a×02)+(b×0)+c
c=0
At t=1 s, v=3 ms2
3=(a×12)+(b×1)+0
3=a+b(2)
At t=2 s, v=0 ms2
0=(a×22)+(b×2)
b=2a(3)
Substitute (3) in equation (2) we get,
3=a2a
a=3
Substitute value of a in equation (2)
3=3+b
b=6
Substitute these a, b and c in equation (1)
v=3t26t
From the graph we can see that the velocity changes its direction after t = 2 s
Distance=∣ ∣[3t336t22]20∣ ∣+∣ ∣[3t336t22]32∣ ∣
|(80)(120)|+|(278)(2712)|
=|4|+|4|=8 m

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