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Question

The figure shows velocity-time graph of a particle moving along a straight line. Identify the correct statement:


A
The particle crosses its initial position at t=3 s.
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B
The particle crosses its initial position at t=2 s.
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C
The average speed of the particle in the time interval, 0t2 s is zero.
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D
Initial speed of particle is zero.
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Solution

The correct option is B The particle crosses its initial position at t=2 s.
Area under vt graph=Displacement
Displacement in time interval 0 to 1 s
=Area(ΔOAB)
=12×1×10=5 m ...(1)


Displacement in time interval 1 to 2 s
=Area(ΔBCD)
=12×1×10=5 m ...(2)
Now, net displacement (sum of total area under curve) from t=0 to 2 s is,
S=+5+(5)=0
Particle will cross its initial position at t=2 s, since net displacement of particle is zero at the end of t=2 s.
Total distance covered in 0t2 s is not zero. So, average speed is also not zero.
And initial speed of particle is not zero. (from the graph)
Hence, only option (b) is correct.

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