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Question

The plot of velocity versus time graph for a particle moving along a straight line is shown.

The value of dot product of velocity and acceleration of particle at t=2 s is

A
1 m2/s3
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B
1 m2/s3
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C
2 m2/s3
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D
2 m2/s3
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Solution

The correct option is B 1 m2/s3
We know that acceleration from vt graph is given by the slope of vt graph
a=dvdt=tan45=1 m/s2.
From vt graph
At t=3 s, v=0
Using first equation of motion, we can say
v=u+at
0=u+(1)(3)
Initial velocity of the particle u=3 m/s
At t=2 s
v=3+1×2=1 m/s
v=1 m/s
We know that, acceleration at t=2 s is a=1 m/s2
Dot product of v and a at t=2 s is v.a=1 m2/s3

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