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/s3We know that acceleration from v−t graph is given by the slope of v−t graph ⟹a=dvdt=tan45∘=1 m/s2. From v−t 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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