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Question

Statement -1 : Let v be the speed of particle at any time t. If dvdt is a non - zero constant then speed of particle may be minimum at some time.
Statement -2 : The speed v of a moving particle may be minimum at time t=t0 when v=0. The speed v of a moving particle may also be minimum at time t=t0 when dvdt=0 and d2vdt2= positive.

A
Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1.
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B
Both statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1.
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C
Statement 1 is correct and statement 2 is incorrect.
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D
Statement 1 is incorrect and statement 2 is correct.
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Solution

The correct option is B Both statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1.
For a stone projected vertically upwards, the speed v is least at highest point even though dvdt is constant. Hence statement 1 is true.
Suppose the velocity of a particle varies with time as v=t3t2t+1. Here the velocity is minimum at t=1 s as v=0 at t=1 s. If we differentiate v w.r.t t, we get dvdt=3t22t1.
Here dvdt=0, at t=1 s and d2vdt2=6t2=6(1)2=4= positive.
Hence, statement 2 is also true but it is not the correct explanation of statement 1.

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