The position of a particle moving along X -axis varies with time as x = u t + A sin ω t . At t = 0 , x = 0 . Between t = 0 and t = t 0 , average velocity of particle is u . Then values of t 0 can

Question

The position of a particle moving along X -axis varies with time as x = u t + A sin ω t . At t = 0 , x = 0 . Between t = 0 and t = t 0 ​ , average velocity of particle is u . Then values of t 0 ​ can NOT be

TestHub · Accepted Answer

Average velocity = [x(t0) - x(0)]/t0 = u + A.sin(wt0)/t0 = u, so sin(wt0) = 0 and t0 = n.pi/w (n = 1, 2, 3, ...). The values pi/w (n = 1), 2pi/w (n = 2) and 4pi/w (n = 4) are all possible for t0, so options A, C and D can all occur. For t0 = pi/(2w), sin(pi/2) = 1, not 0, so the average velocity cannot be u. Hence pi/(2w) cannot be t0. Answer: Option B.

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Options:

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JEE Main 2027 (Class 12+)

JEE Main 2027 (Class 12)