A particle moving along X -axis has acceleration f , at time t given by f = f 0 1 - t T , where f 0 and T are constants. The particle at t = 0 and the instant when f = 0 , the particle's velocity v x is

Question

A particle moving along X -axis has acceleration f , at time t given by f = f 0 1 - t T , where f 0 and T are constants. The particle at t = 0 and the instant when f = 0 , the particle's velocity v x is, f 0 T, 1 2 f 0 T 2, f 0 T 2, 1 2 f 0 T

MARKS App · Accepted Answer

Acceleration f = d v d t = f 0 1 + t T or d v = f 0 1 - t T · d t . . . . . . . . . E q ( i ) Integrating Eq. ( i ) on both sides, we get v = f 0 t - f 0 T · t 2 2 + C After applying boundary conditions v = 0 at t = 0 We get, C = 0 ⇒ v = f 0 t - f 0 T · t 2 2 . . . . . . . . . . E q ( i i ) As f = f 0 1 - t T When f 0 = 0 , t = T Substituting t = T in Eq. ( ii ) , then velocity v x = f 0 T - f 0 T · T 2 2 = 1 2 f 0 T

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