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BITSAT2017PhysicsMotion in One DimensionActual

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

Options

  1. Af 0 T
  2. B1 2 f 0 T 2
  3. Cf 0 T 2
  4. D1 2 f 0 T

Correct answer

D. 1 2 f 0 T

Step-by-step solution

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

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