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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion

A particle starts its motion at t = 0 and its position is given by the equation x = 5 (20 t + /3) , where x is in centimetre and t is in second. Find the time at which the particle first attains maximum speed.

Options

  1. A120 s
  2. B15 s
  3. C60 s
  4. D30 s

Correct answer

D. 30 s

Step-by-step solution

Given the position of the particle: x = 5 (20 t + /3) The velocity of the particle is the rate of change of position: v = dx dt = 100 (20 t + /3) The speed of the particle is maximum when it passes through the mean position ( x = 0 ), which corresponds to |v| being maximum, or | (20 t + /3)| = 1 . This condition is satisfied when: 20 t + 3 = n For the first time after t = 0 , we set n = 1 : 20 t + 3 = 20 t = - 3 = 2 3 t = 2 60 = 30 s

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