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COMEDK202510 May 2025Morning ShiftPhysicsMotion in One DimensionActual

A particle starts from rest and moves along the x -axis with a velocity that varies as v = 100+4 x ~ms ⁻¹ . The acceleration of the particle is:

Options

  1. A2 m s⁻²
  2. B5 m s⁻²
  3. C25 ~ms ⁻²
  4. D4 m s⁻²

Correct answer

A. 2 m s⁻²

Step-by-step solution

Given the velocity v = 100 + 4x . The acceleration a of a particle moving in one dimension is given by a = v dv dx . Differentiating v = (100 + 4x)^ 1/2 with respect to x : dv dx = 1 2 (100 + 4x)^ -1/2 4 = 2 100 + 4x . Substituting v and dv dx into the expression for acceleration: a = 100 + 4x 2 100 + 4x . a = 2 ms ⁻² . Answer: 2 m s⁻²

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