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KVPY2011PhysicsMotion in One Dimension

A body of 0.5 ~kg moves along the positive x -axis under the influence of a varying force F (in Newtons) as shown below. If the speed of the object at x=4 ~m in 3.16 ~ms ⁻¹ then its speed at x=8 ~m is

Options

  1. A3.16 ~ms ⁻¹
  2. B9.3 ~ms ⁻¹
  3. C8 ~ms ⁻¹
  4. D6.8 ~ms ⁻¹

Correct answer

D. 6.8 ~ms ⁻¹

Step-by-step solution

According to work-energy principle array l W _ C + W _ nc + W _ ext = KE ₄⁸ Fdx = 1 2 mv _ f ²- 1 2 mv _ i ² array 1 2 3 8- 1 2 1.5 4= 1 2 1 2 [v_ f ²-(3.16)² ]v_ f =6.8 ~m / s

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