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MHT CET202519 Apr 2025Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Force is applied to a body of mass 3 kg at rest on a frictionless horizontal surface as shown in the force against time (F - t) graph. The speed of the body after 1 s is

Options

  1. A8 ~m / s
  2. B6 ~m / s
  3. C4 ~m / s
  4. D2 ~m / s

Correct answer

D. 2 ~m / s

Step-by-step solution

The impulse-momentum theorem states that the change in momentum equals the area under the force-time graph: J = m(v - u) . From t=0 to t=1 s, the graph consists of two rectangles. The first rectangle (0 to 0.5 s) has area (8)(0.5) = 4 , and the second (0.5 to 1 s) has area (4)(0.5) = 2 , making the total impulse J = 6 Ns . With m = 3 kg and initial velocity u = 0 , we have 6 = 3v , so v = 2 m/s . The speed after 1 second is 2 m/s .

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