A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v=α √x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x=0 to x=d, will be :

Solution

Physics sir · 3 steps

Do not chase the force here; the work-energy theorem says total work is just the change in kinetic energy.

1. Work-energy theorem. The total work done by all forces on a particle equals its change in kinetic energy, W = K_f - Kᵢ. So you only need the speed at the start and at the end.
2. Speeds at the ends. At x = 0, v = α√0 = 0, so the particle starts from rest. At x = d, v = α√d, so v² = α² d.

   W = 1/2m(α√d)² - 0 = (mα² d)/2

3. So. The total work done is (mα² d)/2, which is option (c).

The idea to keep. When a question asks for the work done by all forces, go straight to the change in kinetic energy. You do not need the force itself, only the speeds at the two ends.

Answer from the NTA final answer key. Solution by PrepWiser.