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A body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies :
Explanation
When a constant force acts on a body of mass 'm' initially at rest, it produces a constant acceleration 'a' according to Newton's Second Law (F = ma). The velocity 'v' of the body at any time 't' is given by the equation of motion v = u + at. Since the body starts from rest (u = 0), the velocity is v = at. The kinetic energy (K) is defined as K = 1/2 m v^2. Substituting the expression for velocity, we get K = 1/2 m (at)^2 = 1/2 m a^2 t^2. The rate of change of kinetic energy (dK/dt) represents the power delivered to the body. Differentiating K with respect to time gives dK/dt = m a^2 t. Since mass and acceleration are constant, the rate of change of kinetic energy is directly proportional to time (t). Thus, it varies linearly with time.
Sources
- [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > Ever heard of ... > p. 67