A particle of mass m is initially at rest at the origin. It is acted upon by a time-dependent force given by F = F₀ ( t) i + F₀ ( t) j . The power developed by this force as a function of time t is:

Step-by-step solution

Given force F = F₀ ( t) i + F₀ ( t) j . The acceleration of the particle is: a = F m = F₀ m ( t) i + F₀ m ( t) j Since the particle starts from rest, its velocity v at time t is obtained by integrating the acceleration: v = ₀^ t a dt v = ₀^ t ( F₀ m ( t) i + F₀ m ( t) j ) dt v = [ F₀ m ( t) ]₀^ t i + [ - F₀ m ( t) ]₀^ t j v = F₀ m ( t) i + F₀ m (1 - ( t)) j The power developed by the force is the dot product of force and velocity: P = F v P = ( F₀ ( t) ) ( F₀ m ( t) ) + ( F₀ ( t) ) ( F₀ m (1 - ( t)) ) P = F₀² m [ (