An object of mass M, initially at rest under the action of a...

An object of mass $M$, initially at rest under the action of a constant force $F$ attains a velocity $v$ in time $t$. Then the average power supplied to the mass is :
(a) $\mathrm{Fv}$
(b) $\frac{1}{2} F v$
(c) zero
(d) $\frac{m v^{2}}{2 t}$

Key Concepts

Work-Energy Theorem

This concept states that the work done by the forces acting on an object is equal to the change in its kinetic energy. It provides a bridge between the force applied and the resulting motion, showing how work translates into kinetic energy, which is particularly useful when an object accelerates from rest.

Average Power

Average power is defined as the total work done divided by the time interval over which the work is performed. It gives a measure of how quickly energy is transferred or transformed in a system, and is distinct from instantaneous power which is defined at a specific moment in time.

Kinematics of Constant Acceleration

Kinematics under constant acceleration deals with the equations that describe motion when acceleration is steady. This framework allows one to relate displacement, initial velocity, final velocity, acceleration, and time, which is essential in determining the work done and subsequently the average power in any uniformly accelerated motion.

Instantaneous vs. Average Power

This concept differentiates between the power at any given moment (instantaneous power, often calculated as the product of force and instantaneous velocity) and the overall power output over a period of time (average power). In scenarios of constant acceleration starting from rest, the average power calculation takes into account the gradual increase in velocity, leading to a value that is lower than the instantaneous power at the final velocity.

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