A body of mass m is accelerated uniformly from rest to a...

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $t$. The instantaneous power delivered to the body as a function of time is given by (A) $\frac{m v^{2}}{t^{2}} t^{2}$ (B) $\frac{m v^{2}}{t^{2}} t$ $[2005]$ (C) $\frac{1}{2} \frac{m v^{2}}{t^{2}} t^{2}$ (D) $\frac{1}{2} \frac{m v^{2}}{t^{2}} t$

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $t$. The instantaneous power delivered to the body as a function of time is given by
(A) $\frac{m v^{2}}{t^{2}} t^{2}$
(B) $\frac{m v^{2}}{t^{2}} t$
$[2005]$
(C) $\frac{1}{2} \frac{m v^{2}}{t^{2}} t^{2}$
(D) $\frac{1}{2} \frac{m v^{2}}{t^{2}} t$

Key Concepts

Newton's Second Law

Newton's Second Law states that the force acting on an object is equal to the mass of the object times its acceleration. This principle is critical when analyzing systems with uniform acceleration because it allows one to determine the force required to accelerate an object, which then plays a central role in computations of work and power.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They allow one to relate displacement, velocity, acceleration, and time. In these kinds of problems, these equations are used to find the instantaneous velocity at any time, forming the foundation for further calculations such as determining instantaneous power.

Uniform Acceleration

Uniform acceleration refers to a constant rate of change of velocity over time. In such scenarios, an object starting from rest will have its velocity increase linearly with time. This concept is fundamental in kinematics and provides the basis for calculating other physical quantities, such as displacement and instantaneous velocity.

Instantaneous Power

Instantaneous power is defined as the rate at which work is done at a specific moment in time. It is calculated as the product of the instantaneous force applied to an object and the object's instantaneous velocity. In problems involving uniformly accelerated motion, power becomes a time-dependent function because the velocity is increasing linearly with time.

Please give Ace some feedback