A body of mass m accelerates uniformly from rest to v1 in...

A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$. The instantaneous power delivered to the body as a function of time $t$ is (a) $\frac{m v_{1} t}{t_{1}}$ (b) $\frac{m v_{1}^{2} l}{t_{1}^{2}}$ (c) $\frac{m v_{1} t^{2}}{t_{1}}$ (d) $\frac{m v_{1}^{2} t}{t_{1}}$

A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$. The instantaneous power delivered to the body as a function of time $t$ is
(a) $\frac{m v_{1} t}{t_{1}}$
(b) $\frac{m v_{1}^{2} l}{t_{1}^{2}}$
(c) $\frac{m v_{1} t^{2}}{t_{1}}$
(d) $\frac{m v_{1}^{2} t}{t_{1}}$

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Key Concepts

Uniform Acceleration

Uniform acceleration refers to a constant rate of change of velocity over time. This concept allows one to use simple kinematic equations to relate velocity, time, and displacement, which is essential when analyzing how a body's speed changes from rest under a constant force.

Instantaneous Power

Instantaneous power is the rate at which work is done at a specific moment in time. It is calculated as the product of the force acting on a body and its instantaneous velocity. This concept is key to understanding energy transfer in systems where velocity is changing with time.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle provides the connection between force, mass, and acceleration, enabling the calculation of forces required to produce a given motion, and consequently, the power delivered to the object.

Work-Energy Principle

The work-energy principle links the work done on an object to its change in kinetic energy. In contexts where an object accelerates uniformly from rest, it serves as an alternative method to derive expressions for quantities like velocity and power, reinforcing the relationship between force, displacement, and energy change.

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