A single constant force 𝐅 acts on a particle of mass m . The particle starts at rest at t=0 . (a

step 1 Here in this given problem in the first part of the problem for the particle its initial velocit

A single constant force 𝐅 acts on a particle of mass m . The...

A single constant force $\mathbf{F}$ acts on a particle of mass $m .$ The particle starts at rest at $t=0 .$ (a) Show that the instantaneous power delivered by the force at any time $t$ is $\mathscr{P}=\left(F^{2} / m\right) t$ (b) If $F=20.0 \mathrm{N}$ and $m=5.00 \mathrm{kg},$ what is the power delivered at $t=3.00 \mathrm{s} ?$

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Key Concepts

Newton's Second Law

This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). It is the fundamental principle that explains how the motion of an object changes when a force is applied and is essential for relating force, mass, and acceleration in problems of dynamics.

Kinematics of Constant Acceleration

When a constant net force is applied to a mass, the object experiences constant acceleration. The kinematic equations for constant acceleration allow us to determine properties such as velocity and displacement as functions of time, which are crucial for analyzing the motion and calculating quantities like the instantaneous velocity required in power calculations.

Instantaneous Power

Instantaneous power is defined as the rate at which work is done at a particular moment and is mathematically expressed as the dot product of force and velocity (P = F · v). This concept is important in dynamics because it provides a measure of how quickly energy is being transferred or transformed in a system, and it directly links the applied force to the instantaneous kinetic state of the moving object.

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