# Calculating Power with Constant Force: Deriving P=(F^2t)/m from Newton's 2nd Law

• dch1runs
In summary, to find the power delivered by a constant force on a particle of mass m moving from rest at t=0, use the definition of power and the scalar product to get P=Fv, then use Newton's 2nd law and the kinematic motion equations to find v as a function of F, t, and m. Substituting this into P=Fv will give the final equation P=(F^2t)/m.
dch1runs
A particle of mass m moves from rest at t=0 under the influence of a single constant force F. Show that the power delivered by the force at any time t is P=(F^2t)/m.
I tried using the definition of power and the definition of the scalar product, which probably is not the way to go about doing this. I feel like there's an obvious step or equation that I'm missing here.

P=F.v=|F||v|cos0=Fv
mv(dv/dt)=P

using P =Fv is good. Now you need to find v as a function of F, T, and m using Newton's 2nd law (and the kinematic motion equations if it doesn't jump right out at you).

## 1. What is power and constant force?

Power and constant force refer to the ability to do work or exert a certain amount of force continuously over time. In scientific terms, power is the rate at which work is done, while constant force is a force that remains unchanged in magnitude and direction.

## 2. How is power and constant force measured?

Power is measured in watts (W), which is equivalent to one joule per second (J/s). Constant force is measured in newtons (N), the standard unit of force in the International System of Units (SI).

## 3. What are some examples of power and constant force in everyday life?

Examples of power and constant force in everyday life include pushing a heavy object, lifting weights, riding a bike, and using a stationary machine like a treadmill or rowing machine. In these scenarios, a person must exert a continuous force to perform the desired action.

## 4. How are power and constant force related?

Power and constant force are directly related, as the amount of power produced is directly dependent on the amount of constant force exerted. The greater the force, the more power is produced.

## 5. Can power and constant force be increased or decreased?

Yes, power and constant force can be increased or decreased depending on the circumstances. For example, a person can increase their power by increasing the amount of force they exert or decreasing the time it takes to do the work. Similarly, constant force can be increased by exerting a greater amount of force or decreased by reducing the magnitude of the force.

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