Mechanics

# Power and speed

Relationship between power and speed

Let us consider a particular case in which a constant force acts on a body during a time interval Δt, where the displacement is , as shown in the figure above. The average power of the force over this time interval is:

In the formula, vm is the average velocity module. If we used differential calculus, we could show that the formula can be extended to instantaneous values. The figure below shows us the instant when the force forms an angle Ψ with the velocity, in this case the power is given by:

**P = F . v. cosӨ**

In the particular case where the force is parallel to the velocity, that is, Ө = 0° and cos 0° = 1, we have that the calculated power is:

**P = F . v**