# Physical interpretation of Force=power/velocity

1. Oct 9, 2014

### Generic Turtle

I understand the derivation of the equation Force=power/velocity, but I'm not sure I quite understand the physical interpretation of this. If you had a constant force acting on a particle in a vacuum, then it would gain velocity and as it did so the power would have to go down for the force to be constant. Since the only transfer of energy is into kinetic energy as the particle is in a vacuum. If the power goes down this means the rate at which it gains kinetic energy decreases. This means its acceleration decreases but that doesn't make sense to me, why given a constant force is acceleration not constant. If you combine it with F=ma this implies that the mass of the particle has to increase for this to be the case. Am I intepreting all this correctly?

2. Oct 9, 2014

### Staff: Mentor

The physical interpretation is that to apply a constant force and hence a constant acceleration, you must increase the power as the speed increases.

When you look at force=power/velocity and conclude that as velocity increases power must decrease to keep force constant, you have it backwards - to keep the value constant as the denominator of a fraction increases, you have to increase the numerator as well.

3. Oct 9, 2014

### Generic Turtle

Oh dear I feel super dumb now :O

Thank you though :)

4. Oct 9, 2014

### NTW

When the force is constant, if the mass is constant too, the acceleration keeps a constant value, since F=ma...

An example of power, velocity and force with constant velocity/zero acceleration is in the case of a glider moving at constant velocity. The force of drag times velocity is the power of the glider; i.e. power=drag*airspeed... Of course, in this case, the energy of the glider comes from the variation of potential energy, as the glider loses altitude... Also, power=weight of the glider*vertical velocity... The drawing shows the forces and the speeds U,V, WW...