# How can a large force result in small power?

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Power is defined as the ratio of work per time, or

1. Power = Work/Time

Work is defined as Force times Displacement, or

2. Work = Force * Displacement

so therefore

3. Power = (Force * Displacement) / Time

but

4. Displacement / Time = Velocity

so

5. Power = Force * Velocity

So if an object has a very small velocity (not moving very far over time, even though a large force may be applied to it, the Power will remain small.  Consider a mechanic starting to push a disabled car from rest -- the car has initially no velocity, then a small velocity, even though a large force is applied, resulting in a small amount of power;  this is because the force is going into overcoming the inertia (mass) of the car, not in increasing its velocity. Consider the reverse case of the car at highway speed (large velocity.)  Even if the force is small, power will be large, as it is a function of velocity.  Stepping on the gas, or "speeding up" the car, is applying a force which will increase velocity and increase power.