Power and Motion

When a constant force F is exerted on an object to maintain a constant speed v the rate of work done P is given by

P = Fvsince power = work done/timesince power = (force × distance)/timeand distance/time = speedso P = Fv, where P is in watts, F is in newtons and v is in ms^-1.When a vehicle moves at a constant speed the resultant force on it is zero, so the driving force is equal to the total resistive forces (drag and friction). All of the output power is then used to do work against these resistive forces.For example, a car travelling at a steady 30 ms^-1 against resistive forces of 600 N needs a driving force of 600 N, so the power output of its engine is

P = 600 × 30 = 18 000 W = 18 kWDrag increases with speed, so a vehicle reaches its top speed when all of its maximum power output is needed to overcome the resistive forces. At top speed v = P_max/F, where F is the total resistive force.P = Fv also gives the power at any instant for an accelerating object, using the force and the speed at that moment.