# Work-Kinetic Energy principle

If net force works on an object, the object experiences acceleration (the object experiences displacement). When the object experiences acceleration, the speed of the object changes. In other words, the work done by the net force is related to the object’s initial and final speed.

The work done on an object by constant net force is:

W_{net} = ΣF s

Newton’s second law states that if there is a net force working on an object, the object experiences acceleration.

W_{net }= (m a) s

If the net force is constant, the acceleration experienced by the object is constant as well. Therefore, we can substitute a non-uniform linear motion equation for acceleration (a) and displacement (s).

Incorporate the non-uniform linear motion equation into the work equation:

Description: EK_{t }= final kinetic energy, EK_{o} = initial kinetic energy, m = mass, v_{t }= final speed, v_{o} = initial speed

This equation constitutes the work-kinetic energy theorem. The work-kinetic energy theorem informs us that net work or the work done by the net force on an object is equal to the change in the object’s kinetic energy. It also informs us that an object’s kinetic energy is equal to the net work required to accelerates the object from a stationary state to moving at a given speed, and vice versa.

Example question 5: Work-kinetic energy theorem

A car with a mass of 1000 kg moves from a stationary state. In an instant, the speed increases into 10 m/s. How much is the net work done by the car’s engines?

Solution :

Known: m = 1000 kg, v_{o} = initial speed = 0 m/s (at first, the car is at rest), v_{t} = final speed = 10 m/s

Wanted : The net work

W_{net} = 1⁄2 m (v_{t}^{2} – v_{o}^{2})

W_{net }= 1⁄2 (1000)(10^{2} – 0^{2}) = (500)(100 – 0) = (500)(100) = 50,000 Joule