When a force acts on an object that moves, it does work. The work done by a constant force is defined as the product of the magnitude of the force, the magnitude of the displacement, and the cosine of the angle between them, so that \(W = Fd\cos\theta\). Work is a scalar quantity measured in joules, where one joule equals one newton-meter. When the force is parallel to the displacement, \(\cos\theta = 1\) and the work is maximum, while when the force is perpendicular to the motion, no work is done at all. Power measures how quickly work is done or how rapidly energy is transferred.
Average power is the work done divided by the time taken, \(P = W/t\), and for a constant force applied to a moving object, it can equally be written as \(P = Fv\). The SI unit of power is the watt, with one watt equal to one joule per second. A higher power rating means the same amount of work is accomplished in less time, which is why a powerful engine can accelerate a car faster than a weak one.
The concept of energy is closely tied to work. An object in motion possesses kinetic energy, given by \(KE = \tfrac{1}{2}mv^2\), which depends on the square of the speed and is the same whether the motion is to the left or to the right. An object raised to a height in a gravitational field has gravitational potential energy, \(PE = mgh\), where \(h\) is the height above a chosen reference level. In the absence of non-conservative forces such as friction or air resistance, the total mechanical energy, the sum of kinetic and potential energy, remains constant: this is the principle of conservation of mechanical energy. Energy can change form between kinetic and potential, but the total stays the same.