A constant force, acting on a particle of mass m, will produce a constant acceleration a. Let us choose the x-axis to be in the common direction of F and a. What is the work done by this force on the particle in causing a displacement x? We have, for constant acceleration, the relations a = ( V - v ) / t and x = ½ ( V + v ) t. Here v is the particle's speed at t = 0 and V is its speed at time t. The the work done is W = F x = m a x = m ( ( V - v ) / t ) ( ½ ( V + v ) ) t = ½ m V² - ½ m v². We call one-half the product of the mass of a body and the square of its speed the kinetic energy of the body. If we represent kinetic energy by the symbol K, then K = ½ m v². We may then state the above equation in this way: The work done by the resultant force acting on a particle is equal to the change in the kinetic energy of the particle.
