Up to now we have been using Newton's laws of motion to predict the future of dynamical systems. Sir Isaac had some other ideas about dynamics which have proven to be useful. In this section of the program we will explore a few of them.
Work is defined as force multiplied by displacement.
Remember in the general case, force and displacement are vectors. Work is a scalar quantity so the multiplication operation we are talking about here is the dot product as discussed back in Vector Arithmetic . Consider a free particle of mass, m, at rest in our reference frame. Now let's consider a tiny time interval D t short enough so that the force is nearly constant during the interval. D t where v 0 is the initial velocity and v is the final velocity.