Sir Isaac Newton did not originally state his famous 2^nd law in the form that we have learned. Instead, he stated it in terms of the linear momentum, p.  Let’s get some idea of how this can be done.

First, starting from Newton’s 2^nd law in the form we stated it, and using the definition of average velocity (we need the calculus to be more precise with this, but we’ll just use average values here), we get the following:

But since p = m v, we have that

This is Newton’s original form of his 2^nd law.  Note that it says that the  change in momentum of an object (that is, a change in the object’s motion) is due to a net external force acting on that object – the same idea that we had before, but just restated in different terms.

From this form of the 2^nd law we immediately get an expression for another important quantity.  The impulse, J of a force on an object is defined to be

J = F_netDt .

From the restated form of Newton’s 2^nd law above, we see that the impulse is also given by

Note that the impulse is a vector quantity, which means that we will have to be careful of direction!