# Impulse and Momentum

In our introductory lesson on momentum, we opened with this equation:

We now want to use this equation to define a new term: *Impulse. * Impulse is a force applied to an object over a period of time, and it changes the object's momentum. Let's do a
simple derivation to show what we are talking about.

Start with Newton's Second Law:

Recall that accleration can be expressed in terms of a change in velocity with respect to time, or

If we substitute this expression for acceleration into Newton's Second Law, then we get

But mDV can also be expressed as Dp, so making one more substitution,

We can now make one more adjustment by multiplying both sides by Dt to obtain the equation

This expression is called the Impulse-Momentum Theorem. It tells us two important things about Impulse. The first is
that we will define the expression FDt to be impulse. So **Impulse =
F****D****t**, or Impulse is the result of a force applied to an object for a period of time.

The second important thing is that this equation also tells us that **Impulse is a Change in Momentum**.
We look at the expression FDt=Dp, and we can read that as “When you apply a force to an object for some amount of time, you will cause a change in momentum of the object.” That is the
Impulse-Momentum Theorem.

When we talk about impulse, it is important to think about it in terms of how long a force is in contact with an object. For example, keeping a tennis racquet in contact with the ball longer for the same amount of force will cause a greater change in velocity in the ball. Why do you think your coach always tells you to follow through with the ball?

Often, it is useful to see what someone else has to say on the topic; Check out these lessons from "The Physics Classroom" (Glenbrook High School). Each contains some practice problems at the end of the lesson.

Momentum and Impulse Connection