1. Impulse

2. Force & Momentum
Recall that Newton’s 2nd Law relates force (f), mass (m), and acceleration (a) in the following way:

3. Force & Momentum Also recall that acceleration is defined as:
When substitute this into Newton’s 2nd Law we get

4. Force & Momentum
Since (m∆v) is the change in momentum, we can now see that the force (F) is equal to the change in momentum divided by time (t).
If we multiply both sides of the equation by the time (t), we get

5. Impulse Now we are left with the equation
On the right, we have the change in momentum. On the left, we have the product of force (F) times time (t), which we will call the impulse.

6. Impulse
We will represent the impulse acting on an object with the symbol (J).
Impulse can be calculated using either of the two equations shown here:
J = Ft
J = mΔv
If you are asked to calculate impulse itself, you must decide which equation is appropriate by looking at what information you are given.

7. Impulse Probably the most useful way to express this equation is
Keep in mind whenever an object’s velocity or momentum is to the right, it is positive (+), and when they are to the left, they are negative (-).

8. Impulse
Example 1: A 75 N force acts on an object for 3 s. Determine the impulse given to the object.

9. Impulse
Example 2: A 60 kg object speeds up from m/s to 35 m/s. How much impulse was necessary to cause this change in speed?

10. Impulse
Example 3: How long must a 10 N force be exerted for in order to change the speed of a 20 kg object from 11 m/s to 18 m/s?

11. Impulse
Example 3:

12. Impulse
Example 4: An 18 kg object is initially moving at 25 m/s. If a 9 N force is applied to the object for 10 s, what will its final velocity be?

13. Impulse
Example 4: