Answer:
The average force times the time of interaction equals the change in momentum
Explanation:
The impulse-momentum theorem states that impulse (equal to the average force times the time of interaction) is equal to the change in momentum:
[tex]I=F \Delta t = \Delta p[/tex]
where
I is the impulse
F is the average force
[tex]\Delta t[/tex] is the time of the interaction
[tex]\Delta p[/tex] is the change in momentum
We can demonstrate this theorem, by re-writing the force as mass (m) times acceleration (a):
[tex]F \Delta t = ma \Delta t[/tex]
The acceleration is equal to the change in velocity divided by the time interval:
[tex]ma \Delta t = m \frac{\Delta v}{\Delta t} \Delta t[/tex]
And by simplifying [tex]\Delta t[/tex], we get:
[tex]= m \Delta v = \Delta p[/tex]
which is equal to the change in momentum.
