Question

It is correct to say that impulse is equal toA) momentum.B) the change in momentum.C) the force multiplied by the distance the force acts.D) all of these.E) none of these.

Answer 1

B) the change in momentum.

Step-by-step explanation:

The impulse is defined as the product between the force applied on an object (F) and the duration of the collision (
`\Delta t`):

`J=F \Delta t` (1)

We can rewrite the force by using Newton's second law, as the product between mass (m) and acceleration (a):

`F=ma`

So, (1) becomes

`J=ma \Delta t`

Now we can also rewrite the acceleration as ratio between the change in velocity and change in time:
`a=(\Delta v)/(\Delta t)`. If we substitute into the previous equation, we find

`J=m(\Delta v)/(\Delta t)\Delta t=m\Delta v`

And the quantity
`m\Delta v` is equivalent to the change in momentum,
`\Delta p`.