Question

select the option that shows that when an impulse produced by a 12 - n force acts over 2.0 s on an ice pack initially at rest on an air table, the momentum is 24 kg·m/s.
δmv = f²/3t=(12² n)/(3·2.0 s)=24 n·s = 24 kg·m/s.
δmv = t/(1/f)=(2.0 s)/(1/(12 n))=24 n·s = 24 kg·m/s.
δmv = ft=(12 n)(2.0 s)=24 n·s = 24 kg·m/s.

Explanation:

Step1: Recall impulse - momentum theorem

The impulse - momentum theorem states that the change in momentum $\Delta mv$ is equal to the impulse $J$, and impulse $J = Ft$, where $F$ is the force and $t$ is the time interval.

Step2: Substitute given values

Given $F = 12\ N$ and $t=2.0\ s$. Then $\Delta mv=Ft=(12\ N)\times(2.0\ s)=24\ N\cdot s$. Since $1\ N = 1\ kg\cdot m/s^{2}$, $24\ N\cdot s = 24\ kg\cdot m/s$.

Answer:

$\Delta mv = Ft=(12\ N)(2.0\ s)=24\ N\cdot s = 24\ kg\cdot m/s$ (the third option)