When you calculate momentum e.g
An object moving at 10 m/s that has a mass of 5kg. This object will have a momentum of 50 kg*m/s.
What I don't understand is, what does the 50 kg*m/s mean? Does it mean the stopping power it would take to bring an object to rest? If so, in this case it would be 50 Newtons?
In a system of masses interacting with each other, If there is no external force, then the sum of their momentums is a constant over time.
This means that you can have something similar to what you where thinking about bringing an object to rest.
Imagine you have to masses that crash into each other with a completely inelastic collision (one where the two masses end stuck together). The initial momentum would be the sum $$\mathbf{p}_1+\mathbf{p}_2=m_1\mathbf{v}_1+m_2\mathbf{v}_2$$ If we call $\mathbf{v}$ the final velocity of the union of both particles we have that the final momentum is $$\mathbf{p}=(m_1+m_2)\mathbf{v}$$ Taking into account that the total momentum is a constant over time we have that in general $$\mathbf{p}=\mathbf{p}_1+\mathbf{p}_2$$
If you ask, what is the momentum that $m_2$ needs to have so that it stops $m_1$, we have to set $\mathbf{v}=0$ (stopped) and we have that: $$\mathbf{p}=\mathbf{0}$$ $$\mathbf{p}_2=-\mathbf{p}_1$$ That is, $m_2$ has to have the same momentum but in the opposite direction.
So answering your question, if a mass has a momentum of $50\;\mathrm{kg\cdot m/s}$ then to stop it you need another mass with the same momentum in the opposite direction. Maybe one mass of $1$ kg and going at $50$ m/s, or one mass of $50$ kg going at $1$ m/s, etc...
Force is the time derivative of the momentum.
If $50N$ force is affecting a body $1s$ long, then it changes its momentum with $50 \frac{kg m}{s}$. If it had exactly this momentum, then its speed will be zero (in our reference frame).
