I'm studying physics right now, I can say I agree with everything you said.
One thing I'd like to expand on to those who don't know how greater energy means greater speed.
The kinetic energy equation is 1/2massvelocity^2=KE
Since the KE increases from the momentum transfer, and mass of the object stays constant, the only thing that can change is velocity, where it has to go up.
ex: KE=2, m=1
2=1/21v^2, v=2
Now if some momentum were transferred, and the kinetic energy increased to KE=8,
8=1/21velocity^2, velocity=4, since the mass can't change
One thing I'd like to expand on to those who don't know how greater energy means greater speed.
The kinetic energy equation is 1/2massvelocity^2=KE
Since the KE increases from the momentum transfer, and mass of the object stays constant, the only thing that can change is velocity, where it has to go up.
ex: KE=2, m=1 2=1/21v^2, v=2
Now if some momentum were transferred, and the kinetic energy increased to KE=8,
8=1/21velocity^2, velocity=4, since the mass can't change