# Galilean Invariance

1. ### joriarty

62
1. The problem statement, all variables and given/known data

Explain which of the following quantities are invariant in Newtonian mechanics.
• Position
• Distance between two points
• Velocity
• Acceleration
• Momentum
• Kinetic Energy
• Potential Energy (I presume gravitational)

2. Relevant equations

N/A

3. The attempt at a solution

I understand that a quantity such as displacement would be invariant if a transformation is applied and that the transformed frame of reference has the same form as the original frame of reference.

However I am unsure exactly how to tackle the problem. Take for example kinetic energy, $${E}_{k}=\frac{1}{2}mv^{2}$$. How would I then determine if this was invariant or not? Can I just invent a one-dimensional transformation such as $$v'=v+a\cdot t$$ (where a is acceleration, t is time), apply this to the kinetic energy equation, and check the form of the result?