Why does kinetic energy depend on velocity squared while momentum depends on velocity?

[larsa]

First of all i am not a native speaker so i apologize for my english.
Kinetic energy is velocity squared multiplied by mass, whereas momentum is just velocity multiplied by mass.
I have read that the reason for this is because conservation of kinetic energy is related to symmetry of the motion in time and conservation of momentum is related to the symmetry in the motion of space.
Could someone give an intuitive or not explanation about this?

Thank you in advance

 

[DrClaude]

Do a search on Noether's theorem on PF. You will find many thread discussing the subject.

 

[larsa]

Do a search on Noether's theorem on PF. You will find many thread discussing the subject.

What i don't understand is how velocity squared is related to symmetry. I have not found any explanation about this. I will look again, thanks

 

[PeroK]

First of all i am not a native speaker so i apologize for my english.
Kinetic energy is velocity squared multiplied by mass, whereas momentum is just velocity multiplied by mass.
I have read that the reason for this is because conservation of kinetic energy is related to symmetry of the motion in time and conservation of momentum is related to the symmetry in the motion of space.
Could someone give an intuitive or not explanation about this?

Thank you in advance

There is no need to apologise for your near perfect English!