Basic question about kinetic energy and momentum

grayb
Hi, I'm learning about momentum and kinetic energy and I wanted to know if the following relationships are true. I think they are true, but I am not sure:

1. If kinetic energy goes down and mass stays constant, momentum goes down
2. If kinetic energy stays constant and mass goes down, momentum goes down
3. If kinetic energy goes up and mass stays constant, then momentum goes up
4. If kinetic energy is constant and mass goes up, momentum goes up

Are they true? Thank you.

Staff Emeritus
KE = p$^{2}$/(2m)
KE $\propto$ p$^{2}$
m $\propto$ p$^{2}$