What happens to Kinetic energy when the mass is doubled?

Question

What happens to kinetic energy when mass is doubled? When speed is doubled?

Answer 1

K = mv2/2

 

Double the mass to 2m

 

     K_2m = 2mv²/2 = 2K      It doubles the kinetic energy

 

Double the velocity to 2v:

 

     K_2v = m(2v)²/2 = 4mv²/2 = 4K       It quadruples the kinetic energy

Answer 2

Consider the formula for K.E. = ½mv²

 

a) what happens if you replace m by (2m) ?  

 

b)  what happens if you replace just v by (2v) and that parenthesized quantity is squared??

 

I trust that you will be able to create the answers, now.