Question

Two identical masses are moving down a slope. One mass is traveling twice as fast as the other mass. how does the kinetic energy of one mass compare to the other?

Answer 1

The greater the speed of two identical masses, the greater the kinetic energy.  So, the mass that is traveling twice as fast as the other has much more kinetic energy.  The formula for kinetic energy is KE=m*v^2 (kinetic energy equals mass times velocity squared), and velocity is the same as speed in this case because it is squared.  So, the mass traveling twice as fast has 4 times the kinetic energy, because 2 squared=2*2=4.

Answer: The mass traveling twice as fast has four times the kinetic energy.

Answer 2

As you learned, kinetic energy is 1/2mv^2. Call the velocity of object 1 v. Then, object 2 travels at 2v. The kinetic energy is object 1 is then 1/2mv^2 and that of object 2 is 1/2m(2v)^2=4(1/2mv^2). Therefore, the kinetic energy os the faster object is  times that of the slower one.