sa0601

If you guys don't mind, I had one more question that I'm probably overthinking as well. The answer to this question is D and I plugged in my own numbers to get that answer. However, I don't understand the concept. Why is it that dividing the velocity by two means you have to divide the Kinetic Energy by 4? I bolded "divide" because that's what "decrease by a factor" means to do.

The kinetic energy E of an object is given by E = .5*m*v^2
where m is the object's mass and v is the velocity of the
object. If the velocity of an object decreases by a factor
of 2 what will happen its kinetic energy?

A. Kinetic energy will increase by a factor of 2.
B. Kinetic energy will increase by a factor of 4.
C. Kinetic energy will decrease by a factor of 2.
D. Kinetic energy will decrease by a factor of 4.

ChipB

same principle as the earlier problem - the kinetic energy of an object is proportional to the velocity of the object squared. An object moving at 10 m/s has four times the KE of an object moving at half that speed.
One way to see this is to calculate the ratio of the two energies:

KE_1/K_2 = (0.5 m v_1^2)/(0.5 m v_2^2) = (v_1/v_2)^2

So if v_2 = one half v_1, then KE_2 = one quarter KE_1