Question

If all else is constant, which would cause the greatest increase in kinetic energy of a moving object?

Mass and velocity are each reduced by one-half.
Mass is reduced by one-half, and velocity is doubled.
Mass is doubled, and velocity is reduced by one-half.
Mass and velocity are each doubled.

Answer 1

Kinetic energy KE = 1/2 m v^2, so KE ∝ m v^2.

For each change the factor by which KE changes:
- Both halved: KE → (1/2)*(1/2)^2 = 1/8 of original.
- Mass 1/2, velocity ×2: KE → (1/2)*(2)^2 = 2× original.
- Mass ×2, velocity 1/2: KE → (2)*(1/2)^2 = 1/2 of original.
- Both doubled: KE → (2)*(2)^2 = 8× original.

Greatest increase: mass and velocity each doubled.