A car traveling at 30 m/s has a certain kinetic energy. If it speeds up to 60 m/s, what happens to its kinetic energy?
AIt doubles
BIt triples
CIt quadruples
DIt increases by 30 m/s worth
KE = ½mv². When speed doubles (30 → 60), speed² quadruples (900 → 3600), so KE quadruples. This is the critical difference between KE and momentum: momentum doubles when speed doubles, but KE quadruples.
Question 2 True / False
Kinetic energy is a vector quantity because a moving object has a direction of motion.
TTrue
FFalse
Answer: False
KE = ½mv² is entirely a scalar. The speed v in the formula is the magnitude of velocity, not velocity itself. Two objects moving in opposite directions at the same speed have identical kinetic energies. Direction matters for momentum (mv), not kinetic energy.
Question 3 Short Answer
An object initially at rest has work W done on it by a net force. Explain why the object's resulting kinetic energy equals W.
Think about your answer, then reveal below.
Model answer: By the work-energy theorem, the net work done on an object equals its change in kinetic energy. Starting from rest (KE = 0), all the work goes into building kinetic energy: W = ΔKE = ½mv² - 0 = ½mv².
This is the work-energy theorem in action. Work and kinetic energy are both measured in joules because work is the mechanism by which kinetic energy changes. Deriving KE from this relationship (rather than memorizing the formula) builds deep understanding of why the ½ and the v² appear.