PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
During a laboratory investigation, a student measures the translational kinetic energy of a low-friction cart as it moves along a straight track. The student observes that when the cart’s speed is doubled, its kinetic energy becomes four times larger.
Assume the cart’s mass remains constant throughout the experiment.
(a) Explain, without substituting numerical values, how the mathematical form of the relationship between translational kinetic energy and speed accounts for the observation that doubling the speed leads to a four-fold increase in kinetic energy.
(b) The student predicts that tripling the cart’s speed would cause its kinetic energy to increase by a factor of nine. Evaluate the validity of this prediction by providing an algebraic justification.