A cyclist’s power output (in watts) is sketched for the interval seconds
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A cyclist’s power output P(t) (in watts) is sketched for the interval 0≤t≤30 seconds. The curve lies entirely above the t–axis from t=0 to t=12, dips below the axis from t=12 to t=22, and then rises back above the axis from t=22 to t=30. The shaded region above the axis appears noticeably larger in total area than the shaded region below the axis, but no numerical scales are provided.
(a) Explain what the sign of P(t) indicates about how the cyclist’s kinetic energy is changing at any given time.
(b) Without performing numerical calculations, determine whether the cyclist’s kinetic energy at t=30 is greater than, less than, or equal to her kinetic energy at t=0. Support your conclusion by interpreting the relative sizes of the shaded regions.
(c) The cyclist claims that a brief period of negative power output cannot completely negate the gains from a longer period of positive power output. Evaluate the validity of this claim using the graphical information provided.