Engine force from velocity graph · CAP 2015 #3
Physics · mechanics
Problem
The following graph represents the speed of a car as a function of time. We know that as the car speeds up there is a friction force with air that can be approximately considered to be proportional to the speed of the car. [Figure: Graph showing velocity vs time with car initially accelerating then reaching constant velocity] Which of the following graphs can be the force of the engine as a function of time? a) [Graph option a] b) [Graph option b] c) [Graph option c] d) [Graph option d] e) [Graph option e]Intuitive explanation
The key insight is recognizing that air resistance grows with speed, so the engine force must decrease over time to maintain the observed velocity curve. Initially, when the car is slow, air drag is small and the engine provides large net force for rapid acceleration. As speed increases, drag grows linearly with velocity, so the engine must do less work to keep acceleration decreasing—eventually reaching zero force when velocity plateaus and drag balances the engine's remaining thrust. Look for a graph showing the engine force starting high and declining toward a constant positive value.
Intuitive explanation
The key insight is recognizing that air resistance grows with speed, so the engine force must decrease over time to maintain the observed velocity curve. Initially, when the car is slow, air drag is small and the engine provides large net force for rapid acceleration. As speed increases, drag grows linearly with velocity, so the engine must do less work to keep acceleration decreasing—eventually reaching zero force when velocity plateaus and drag balances the engine's remaining thrust. Look for a graph showing the engine force starting high and declining toward a constant positive value.