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AP Physics C: Mechanics
4.2 Change in Momentum and Impulse
IntermediateMCQGraphicalMathematical19.7k
A 2D line graph of force F in newtons versus time t in seconds. The horizontal axis is labeled t (s) with tick marks at 0, 1.0, 2.0, and 3.0. The vertical axis is labeled F (N) with tick marks at 0, 6, 12, and 18. A curve starts at the origin (0, 0) and curves upward quadratically (concave up) to a peak point at (3.0, 18). At t = 3.0 s, a vertical dashed line drops down from (3.0, 18) to (3.0, 0) on the horizontal axis. A dashed horizontal reference line extends from (0, 18) to (3.0, 18). No other labels, lines, text, or axes appear.
Force versus time graph for the cart during the interaction.
A cart of mass \(m = 2.0 \text{ kg}\) moves along a straight horizontal track. A sensor measures the net force \(F(t)\) applied to the cart during an interaction, as shown in the force-versus-time graph. The force increases quadratically from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\) according to \(F(t) = c t^2\), reaching a maximum value of \(18 \text{ N}\) at \(t = 3.0 \text{ s}\), after which the force drops instantly to zero. What is the average force \(F_{\text{avg}}\) exerted on the cart during the time interval from \(t = 0 \text{ s}\) to \(t = 3.0 \text{ s}\)?

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