Change in Momentum and Impulse
Push a cart hard for a moment, or push it gently for a while. Both can deliver the same total kick. That total is the impulse, $\vec J = \vec F_{\text{avg}}\,\Delta t$, and it equals the change in the cart's momentum, $\Delta \vec p = \vec p_f - \vec p_i$. Impulse depends on how long the force acts, not just how strong it is. On a force-versus-time graph, it is the area under the curve, not the peak height.
Three traps lie ahead. The first treats force and impulse as the same thing, so a big short jolt looks like a bigger kick than a small steady push. It isn't. The second misreads the F-versus-t graph, grabbing the peak or the slope when the answer is the area. The third is the bounce trap: $|p_f| - |p_i| = 0$ does not mean $\Delta \vec p = 0$. The lesson walks all three.
The work
3 ways in · any order
Lesson
Change in Momentum and Impulse
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Impulse is force applied over time, and it equals the change in a system's momentum. The lesson builds up $\vec J = \vec F_{\text{avg}}\,\Delta t = \Delta \vec p$, explains why the area under an F-versus-t graph is impulse, and works through the three traps. It ends with a ten-scenario applet that drills each one directly.
Diagnostic
10-item topic check
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Ten items covering: ranking impulse by force alone, mixing up slope and area when reading force-time and momentum-time graphs, sign errors, and treating $\Delta \vec p$ as a scalar instead of a vector. Each distractor maps to a specific misconception so the targeted-practice round can drill exactly what you missed.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.