content(warnings): Add W6-W7, X2-X3, N4 — energy misconceptions + cross-refs

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2026-05-04 23:36:54 -05:00
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@@ -36,6 +36,8 @@ In particular, if the object is released from rest, then
v(t)=v_T\left(1-e^{-bt/m}\right).
\]}
\nt{The linear drag model $F_D=bv$ is valid for low-Reynolds-number flow (small objects, slow speeds, viscous fluids). For most everyday situations (baseballs, skydivers, cars at highway speed), drag is approximately quadratic: $F_D=\tfrac12 C\rho A v^2$, where $C$ is the drag coefficient, $\rho$ is the fluid density, and $A$ is the cross-sectional area. The AP exam typically uses the linear model for analytical tractability, but recognizes the quadratic model qualitatively.}
\pf{Short derivation of the velocity function}{Start with Newton's second law for vertical fall in the downward-positive direction:
\[
m\frac{dv}{dt}=mg-bv.