Variable forces and motion with non-constant acceleration

What this note covers

1. From constant to variable acceleration
2. The chain-rule identity a = v dv/dx
3. Resistance proportional to velocity and terminal velocity
4. Resistance proportional to the square of velocity
5. Acceleration as a function of displacement: spring and bungee problems
6. Setting up and solving the ODE: a systematic method
7. Interpreting solutions and checking physical reasonableness

7 sections · 14 key terms & formulas · 6 common mistakes