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Separation of variables tutorial

Key concepts: Differential equations Separation of variables Speed and distance Question 1: "A car of mass, m, is moving at a speed v0 is put in neutral and gradually gets slowed down by an air resistance force that is some number times the speed of the car. Determine its speed as a function of time." To figure out this question, we need:

  1. A sketch of the situation we are trying to describe

  2. A differential equation that tells us how the change in speed depends on time and other variables

  3. A strategy for solving this equation

  4. A way of checking that the result makes sense