But first, just a bit more review of integration.
Let's look a very simple situation in which the wind pushes an iceboat across a frozen lake. The wind is constant in size and pushes exactly in the direction of the boat's motion.
But real life is rarely so simple. You need to know how to deal with more complicated situations. Let's take a look at several ...
The force is constant, but not exactly in the direction of motion. This isn't so bad; you just need to use the dot product to find the component of the force in the direction of motion.
But what if the direction of the force, or the object, CHANGES as the object moves? Then there's no way around it. You need to carry out an integration, using the proper force, and the proper component, at every point.
If we have time, we might try some additional examples ...
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