An Arrow Has Two Numbers. A Speed Has One.

You'll learnto differentiate a vector-valued function one component at a time with every ordinary rule intact, to tell velocity from speed by the type of the answer, to find a magnitude rather than adding components or measuring the wrong arrow, and to see constant speed and nonzero acceleration coexist.

A vector-valued function is two parametric equations wearing one bracket, and its derivative is taken one component at a time with every rule from Units 2 and 3 unchanged. The one genuinely new idea is small and costs a great many points: velocity is a vector and speed is a number, and a question asking for one will not accept the other. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · VELOCITY IS AN ARROW, SPEED IS ITS LENGTH · v2

differentiate each slot, then decide what type the answer is

Before you start

What you're looking at

One plane at equal scale. The path is r(t) = ⟨3t², 2t³⟩ for t from 0 to 1, the same curve as Topic 9.3, and everything happens at t = 1, where the particle is at (3, 2).

The question

One function gives where the particle is, how it is moving and how fast. Two of those are arrows and one is a number, and telling them apart is most of this topic.

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