Answered: Suppose r'(t) has units of m/s. Explain…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units) and carries information only about direction.

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Suppose r'(t) has units of m/s.

To explain why $Let r(t) be a differential vector valued function Now we look for the derivative r'(t) The vector r'(t) points in the direction of travel and its length tells us the speed of travel Now we if we are interested in finding the direction of r' but not its length The standard unit tangent vector denoted by T(t) is given by: T (t) = \frac{r' (t)}{|r' (t)|}$ is dimensionless (has no units) and carries information only about direction.

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