Problem

Velocity and acceleration from position Consider …

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Problem 14 Easy Difficulty

Velocity and acceleration from position Consider the following position functions.
a. Find the velocity and speed of the object.
b. Find the acceleration of the object.
$$r(t)=\langle 3 \cos t, 4 \sin t\rangle, \text { for } 0 \leq t \leq 2 \pi$$

Answer

Topics

Vectors

Vector Functions

Book Cover for Calculus Early Tran…

Calculus Early Transcendentals 3rd Edition

Chapter 14

Vector-Valued Functions

Section 3

Motion in Space

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Video Transcript

So what do you get? The velocity? Just like the past two problems. We're just going to start by taking the derivative of the position or function given up here. And so, for this problem, that's gonna be equal to three times negative sign of see, cause we have to take the derivative. So gonna write minus three sign ups and then the derivative of sine of t s co signer chased. We're gonna do four coastline of cheap and then we want to get the speed. And that comes from the magnitude of the velocity vector just right in his three side of t squared plus four co sign if t squared and then all the added It's where it'd And then that doesn't simplify asked anything, but I'll rewrite it just for the sake of keeping this page organized. So that's all recalled of this little once where this just ran out of space, traded and then for acceleration that's equaled Osti director, the derivative of that. And so that means that we're going to take the derivative of minus three sign of C, which is becomes minus three co sign of tea and then the derivative of co sign of T is minus sine of t. So that becomes minus four. Sign of tea

Maya M.

University of California, Davis

Topics

Vectors

Vector Functions

Book Cover for Calculus Early Tran…

Calculus Early Transcendentals 3rd Edition

Chapter 14

Vector-Valued Functions

Section 3

Motion in Space

Top Calculus 3 Educators

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University

Joseph L.

Boston College