   Chapter 12.3, Problem 16E

Chapter
Section
Textbook Problem

# Finding Velocity and Acceleration Vectors in Space In Exercises 11-20, the position vector r describes the path or an object moving in space.(a) Kind the velocity vector, speed, and acceleration vector of the object.(b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. Position Vector Time r ( t ) = 〈 2 cos t , sin 3 t , t 2 〉 t = π 4

(a)

To determine

To Calculate: The velocity vector, speed, and acceleration vector of the object.

Explanation

Given:

The given position vector and time is r(t)=4cost,sin3t,t2,  t=π4

Calculation:

Consider, the position vector;

r(t)=2cost.i^+sin3t.j^+t2.k^

The velocity vector (at any time) is,

v(t)=ddt(r'(t))=2sint.i^+3cos3t

(b)

To determine
The velocity vector and acceleration vector of the object at the given value of t.

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