   Chapter 12.3, Problem 5E

Chapter
Section
Textbook Problem

# Finding Velocity and Acceleration Along a Plane Curve In Exercises 3-10, the position vector r describes the path of an object moving in the x y-plane.(a) Find the velocity vector, speed, and acceleration vector of the object.(b) Evaluate the velocity vector and acceleration vector of the object at the given point.(c) Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point.Position Vector Point r ( t ) = 2 cos t i + 2 sin t j ( 2 , 2 )

(a)

To determine
The velocity vector, speed and acceleration vector of the object for a provided position vector r(t)= +2cost.i^+2sint.j^  and at a given point (2, 2).

Explanation

Given:

The given vector and given point is r(t)= +2cost.i^+2sint.j^      (2, 2)

Explanation:

Consider the provided position vector is:

r(t)= +2cost.i^+2sint.j^

Derivative of the position vector gives velocity vector: v(t) = r'(t)=2sint

(b)

To determine
The velocity vector and acceleration vector at the given point (2, 2).

(c)

To determine
The sketch a graph and the velocity and acceleration vector at the given point.

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