   Chapter 12.3, Problem 7E

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 ) = 〈 t − sin t , 1 − cos t 〉 ( π , 2 )

(a)

To determine
The velocity vector, speed and acceleration vector of the object for a provided position vector r(t)= tsint,  1-cos t and at a given point (π, 2).

Explanation

Given:

The given vector and point is r(t)= tsint,  1-cos t      (π, 2)

Explanation:

Consider the provided position vector is:

r(t)= tsint,  1-cos t

Derivative of the position vector gives velocity vector:

v(t) =r'(t)= (1cost)

(b)

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

(c)

To determine

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

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