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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

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

**(a)**

To determine

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

Explanation

**Given:**

The given vector and given point is

**Explanation:**

Consider the provided position vector is:

Derivative of the position vector gives velocity vector:

**(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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P-10PSCh-12 P-11PSCh-12 P-12PSCh-12 P-13PSCh-12 P-14PS

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