Explanation Given: Equation of the curve in vector form is given by r ( t ) = r 〈 cos ω t , sin ω t 〉 = 8 〈 cos ω t , sin ω t 〉 Calculation: We have position vector r ( t ) = r 〈 cos ω t , sin ω t 〉 = 8 〈 cos ω t , sin ω t 〉 ð Velocity, v ( t ) = r ' ( t ) = 8 ω 〈 − sin ω t , cos ω t 〉 It is given that speed = 4 cm/s ð | v ( t ) | = 4 c m / s = | 8 ω 〈 − sin ω t , cos ω t 〉 | = 8 ω sin 2 ω t + cos 2 ω t = 8 ω So, we have ω = 1 2 r a d / s ð v ( t ) = 4 〈 − sin ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

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Chapter 14.5, Problem 7E

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Acceleration, a(t) for a particle moving around a circle of radius 8 cm at a constant speed of v = 4 cm/s. Draw the path and acceleration vector at $t = \frac{π}{4}$ .

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Chapter 14.5, Problem 6E

Chapter 14.5, Problem 8E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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Acceleration, a(t) for a particle moving around a circle of radius 8 cm at a constant speed of v = 4 cm/s. Draw the path and acceleration vector at t = π 4 .

Solution Summary: The author illustrates the equation of the curve in vector form by drawing the path and acceleration vector at t = 4.

Concept explainers

Acceleration, a(t) for a particle moving around a circle of radius 8 cm at a constant speed of v = 4 cm/s. Draw the path and acceleration vector at $t = \frac{π}{4}$ .

Want to see the full answer?

Chapter 14 Solutions

Acceleration, a(t) for a particle moving around a circle of radius 8 cm at a constant speed of v = 4 cm/s. Draw the path and acceleration vector at t = π 4 .

Solution Summary: The author illustrates the equation of the curve in vector form by drawing the path and acceleration vector at t = 4.

Concept explainers

Acceleration, a(t) for a particle moving around a circle of radius 8 cm at a constant speed of v = 4 cm/s. Draw the path and acceleration vector at t=π4.

Want to see the full answer?

Chapter 14 Solutions

Acceleration, a(t) for a particle moving around a circle of radius 8 cm at a constant speed of v = 4 cm/s. Draw the path and acceleration vector at $t = \frac{π}{4}$ .