Explanation Given information: The motion on the circle is x 2 + y 2 = 16 . The position of a particle in the xy -plane is, r ( t ) = ( 4 cos t 2 ) i + ( 4 sin t 2 ) j (1) Time, t = π t = 3 π 2 Formula used: Write the expression for velocity of a particle. v = d r d t Write the expression for acceleration of a particle. a = d v d t = d 2 r d t 2 Calculation: The velocity of the particle is, v = d r d t = ( 4 ( − 1 2 ) sin t 2 ) i + ( 4 ( 1 2 ) cos t 2 ) j = ( − 2 sin t 2 ) i + ( 2 cos t 2 ) j At t = π , the velocity of the particle is, v = − 2 sin ( π ) 2 i + 2 cos ( π ) 2 j = − 2 ( 1 ) i + 2 ( 0 ) j = − 2 i At t = 3 π 2 , the velocity of the particle is, v = − 2 sin ( 3 π 2 ) 2 i + 2 cos ( 3 π 2 ) 2 j = − 2 sin 3 π 4 i + 2 cos 3 π 4 j = − 2 ( 2 2 ) i + 2 ( − 2 2

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Chapter 13.1, Problem 10E

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Determine the particle’s velocity and acceleration vectors at time t=π and t=3π2. And sketch the vectors position on the curve in the xy plane.

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Chapter 13.1, Problem 9E

Chapter 13.1, Problem 11E

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Chapter 13 Solutions

Pearson eText for Thomas' Calculus: Early Transcendentals -- Instant Access (Pearson+)

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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Determine the particle’s velocity and acceleration vectors at time t = π and t = 3 π 2 . And sketch the vectors position on the curve in the xy plane.

Determine the particle’s velocity and acceleration vectors at time t=π and t=3π2. And sketch the vectors position on the curve in the xy plane.

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Chapter 13 Solutions