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Acceleration, velocity, position Suppose the acceleration of an object moving along a line is given by a(t) = -kv(t), where k is a positive constant and v is the object's velocity. Assume the initial velocity and position are given by v(0) = 10 and s(0) = 0, respectively. a. Use a(t) = v'(t) to find the velocity of the object as a func- tion of time. b. Use v(t) = s'(t) to find the position of the object as a function of time. dv ds - (by the Chain Rule) to find the dt ds dt dv c. Use the fact that- velocity as a function of position.

Acceleration, velocity, position Suppose the acceleration of an object moving along a line is given by a(t) = -kv(t), where k is a positive constant and v is the object's velocity. Assume the initial velocity and position are given by v(0) = 10 and s(0) = 0, respectively. a. Use a(t) = v'(t) to find the velocity of the object as a func- tion of time. b. Use v(t) = s'(t) to find the position of the object as a function of time. dv ds - (by the Chain Rule) to find the dt ds dt dv c. Use the fact that- velocity as a function of position.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Acceleration, velocity, position Suppose the acceleration of an object moving along a line is given by a(t) = -kv(t), where k is a positive constant and v is the object's velocity. Assume the initial velocity and position are given by v(0) = 10 and s(0) = 0, respectively. a. Use a(t) = v'(t) to find the velocity of the object as a func- tion of time. b. Use v(t) = s'(t) to find the position of the object as a function of time. dv ds - (by the Chain Rule) to find the dt ds dt dv c. Use the fact that- velocity as a function of position.
Transcribed Image Text:Acceleration, velocity, position Suppose the acceleration of an object moving along a line is given by a(t) = -kv(t), where k is a positive constant and v is the object's velocity. Assume the initial velocity and position are given by v(0) = 10 and s(0) = 0, respectively. a. Use a(t) = v'(t) to find the velocity of the object as a func- tion of time. b. Use v(t) = s'(t) to find the position of the object as a function of time. dv ds - (by the Chain Rule) to find the dt ds dt dv c. Use the fact that- velocity as a function of position.
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