a. Explanation Given information : The position of an object moving along a line is given by the function s ( t ) = 1 + sec t o n 0 ≤ t ≤ π 4 Concept Involved: Rectilinear Motion: An object that moves along a straight line with position s ( t ) has velocity v ( t ) = d s d t and acceleration a ( t ) = d v d t = d 2 s d t 2 when these derivatives exist. Calculation: Description Steps Finding the derivative of position function s ( t ) = 1 b. To determine To find : the acceleration at time t. c. To determine To compute : the total distance travelled by the object during the indicated time interval and describes the motion of the object. d. To determine To tell : when the object is accelerating and when it is decelerating.

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.4, Problem 22PS

To determine

Tofind : the velocity at time t.

To determine

To find : the acceleration at time t.

To determine

To compute : the total distance travelled by the object during the indicated time interval and describes the motion of the object.

To determine

To tell : when the object is accelerating and when it is decelerating.

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Chapter 3.4, Problem 21PS

Chapter 3.4, Problem 23PS

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A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?

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Chapter 3 Solutions

Student's Solution and Survival Manual for Calculus

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Tofind : the velocity at time t.

Solution Summary: The author explains the function s(t)=1+sect on 0t4 and calculates the acceleration at time t. The total distance travelled by the object during the indicated time interval is 2

Concept explainers

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Tofind : the velocity at time t.

To find : the acceleration at time t.

To compute : the total distance travelled by the object during the indicated time interval and describes the motion of the object.

To tell : when the object is accelerating and when it is decelerating.

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Chapter 3 Solutions