Explanation Given: Force F = 〈 12 t + 4 , 8 − 24 t 〉 acts on a 2-kg mass. Calculation: We have F = 〈 12 t + 4 , 8 − 24 t 〉 We know that F = m a = 2 a Comparing both the results we will get 2 a = 〈 12 t + 4 , 8 − 24 t 〉 ð r ' ' ( t ) = a = 〈 6 t + 2 , 4 − 12 t 〉 Integrating we will get r ' ( t ) = v = 〈 3 t 2 + 2 t + c 1 , 4 t − 6 t 2 + c 2 〉 Using initial velocity condition, we will get 〈 2 , 3 〉 = 〈 c 1 , c 2 〉 ð r ' ( t ) = v = 〈 3 t 2 + 2 t +

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 14, Problem 28CRE

To determine

The position of the mass at t = 2 s if it is located at (4, 6) at t = 0 and has initial velocity (2, 3) in m/s if a force $F = 〈 12 t + 4, 8 - 24 t 〉$ (in newtons) acts on a 2-kg mass.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14, Problem 27CRE

Chapter 14, Problem 29CRE

Students have asked these similar questions

4. Use method of separation of variable to solve the following wave equation მłu J²u subject to u(0,t) =0, for t> 0, u(л,t) = 0, for t> 0, = t> 0, at² ax²' u(x, 0) = 0, 0.01 x, ut(x, 0) = Π 0.01 (π-x), 0

Solve the following heat equation by method of separation variables: ди = at subject to u(0,t) =0, for -16024 ძx2 • t>0, 0 0, ux (4,t) = 0, for t> 0, u(x, 0) = (x-3, \-1, 0 < x ≤2 2≤ x ≤ 4.

ex 5. important aspects. Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all 6 33

Chapter 14 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The position of the mass at t = 2 s if it is located at (4, 6) at t = 0 and has initial velocity (2, 3) in m/s if a force F = 〈 12 t + 4 , 8 − 24 t 〉 (in newtons) acts on a 2-kg mass.

Solution Summary: The author calculates the position of the mass at 2 s if it is located at (4, 6) at t = 0 and has initial velocity in m/s.

Concept explainers

Videos

The position of the mass at t = 2 s if it is located at (4, 6) at t = 0 and has initial velocity (2, 3) in m/s if a force $F = 〈 12 t + 4, 8 - 24 t 〉$ (in newtons) acts on a 2-kg mass.

Want to see the full answer?

Chapter 14 Solutions

The position of the mass at t = 2 s if it is located at (4, 6) at t = 0 and has initial velocity (2, 3) in m/s if a force F = 〈 12 t + 4 , 8 − 24 t 〉 (in newtons) acts on a 2-kg mass.

Solution Summary: The author calculates the position of the mass at 2 s if it is located at (4, 6) at t = 0 and has initial velocity in m/s.

Concept explainers

Videos

The position of the mass at t = 2 s if it is located at (4, 6) at t = 0 and has initial velocity (2, 3) in m/s if a force F=〈12t+4,8−24t〉 (in newtons) acts on a 2-kg mass.

Want to see the full answer?

Chapter 14 Solutions

The position of the mass at t = 2 s if it is located at (4, 6) at t = 0 and has initial velocity (2, 3) in m/s if a force $F = 〈 12 t + 4, 8 - 24 t 〉$ (in newtons) acts on a 2-kg mass.