An object of mass m moves from x 1 to x 2 during the time interval [t
Question:
An object of mass m moves from x1 to x2 during the time interval [t1, t2] due to a force F(x) acting in the direction of motion. Let x(t), v(t), and a(t) be the position, velocity, and acceleration at time t. The object’s kinetic energy is KE = 1/2 mv2.
Transcribed Image Text:
(a) Use the Change of Variables Formula to show that the work performed is equal to S 11 W = ₁²² X1 F(x) dx = dt F(x(t))v(t) dt (b) Use Newton's Second Law, F(x(t)) = ma(t), to show that d (1 ( 1 mv (1)²) = F(x(1))v(1) (c) Use the FTC to prove the Work-Energy Theorem: The change in kinetic energy during the time interval [t₁, 1₂] is equal to the work performed.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (3 reviews)
a Let x xt and x xt then x xt gives dx vt dt By substitution ...View the full answer
Answered By
Asim farooq
I have done MS finance and expertise in the field of Accounting, finance, cost accounting, security analysis and portfolio management and management, MS office is at my fingertips, I want my client to take advantage of my practical knowledge. I have been mentoring my client on a freelancer website from last two years, Currently I am working in Telecom company as a financial analyst and before that working as an accountant with Pepsi for one year. I also join a nonprofit organization as a finance assistant to my job duties are making payment to client after tax calculation, I have started my professional career from teaching I was teaching to a master's level student for two years in the evening.
My Expert Service
Financial accounting, Financial management, Cost accounting, Human resource management, Business communication and report writing. Financial accounting : • Journal entries • Financial statements including balance sheet, Profit & Loss account, Cash flow statement • Adjustment entries • Ratio analysis • Accounting concepts • Single entry accounting • Double entry accounting • Bills of exchange • Bank reconciliation statements Cost accounting : • Budgeting • Job order costing • Process costing • Cost of goods sold Financial management : • Capital budgeting • Net Present Value (NPV) • Internal Rate of Return (IRR) • Payback period • Discounted cash flows • Financial analysis • Capital assets pricing model • Simple interest, Compound interest & annuities
4.40+
65+ Reviews
86+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
An object of mass m is moving horizontally through a medium which resists the motion with a force that is a function of the velocity; that is, where v = v(t) and s = s (t) represent the velocity and...
-
Calculate escape velocity, the minimum initial velocity of an object to ensure that it will continue traveling into space and never fall back to Earth (assuming that no force is applied after...
-
The kinetic energy KE of an object of mass m moving with velocity v is defined as KE = 1/2 mv 2 . If a force f(x) acts on the object, moving it along the x-axis from x 1 to x 2 , the Work-Energy...
-
Assume that global lightning on the Earth constitutes a constant current of 1.00 kA between the ground and an atmospheric layer at potential 260 kV. (a) Find the power of terrestrial lightning. (b)...
-
Consider the following potential events that might have occurred to Global on December 30, 2010. For each one, indicate which line items in Globals balance sheet would be affected and by how much....
-
In continuing their discussion from Question 13, Mike says that even in the case of a capital deficiency, all cash should still be distributed on the basis of cap ital balances. Is Mike correct?...
-
Tandrin Aviation Holdings Ltd. agreed to sell a jet aircraft to Aero Toy Store, LLC, for \($31.75\) million. ATS paid a \($3\) million deposit to a third party with the balance due upon delivery....
-
As of June 30, 2016, the bank statement showed an ending balance of $19,500. The unadjusted Cash account balance was $15,200. The following information is available: 1. Deposit in transit, $2,400. 2....
-
4. Consider the tables of values for the two functions shown. x y = f(x) -2 5 y = g(x) -2 -1 6 -1 0 8 1 1 7 0 2 9 2 Complete the table of values for the composite function y = f(g(x)). - x y =...
-
Calculate the average over the given interval. (x) = x 3 , [0, 4]
-
Sketch the region enclosed by the curves and compute its area as an integral along the x-or y-axis. x = y 3 18y, y + 2x = 0
-
Some VHWOs and ONPOs combine educational and program brochures with their fund-raising mailings and charge part or all of the cost of the mailings to program services. Why? Also, when is this...
-
Identify the limitations that may be imposed in a variable interest entity. how these limitation be imposed?
-
How frequently are defined benefit pension plans required to make installment payments of their required contributions? How frequently are defined benefit pension plans required to make installment...
-
What does accounts recieveable turnover show about how efficiently a company manages its assets?
-
prepare the balance sheet for the following: Accumulated depreciation, retaines earnings, cash, bonds payable, accounts receivable, plant and equipment, accounts payable, allowance for bad debts,...
-
Respond to the following in a minimum of 175 words: Are outside financial analysts helpful or hurtful to investors? Do you believe outside financial analysts are objective or subjective with their...
-
A project has a cost (projected outflow of ($14,000) in year 0. This project has the following projected inflows in years 1-5: Year 1............................$ 2,000 Year 2...
-
Identify one local business that uses a perpetual inventory system and another that uses a periodic system. Interview an individual in each organization who is familiar with the inventory system and...
-
Two 2009 Tax Rate Schedules are given in the accompanying table. If x equals taxable income and y equals the tax due, construct a function y = f(x) for Schedule X. REVISED 2009 TAX RATE SCHEDULES...
-
In problem, find the domain of each function. f(x) = x 2 /x 2 + 1
-
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x 2 ) and show all stages....
-
1. You can buy a contract which will pay $ 10,000 per year for 3 years for $26,500. If investments of similar risk return 8% per annum, compounded annually, should you buy the contract? 2. How much...
-
Find the solution to each of these recurrence relations with the given initial conditions. Use an iterative approach such as that used in Example 10. a) an = a1+n+2, b) an2a1+1, ao do = 1 = 1
-
Describe how you go about starting a small business and what resources are needed.
Study smarter with the SolutionInn App