Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so

Question:

Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv.

(a) Show that its velocity and position at time t are given by

(b) Conclude that the body travels only a finite distance, and find that distance.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

See More Books

Question Posted: Jul 03, 2023 02:52 AM

See More 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...
As risk manager, you are concerned about the additional liability exposure the firm will face if it accepts a risky project. You obtain an estimate of the annual total loss distribution from an...
Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T1t2 after time t, in minutes, where...
7. A 2.0 kg ball is moving at a velocity of 5.0 m/s. It collides with a stationery ball of mass 2 kg. After the collision the first ball A moves off in a direction 30 to the left of its original...
Daniels Cement Company purchased new cement pouring equipment at a cost of $22,500 at the beginning of July 2009. The equipment was estimated to have a salvage value of $2,500 at the end of its...
What is the ratio of the sunlight intensity reaching Pluto compared with the sunlight intensity reaching Earth? (On average, Pluto is 39 times as far from the Sun as is Earth.)
The following scenarios describe situations faced by hypothetical companies that currently have a centralized organization structure. As you review each of the scenarios, provide your opinion as to...
Kelly Pitney began her consulting business, Kelly consulting P.C., on April 1, 2012. The accounting cycle for Kelly Consulting for April, including financial statements, was illustrated on pages...
Consider the arithmetic series 7+13+19+25+31+37+43 +...and answer thequestions which follow. a) (i) T. (ii) Express Tin terms of S (2) (2) b) (i) T =........... ... S =... (2) (ii) Express T2 in...
A process stream is heated using a shell and tube heat exchanger. The exit temperature is controlled by adjusting the steam control valve shown in figure. During an open-loop experimental test, the...
In Problems 1 through 12 first solve the equation f (x) = 0 to find the critical points of the given autonomous differential equation dx/dt = f (x) Then analyze the sign of f (x) to determine whether...
Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv 3/2 . Show that Conclude that under a 3/2 -power resistance a body coasts only a finite distance before coming...
Journalize the following assumed transactions for The Soda Pop Company. Show amounts in billions. a. Cash purchases of inventory, $4.5 billion b. Sales on account, $18.9 billion c. Cost of goods sold...
1. A grocery owner incurred the following losses for the taxable year: Loss on sale of home theatre P10,000 Loss on sale of real property considered as capital asset 80,000 Loss on inventories in...
All of the following are false about transfer pricing except: the cost approach can base the transfer price on either the variable cost or full absorption cost. companies should always use the...
Find 3 (2 +62 $7) dz dx x3
If completing a migration from QuickBooks Desktop, what is the first thing you need to do? A. Run your financial statements. B. Update QuickBooks. C. Confirm file size. D. Delete old accounts. 2. You...
Sydney Ltd decided to change its accounting for employee entitlements, to accrue the expense sooner than had been done previously. The effect on provision for employee entitlements as at the end of...
Suppose a manager at a local Dominos Pizza would like to determine if the average time it takes to deliver a pizza and return to the store differs for the four employees who make the deliveries. The...
A company pledges their receivables so they may Multiple Choice Charge a factoring fee. Increase sales. Recognize a sale. Collect a pledge fee. Borrow money. Failure by a promissory notes' maker to...
Suppose that dP/dt = 0.15P(t) represents a mathematical model for the growth of a certain cell culture, where P(t) is the size of the culture (measured in millions of cells) at time t > 0 (measured...
The snowplow problem is a classic and appears in many differential equations texts, but it was probably made famous by Ralph Palmer Agnew: One day it started snowing at a heavy and steady rate. A...
In meteorology the term virga refers to falling raindrops or ice particles that evaporate before they reach the ground. Assume that a typical raindrop is spherical. Starting at some time, which we...
A, B, C and C have a capital of 5 000 000 where the first is with company capital, the second has 30% debt while the 3rd is 70% with borrowed capital? What is the level of leverage for each? How much...
Remi has two properties that are surplus to the firms requirements and are leased out. Details of rent in advance and rent in arrears at the beginning and end of the year are as follows: 31 October...
Lucys parents placed $5,000 in a bank account at 3% interest compounded quarterly upon her 10th birthday. Hunter earned $15,000 working and placed it in a bank account upon his 16th birthday. His...

Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so

Question:

and v(t) = voe-kt x(t) = xo + (2) (1 - e-kt).

Step by Step Answer:

a b The solution of the initial value ...View the full answer

Differential Equations And Linear Algebra

Students also viewed these Mathematics questions