An engineer designing a system to control a router for a machining process modelima the system so that the router's acceleration (in /s2) during an interval of time is given by a = -0.4v, where v is the velocity of the router in in/s. When t=0, the position is so and the velocity is v2 in/s. What is the position at t-3 s? (10 points)

Answers

Answer 1

The position at t=3s is determined by the initial velocity and the equation above.

The integrating factor is defined as the function chosen to solve the given differential equation. It is most typically employed in first-order ordinary linear differential equations.

Where P(x) indicates the function of x and signifies the integrating factor.

To find the position of the router at t=3s,

we need to solve for the velocity and position at t=3s.

Starting with velocity, we have:

dv/dt = -0.4v

This is a first-order linear differential equation, which can be solved using an integrating factor method:

\(v = v2e^{(-0.4t)}\)

Next, we integrate this to find the position:

dx/dt = v

\(x = v2 / 0.4 \times (1 - e^{(-0.4t)})\)

Plugging in t=3 and the initial velocity, v2, we get:

x = \(v2 / 0.4 \times (1 - e^{(-0.4 \times 3)})\)

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Related Questions

A cognitive bias is a kind of logical fallacy.
True or false?

Answers

Answer:

True

Explanation:

It definetly is because, if we are biased it sets us up to fail on some things.

If a ball leaves the ground with a velocity of 4.67 m/s,
how high does the ball travel?

Answers

Answer:

\(Vf^2=Vo^2+2aS\\(0m/s)^2=(4.67m/s)^2+(2*-10m/s^2)S\\-(4.67)^2 m^2/s^2=-20m/s^2*S\\S=(21.8089/20) m\\S=1.090445 m\\\)

?
_2. Region surrounding the nucleus where electrons are found.
?
_3. Positively charged center of an atom.
?
4. Particles that differ in number between isotopes.

Answers

Answer:

Electron shell

Nucleus

Neutrons

Explanation:

An atom is made up of three fundamental subatomic particles which are the protons, neutrons and electrons.

Protons are the positively charged particles. Neutrons do not carry any charges. Both protons and neutrons are found in the tiny nucleus at the center of that atom. The electrons are negatively charged. They are found outside the nucleus in electronic shells.

An object has a mass of 450g. What is the gravitational force of the object by earth?

Answers

Answer:

4.41N or 4.5N (check explanation)

Explanation:

450g = 0.45kg

F = ma

Using 10m/s² = 10(0.45) = 4.5N

Using 9.8m/s² = 9.8(0.45) = 4.41N

which theory says dreaming is an unimportant by-product of neural firing during sleep

A. latent content theory
B. activation-synthesis
C. Freudian theory
D. information- processing

Answers

Answer:

B. Activation-Synthesis

Explanation:

Apex

. An electron has a de Broglie wavelength of 2.80 *
10-10 m. Determine (a) the magnitude of its momentum and (b) its
kinetic energy (in joules and in electron volts

Answers

The de- Broglie wavelength of 2.80× 10⁻¹⁰ m is associated with a momentum of 2.36 × 10⁻²⁴ Kg m/s. The kinetic energy will be 3.07 × 10⁻¹⁸ J which is equal to 19.015 ev.

What is de-Broglie wavelength?

De-Broglie proposed  the dual nature of matter which stated that matter can behave as both wave and particle. For a matter wave, the wavelength of the wave will be the ratio of the Planck's' constant h and its momentum p.

thus, λ = h/p

Given the wavelength = 2.80× 10⁻¹⁰ m.

momentum p = h/λ

= 6.62 × 10 ⁻³⁴ / (2.80× 10⁻¹⁰ m)

=  2.36 × 10⁻²⁴ Kg m/s

The kinetic energy ke = 1/2 mv² = p² /2m.

mass of an electron = 9.1 × 10 ⁻³⁴ Kg.

hence, Ke =  (2.36 × 10⁻²⁴ Kg m/s )² /  9.1 × 10 ⁻³⁴ Kg

                 = 3.07 × 10⁻¹⁸  J.

1 J = 6.24 × 10¹⁸ ev.

thus, KE in ev = 3.07 × 10⁻¹⁸  J ×  6.24 × 10¹⁸ ev = 19 ev.

Therefore, the kinetic energy of the electron is 19 ev.

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What characteristics determine how easily two substances change temperature? Check all that apply.
volume of the two substances in contact
amount of time the two substances are in contact
Oarea in contact between the two substances
specific heat of the material that makes up the substances
density of the two substances in contact

Answers

Answer:

The characteristics that determine how easily two substances change temperature are:

specific heat of the material that makes up the substancesarea in contact between the two substances

The volume and density of the substances and the amount of time they are in contact do not directly affect how easily they change temperature.

Explanation:

an electric kettle takes 2kw at 240v. Calculate the current and the resistance of the heating element

Answers

The power output is given 2000 watt and voltage is 240 v. Then the current through the heating element is 8.3 A and the resistance is 29 ohms.

What is power ?

The power used by an object is the rate of its work done or energy. It is the energy divided by time. The power output in a circuit is the product of the potential difference V and current I.

P = I V

Given,

P = 2 kw = 2000 W

v = 240 V.

Then I = P/v

I = 2000 w/240 v = 8.3 A.

According to Ohm's law, voltage v is the product of the current and resistance through the material.

hence,

V = I R

then, R = V/I

R = 240 V/8.33 A

  = 29 Ω.

Therefore, the current and resistance through the heating element are 8.3 A and 29 ohms respectively.

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Which of these is a likely impact of stronger than normal trade winds in the Pacific Northwest of the United States?

Answers

Answer: The statement that is a likely impact of stronger than normal trade winds in the Pacific Northwest to the United States is "Jet stream would be displaced southwards causing heavy rain and flooding."

Explanation: Hope this helps!

The rate of decay of a radioactive sample is given by R1 at time t1 and R2 at a later time t2 . The mean life of this radioactive sample is:​

Answers

Hope this answer helps you

The rate of decay of a radioactive sample is given by R1 at time t1 and R2 at a later time t2 . The mean

If Tom were so foolish as to play his keyboard instrument under water, where the speed of sound is 1500 m/s , what would be the wavelength of the B note in water ? Explain why the B tone has a longer wavelength in water than in air. (frequency of middle B tone is 494 Hz )

Answers

Answer:

λ = 3.04 m

Explanation:

At any traveling wave, there exists a fixed relationship between speed, wavelength and frequency, as follows:

       \(v = \lambda* f (1)\)

We know the value of speed of sound in water (1500 m/s), and the frequency of middle B tone (494 Hz) , so we can find the wavelength λ (in meters) as follows:

       \(\lambda_{w} = \frac{v_{sw}}{f} = \frac{1500m/s}{4941/s} = 3.04 m (2)\)

Since the frequency is the same at any medium, and the speed of sound in air is lower than in water (334 m/s) this means that the wavelength in water must be longer than in air.

Two horizontal forces, 225 N and 165 N, are exerted
on a canoe in the same dieclon. Find the net
honzontal force on the cance

Answers

Answer:

290 N of horizontal force

Explanation:

To calculate the Net force of an object you find the sum of each force.

225 N + 165 N = 290 N

Since the reference direction is horizontal, that's how i got 290 N of horizontal force.

I hope you found this helpful...

The net force on the canoe is equal to 390N when both forces act in the same direction.

What is the net force?

The net force can be defined as the vector sum of all the forces acting on a particle. The net force is a single force indicating same the effect of the original forces on the motion of the particle. The net force is equal to the same acceleration as all actual forces together.

The net force will become the resultant force. The net force has the same effect on the rotational motion as all actual forces together.

If the two acting forces on the canoe are acting in the same direction then the net force il be equal to the sum of these two forces.

Given, the one horizontal force on the canoe, F₁ = 225N

The other horizontal force on the canoe, F₂ = 165 N

The net force on the canoe, F = F₁ + F₂ = 225 + 165 = 390 N

Therefore,  the net horizontal force on the canoe is equal to 390 N.

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using the pattern of seafloor magnetic anomalies (stripes) and the timescale of magnetic reversals to the right, calculate the average rate at which point a has moved away from point b since 50 ma ?

Answers

The average rate at which point A has moved away from point b since 50 ma is 240 km/my.

What is magnet?

Magnetism is a physical quality mediated by a magnetic field that refers tο the ability to create attracted and repulsive οccurrences in other substances. Diamagnetic materials are thοse that magnetize freely when put in a magnetic field. Hοwever, the magnetization is oriented in the οpposite direction as the magnetic field. These materials' magnetism is referred to as diamagnetism.

To calculate the average spreading rate of point A with respect to point B we have to find the distance of Point A from point B.  For this we have the scale of the map i.e. 3000 km. By measuring the length of red bar, I got 3cm= 3000km . It means 3cm on the map equals to 3000km on the ground. So now for calculating the distance of point A from point B, we have to measure the length. The length i got is 12cm. From the scale ,

3cm= 3000km

1cm= 1000km

12cm= 12000km

Now we have distance =  12000km

time= 50my

so the average rate of spreading = distance / time

= 12000/ 50

=240 km/my

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Complete question:

using the pattern of seafloor magnetic anomalies (stripes) and the timescale of magnetic reversals to

when your car accelerates away from a stop sign, you feel like you're being pushed back into your seat.

Answers

No, when your car accelerates away from a stop sign, you feel like you're being pushed back into your seat. There is no force pushing you backward, just the seat pushing forward.

In the inertial reference frame, the only force acting on occupants while sitting inside the accelerating car is the force that causes occupants to accelerate which is given by mass times the acceleration. So from the inertial reference frame occupant accelerates.

What is the acceleration?

One of the important notions like Speed and Velocity, in Physics that is used to explain motion and to solve problems concerned to it, is called the acceleration.

No, when your car accelerates away from a stop sign, you feel like you're being pushed back into your seat. There is no force pushing you backward, just the seat pushing forward.

In the inertial reference frame, the only force acting on occupants while sitting inside the accelerating car is the force that causes occupants to accelerate which is given by mass times the acceleration. So from the inertial reference frame occupant accelerates.

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Convert using chain link method 5.3 MIN/m² to N/mm²​

Answers

Answer:

hohdoqjqwfojiqjwiojdq

Explanation:

huehqofjoiqjdoiwjqiojfiwjfiojeqojefiqjojeqiojoiewqdqwwqdwqd

Need help for this Asap please ​

Need help for this Asap please

Answers

The coefficient of static friction between the block of wood and the table is 0.449.

How to calculate the friction

The weight of the block of wood is Mg = 4.0 kg × 9.81 m/s^2 = 39.24 N.

The coefficient of static friction μs is given by the equation μ_s = fs/N, where N is the normal force from the table.

Since the block is not accelerating vertically, we know that N = Mg, so we have:

μs = fs/N = 17.64 N / 39.24 N = 0.449

Therefore, the coefficient of static friction between the block of wood and the table is 0.449.

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A student trying to calculate the
parameters of a satellite orbit obtained
a quantity Q which is related with the
orbital radius R., radius of the earth
R and acceleration due to gravity, g
½
2
by the formula Q
(SR²)
gR
dimensional analysis, find out what Q
represents.
Select one:
Tangential force
O Orbital speed
.
Centripetal acceleration
O Torque on the satellite
Using

A student trying to calculate theparameters of a satellite orbit obtaineda quantity Q which is related

Answers

Orbital speed is defined as Fg=GmM(R+h)2, where m is the satellite's mass and h is its height above the planet's surface.

How do you determine a satellite's orbital velocity?

The orbital mobility is given by the formula g(R+h) = gr. Orbital velocity refers to the velocity needed to counteract the gravitational pull on the moon with its inertia, or propensity to continue moving.

What factors affect a satellite's orbital velocity?

The planetary velocity of a satellite that orbits the Earth is determined by the height of the satellite above the planet. The needed orbital velocity increases with the distance from the Earth. At lower altitudes, a satellite encounters traces of Upper orbit, which causes drag.

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Ite
Imagine a scenario in which an animal's force is pushing itself forward 5 N, friction is pushing it 4 N backward,
gravity is pushing the animal 10 N down, and the animal is pushing itself 10 N up. Describe the movement of
the animal. (1 point)
Ite!
Iter
o It moves forward and upward because those are the greatest net forces.
Iten
o It moves 10 N down and 10 N up as those are the greatest forces acting on the animal.
Item
Item
It only moves forward because there is a net force forward.
Item
o It moves 29 N forward because that's the net force.
Item
Item 1
Item 1

Answers

It only moves forward because there is a net force forward.

Let us note that when an object is acted upon by a system of forces, the object only moves in the direction of the net force.

We have an animal acted upon by the following forces;

5 N forward4 N backward10 N upward10 N downwards

The upwards and downwards forces are exactly balanced so the animal neither moves upwards or downwards.

However, the animal does move forward because there is a net force that pushes the animal forward.

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Answer:C. It only moves forward because there is a net force forward.

Explanation:

. The ________________ theory of matter states that all particles of matter are in constant motion. (Page 432)

Answers

Answer:

The kinetic molecular theory of matter states that all particles of matter are in constant motion.

Explanation:

Kinetic means active and lively and has to do with the motion of material bodies and forces.

Please give Brainliest.

how much pressire is created when a force of 55n is applied over sn area of 8m²​

Answers

Given

how much pressure is created when a force of 55N is applied over an area of 8m²

Solution

We have been asked to determine the pressure exerted when given magnitude of force acting on given area.

\(☄\bf \qquad \mathcal{Pressure} = \mathcal{\dfrac{Force}{Area}}\)

Put all given value we obtain

\(\qquad \sf \longrightarrow \:Pressure \: = \dfrac{55}{8} \\ \\ \\ \qquad \sf \longrightarrow \:Pressure \: = \cancel\dfrac{55}{8} \\ \\ \\ \qquad \sf \longrightarrow \:Pressure \: = 6.875 \: Pa.\)

Therefore,

6.875 Pascal Pressure is created .

The table below shows the right ascensions of two stars at a location.


Name of star Right ascension
Star 1 2 hours
Star 2 4 hours 20 minutes

HELP ME PLS

What is the degree difference between the two stars that rise at the location?
20 degrees
30 degrees
35 degrees
60 degrees

Answers

Answer:

Star 1 2 hours

35

Explanation:

Answer:

the answer would be 35 degrees :))))

Explanation:

it was the correct on the quiz,,, good luckk :3!!

a girl pushes an 18.15 kg wagon with a force of 3.63 N. what is the acceleration?

A. 0.06 m/s2
B. 5 m/s2
C. 0.2 m/s2

Answers

Answer:0.2 m/s^2

Explanation:

mass=18.15kg

Force=3.63N

Acceleration=force ➗ mass

Acceleration=3.63 ➗ 18.15

Acceleration=0.2 m/s^2

A girl pushes a wagon of mass 18.15 kg with a force of 3.63 N, so the acceleration of the wagon will be 0.2 m/s².

What is acceleration?

In mechanics, acceleration is the measure of how rapidly an object's velocity changes over time. Accelerations as a vector quantity. An object's acceleration depends on the direction of the net force exerted on it.

A vector quantity, acceleration, is something that has both a magnitude and a direction. As a vector quantity, velocity is also. The ratio of the velocity vector change over a time interval to that interval is the definition of acceleration.

Mass, m =18.15 kg

Force, f = 3.63 N

Force = m × a

a= f / m

a =3.63 / 18.15

a = 0.2 m/s²

Hence, the acceleration of the wagon will be 0.2 m/s².

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4. Which of the following quantities remain the same in all parts of a series circuit?
A. Voitage B. Current C. Power D. Resistance.

Answers

The current remains the same in all parts of a series circuit.

The correct option is B.

What is a circuit?

A circuit is a complete path for the flow of electric current.

A series circuit is a circuit that the component of the circuit are connected end-to-end and the flow of current is in one direction.

Another form of connection is the parallel connection in which current flows through alternate paths.

In a series circuit, the flow of current is constant and remains the same in all parts of a series circuit. However, the voltage across the circuit varies.

In a parallel circuit,  the voltage is constant and remains the same in all parts of a parallel circuit.  However, the flow of current across the circuit varies.

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How fast is a 6 kg toy car moving when it has 40 kg * m/s of
momentum? Help please thank you giving Brianlest

Answers

Answer:

approximately 6.67 m/s

Explanation:

the equation for speed when given momentum and mass is

Speed=momentum/mass

Answer:

Below

Explanation:

Momentum = m * v

 40              =   6 * v

40/6 = v = 6  2/3   m/s     ( or ~  6.7 m/s)

What are political obstacles keeping wind turbine from being used?

Answers

Explanation:

Turbines might cause noise and aesthetic pollution.

Although wind power plants have relatively little impact on the environment compared to conventional power plants, concern exists over the noise produced by the turbine blades and visual impacts to the landscape.

The inflexibility, variability, and relative unpredictability of wind power as a means for electricity production, are the most obvious barriers to an easy integration and widespread application of wind power." Thus, the uncertainty of the wind requires a system that is always available to replace all the electrical output created by the wind turbine system. In other words, it is too expensive to have wind turbines lying around that don't do anything.

A 4-kW resistance heater in a water heater runs for 3 hours to raise the water temperature to the desired level. Determine the amount of electric energy used in both kWh and kJ.

Answers

Answer:

12kWhr

Explanation:

Energy = Power * Time

Power = 4kW

Time = 3hrs

Substitute into the formula

Energy used up = 4kW * 3hrs

Energy used up = 12kWhr

A certain satellite travels in an approximately circular orbit of radius 8.8 × 10^6 m with a period of 6 h 12 min. Calculate the mass of its planet from this information.

Answers

The mass of the planet is  5.98 × 10^24 kg.

To calculate the mass of the planet, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its orbit.

First, we need to convert the period of the satellite's orbit to seconds. We know that there are 60 minutes in an hour, so the period can be expressed as (6 × 60 + 12) minutes, which equals 372 minutes. Multiplying this by 60 seconds, we get a period of 22,320 seconds.

Next, we need to find the semi-major axis of the orbit. In a circular orbit, the semi-major axis is equal to the radius of the orbit. Therefore, the semi-major axis is 8.8 × 10^6 m.

Now, we can apply Kepler's Third Law to calculate the mass of the planet. The formula is T^2 = (4π^2/GM) × a^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the planet, and a is the semi-major axis of the orbit.

Rearranging the formula, we can solve for the mass of the planet:
M = (4π^2/G) × a^3 / T^2

Plugging in the values, we get:
M = (4 × π^2 / 6.67430 × 10^-11) × (8.8 × 10^6)^3 / (22,320)^2

Evaluating this expression, we find that the mass of the planet is approximately 5.98 × 10^24 kg.

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When dim blue light shines on a piece of metal, electrons are ejected from its surface, but not when bright red light shines on the metal. Does this phenomenon provide evidence for the wave model or the particle model of light? Why?

Answers

Answer: The particle model, because only high-energy frequencies of lights can remove electrons.

Explanation: just did the test and got it right :)

A physics instructor wants to project a spectrum of visible light colors from 400 nm to 700 nm as part of a classroom demonstration. She shines a beam of white light through a diffraction grating with 500 lines per mm, projecting a pattern on a screen 2.4 m behind the grating. How wide is the spectrum corresponding to m=1?

Answers

Answer:

औडंठः की दुनिया कार्टून दर्शन होली है और यह बियर का अच्छा विकल्प है। विकल्प है। यो कुरा मेरो आफ्ना लागि विचार र त्यहाँको बडेमाको बिल्डिङ भित्र म जिन्दगी एक यात्रा हो कहाँबाट शुरु भइ कहाँ पुगेर अन्त हुन्छ

In a hydraulic lift, the radius of the small and large pistons are
2.50cm and 10.0cm respectively. A vehicle weighing 12.0kN is to be
lifted by the large piston. Calculate
a) the force that must be applied to the small piston
b) the distance that the small piston has to be pushed down to raise the vehicle a diatance of 2.00cm​

Answers

Answer:

the answer is 52.15cm×35.5

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I think of a number, multiply it bytwo, then subtract mine a patient being discharged from the hospital after acute coronary syndrome will be participating in cardiac rehabiliation. which information will the nurse provide about the early recovery phase of rehabiliation? Explain how would you find out the 7% tax and 10% tip for a $23.96 family meal. how much is 7% tax? how much is 10% tip? what would be the total? * which of the following was not a requirement of former confederate states under the radical republican plan for reconstruction (reconstruction act of 1867)? A store has 127 boxes of cookies. There are 21 cookies in each box. What is the total number of cookies in the boxes 1. Einterz RM, Kimaiyo S, Mengech HN, et al. Responding to the HIV pandemic: the power of an academic medical partnership. Acad Med. 2007;82(8):812-818. What is the order of the State court system? A worker takes a mixture of cast iron and steel metal and places it inside a furnace that reaches 1500C. The molten cast iron is poured into a mold. The mold is hung out to dry. Later, the worker removes a cast iron skillet from the mold. What two phase changes occured in order to make the skillet? inefficient output and price, few choices for consumers, and rent seeking are all problems associated with a. taxes. b. competitive markets. c. monopolies. d. scarcity. e. Trade. Problem 2A container holds 27/2 gallons of oil. How many containers are needed to hold 356/3 gallons of oil? What is the supplement of an angle thatmeasures 21 degrees? How many acres are contained in the parcel described as the SW of the SE of the NW of Section 15? 6.6 causes of migration in an interconnected world economic imperialism and new types of transportation led to S(-1,2), W(0, 4)find the slope The Bruce family set out 8 0clock in the morning. They arrived at the old port of Ambertini at 09:05. How long their journey took?pls Who is the intended audience for A Modest Proposal? We feel uncomfortably warm on a muggy day because water molecules areA) evaporating from our moist bodies.B) condensing on our bodies.C) evaporating and condensing on our bodiesat the same rate. The area of a circle is 99.88cm2.Find the length of the radius rounded to 2 DP.r =cmWhat is the length of the radius rounded to 2dp Answer first and i will mark brainliest Suppose that the series a_n (z z_0)^n has radius of convergence R_0 and that f(z) = a_n (z z_0)^n whenever |z z_0| < R_0. Prove that R_0 = inf{|z - z_0|: f(z) non-analytic or undefined at z} (R_0 is essentially the distance from z_0 to the nearest point at which f(z) is non-analytic)