state the equation of continuity.

Answers

Answer 1

Answer:

ρ A v = constant.

The equation proves the law of conservation of mass in fluid dynamics. Also, if the fluid is incompressible, the density will remain constant for steady flow. So, ρ1 =ρ2.


Related Questions

How do you think you could change how much drag a paper plane has?

Answers

Answer: You can change many things ranging from the size and shape of the paper plane. Cutting slits into the plane allows the air to carry it further.

what is the calibration nut on a bimetallic stemmed thermometer used for?

Answers

The calibration nut on a bimetallic stemmed thermometer is used for:  determining if the product's temperature has exceeded safe limits during shipment or subsequent storage.

What is bimetallic stemmed thermometer?

Bimetallic stemmed thermometer can check temperatures from 0˚F to 220˚F (–18˚C to 104˚C) and this thermometer measures temperature through its metal stem. When checking the temperature, insert the stem into the food up to dimple.

Bimetal thermometers work on the principle that different metals expand at different rates as they get heated. By using two strips of different metals in thermometer, movement of the strips correlates to the temperature and can be indicated along scale.

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Why is titanium non-magnetic?

Answers

Titanium is a non-magnetic metal because of its digital configuration and crystal shape.

In its pure shape, titanium has a hexagonal near-packed (hcp) crystal structure, this means that that its atoms are organized in a specific pattern in the crystal lattice.

This association outcomes inside the absence of unpaired electrons that could create magnetic moments, making it non-magnetic. Moreover, the electron configuration of titanium does not permit for magnetic moments to shape.

Titanium has four valence electrons, which are positioned within the 3-d and 4s orbitals.

The electrons in the 3d orbital are paired, which means that they've opposite spins and cancel out any magnetic second that could be created by means of the electrons inside the 4s orbital.

But, whilst titanium is alloyed with other metals, inclusive of iron or nickel, it may turn out to be magnetic because of the magnetic houses of these metals.

This belongings is utilized in various programs, inclusive of in the manufacturing of plane and medical implants, where the non-magnetic houses of titanium are important to keep away from interference with electromagnetic gadgets.

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A 0.22-caliber handgun fires a 28-g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?

Answers

The de Broglie wavelength of the bullet 5.93 x 10^-35 m. For a bullet, the de Broglie wavelength is extremely small, and its wave-like behavior is not easily noticeable or significant. The behavior of a bullet is mostly described by its classical, particle-like properties.

The de Broglie wavelength of an object can be calculated using the formula:

λ = h / (mv)

where h is Planck's constant (6.63 x 10^-34 J s), m is the mass of the object (in kilograms), and v is the velocity of the object.

In this case, the mass of the bullet is 28 g = 0.028 kg, and its velocity is 765 m/s, so the de Broglie wavelength can be calculated as:

λ = (6.63 x 10^-34 J s) / (0.028 kg * 765 m/s) = 5.93 x 10^-35 m is the de Broglie wavelength of the bullet.

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a car starts from rest on a curve with a radius of 130 m and tangential acceleration of 1.3 m/s2 . Through what angle will the car have traveled when the magnitude of its total acceleration is 2.6 m/s2?

Answers

The car will have traveled through an angle of approximately 119.7 degrees when the magnitude of its total acceleration is 2.6 m/s^2.

What is the angle of approximate calculation?

The magnitude of the total acceleration of a car on a curved path can be given by:

a = √(at^2 + ac^2)

where at is the tangential acceleration (1.3 m/s^2), and ac is the centripetal acceleration, which is given by:

ac = v^2 / r

where v is the velocity of the car and r is the radius of the curve (130 m).

Setting a = 2.6 m/s^2, we can solve for v:

v = √(r * a^2 - at^2) = √(130 * 2.6^2 - 1.3^2) = 27.47 m/s

The angle through which the car will have traveled can be found using the equation for the arc length s:

s = r * θ

where θ is the angle in radians. Substituting the values for v and t into the equation for s, we can solve for θ:

θ = s / r = v * t / r

Since the car started from rest, t can be found from the equation for acceleration:

at = v / t

t = v / at = 27.47 / 1.3 = 21.06 s

Finally, substituting t into the equation for θ, we get:

θ = v * t / r = 27.47 * 21.06 / 130 = 2.07 radians = 119.7 degrees

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.

what are catastrophic events and how are they categorized?

Answers

Catastrophic events are large-scale disasters that disrupt the normal functioning of a community or region and cause extreme damage and loss of life. These events can be natural disasters such as earthquakes.

What is the disasters ?

Disasters are events that cause significant damage, loss of life, and suffering to people and the environment. They come in many forms such as natural disasters like earthquakes, floods and hurricanes, or man-made disasters like oil spills and nuclear accidents. Disasters can have long-term effects on the environment, economy, and people’s lives, and can leave entire communities struggling to recover. Governments and organizations around the world work together to reduce the impacts of disasters and prepare for future events.

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Catastrophic events are large-scale disasters that disrupt the normal functioning of a community or region and cause extreme damage and loss of life. These events can be natural disasters such as earthquakes.

What is the disasters ?

Disasters are events that cause significant damage, loss of life, and suffering to people and the environment. They come in many forms such as natural disasters like earthquakes, floods and hurricanes, or man-made disasters like oil spills and nuclear accidents. Disasters can have long-term effects on the environment, economy, and people’s lives, and can leave entire communities struggling to recover. Governments and organizations around the world work together to reduce the impacts of disasters and prepare for future events.

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On a good day and with a strong tailwind, Mr. H's Yugo can average a speed of 24.7 m/h. Ignoring stop lights and other influences
that slow him down, how much time (in hours) does it take Mr. H to drive his Yugo the 11.9 miles down the two-lane highway to town?

Answers

The answer would be 25 minutes
Final answer:

Using the formula for time, which is distance divided by speed, it would take Mr. H approximately 0.48 hours to drive the 11.9 miles to town at a speed of 24.7 miles/hour, presuming a strong tailwind and no stops.

Explanation:

To find the time it takes for Mr. H to drive to town, we can use the formula time = distance/speed. In this case, the distance is 11.9 miles and the speed is 24.7 miles/hour. Therefore, the time it would take Mr. H to drive to town is 11.9 miles / 24.7 miles/hour = 0.48 hours approximately. This means that on a day with a strong tailwind, and ignoring stop lights and other influences, it would take Mr. H about 0.48 hours to drive his Yugo the 11.9 miles to down the two-lane highway to town.

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a boy on a skateboard pushes off the ground with his foot. he and the skateboard accelerate down the sidewalk due to the force

Answers

A boy on a skateboard pushes off the ground with his foot. he and the skateboard accelerate down the sidewalk due to the force on the ground in one direction.

The ground applies an equal and opposite force on the boy in the opposite direction. This force causes the boy and the skateboard to accelerate forward.

According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.

Therefore, the acceleration of the boy and the skateboard will depend on the force applied by the boy's foot and the combined mass of the boy and the skateboard.

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The energy required for the phase change from solid to liquid for a substance is known as the heat of _____.
a.) vaporization
b.) sublimation
c.) fusion
d.) fission
e.) condensation
Phase Change
When a substance changes from one state of matter to another it is called a phase change. Common endothermic phase changes are melting, vaporization, and sublimation. Common exothermic phase changes are freezing, condensation, and deposition.

Answers

The energy required for the phase change from solid to liquid for a substance is known as the heat of fusion (C)

The amount of energy that must be supplied to a solid substance (usually in the form of heat) in order to cause a change in the substance's physical state and convert it into a liquid is referred to as the latent heat of fusion, which is also known as the enthalpy of fusion (when the pressure of the environment is kept constant). Because of the usage of this energy in the process of counteracting the attractive force that exists between the molecules, the kinetic energy of the particles does not increase, and as a result, the temperature does not go up.

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An electron traveling horizontally enters a region where a uniform electric field is directed upward. What is the direction of the force exerted on the electron once it has entered the field?.

Answers

It moves downward. An electron moving horizontally passes between two horizontal plates, the upper charged negatively, the lower positively. A uniform, upward-directed electric field exist in the region between the plates, and this field exert an electric force downward on the electron.

What is an electron?

Electrons are involved in gravitational, electromagnetic, and weak interactions, as well as many other physical phenomena, including electricity, magnetism, chemistry, and thermal conductivity.

Since an electron has charge, it has an electric field surrounding it. If the electron is moving in relation to the observer, the observer will track the electron and produce a magnetic field.

According to the Lorentz force law, an electron's velocity will be impacted by electromagnetic fields created by external sources.

When accelerated, electrons emit or take in energy in the form of photons.

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Which energy source contributes to the greatest emissions of gases in the environment during the energy production process?-bio fuels-fossil fuels-nuclear energy-solar energy

Answers

"The energy source that contributes to the greatest emissions of gases in the environment during the energy production process is fossil fuels." The correct option is B.

Fossil fuels, such as coal, oil, and natural gas, release large amounts of carbon dioxide (CO₂) and other pollutants into the atmosphere when burned for energy production. CO₂ is the primary greenhouse gas responsible for climate change and global warming. In addition, the extraction and transportation of fossil fuels also results in emissions of methane and other pollutants.

While nuclear energy (c) produces minimal emissions during energy production, the mining and processing of nuclear fuel can result in emissions of greenhouse gases.

Solar energy (d) and biofuels (a) are considered to be cleaner sources of energy, as they produce much lower emissions of greenhouse gases and other pollutants during energy production. However, the manufacturing and transportation of solar panels and biofuel crops can result in emissions of greenhouse gases.

Therefore, the energy source that contributes to the greatest emissions of gases in the environment during the energy production process is fossil fuels.

The given question is incomplete. The complete question is 'a. bio fuels

b. fossil fuels

c. nuclear energy

d. solar energy'

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Which of the following would NOT be considered proper safety equipment for an outdoor excursion?

Answers

The long sleeves and pants for places with rocks and thick forest growth

are not considered proper safety equipment for an outdoor excursion.

What are safety equipments ?

When we are planning for a journey, we must bring the safety equipments with us especially if we are going to a mountain or watery areas.

Life jackets, jackets for cold etc. must be there during a boat travel, or travel through colder regions. Similarly seat belts for car travel and helmet for biking is necessary.

It is good to avoid long skirts or sleeves during biking to avoid any hanging  anywhere. Long sleeves are not considered as a safety equipment anywhere.

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The options of your question include:

A. helmet for biking

B .long sleeves and pants for places with rocks and thick forest growth

C. bathing suit for water activities

D. a compass or GPS device

How do you find the volume of the parallelepiped with adjacent edges pq,pr and ps where p(3,0,1),q(−1,2,5),r(5,1,−1) and s(0,4,2)?

Answers

The box product of the three vectors yields the volume of a parallelepiped with the vectors and and as its sides. Volume is equal to [a, b, c].

Describe a parallelepiped example.

There are six square-shaped parallelepiped faces on the cube. Dice, ice cubes, Rubik's cubes, etc. are some examples. A face diagonal joins two vertices on the same face but not on the same edge. In this instance, the Face diagonal coincides with the Square diagonal.

Do parallelepipeds count as prisms?

An object with parallelograms for faces is called a parallelepiped. Similar to a parallelepiped, a hexahedron with six parallelogram faces is a parallelepiped as well. A few examples of parallelepipeds are the cube, cuboid, and any rectangular prism.

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You push a 3500 kg SUV with a constant 450 N of force and start it from rest. How much
horsepower are you applying when the SUV is going 1.5 m/s?
(Show work please)

Answers

The power that is applied is approximately 0.9 horsepower when the SUV is going at a velocty of 1.5 m/s.

What is horsepower?

A horsepower is a unit of power that is commonly used to describe the power output of engines and motors.

One horsepower is equivalent to 746 Watts.

The power exerted on the SUV is calculated using the formula below:

P = F * v

where:

P is the power in Watts,F is the force in Newtons, andv is the velocity in m/s.

Substituting the given values, we get:

Power = 450 N * 1.5 m/s

Power = 675 Watts

To convert this to horsepower, divide by 746:

675 W / 746 W/hp

Power  = 0.9 horsepower

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What does the change in the period with respect to the eccentricity tell you about the dependence of the period on the eccentricity?

Answers

What does the shift in the period's relationship to its eccentricity reveal about the period's reliance on the eccentricity The duration is independent of eccentricity.

How is an ellipse's eccentricity determined?

Weirdness e = c/a if the focus's distance from the ellipse's center is "c" and the tip of the ellipse's distance from the central is "a." E = 1 b 2 a 2 is another formula to get the eccentricity of an ellipse. 

What does geometric eccentricity mean?

The term "eccentricity" is defined in terms of the fixed-point known as focus as well as the fixed-line known as the perpendicular line in the plane. The definition of eccentricity in geometry, the eccentricity formula, and the eccentric of several conic sections, including parabola, ellipse, and hyperbola, will all be covered in detail in this article along with worked-out examples.

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how much is kg in gigapascal?

Answers

1 kgf/in² is equal to 6.89475729 × 10^-3 GPa. Here kgf/in² is the  Imperial unit of pressure and GPa is the unit of pressure in the International System of Units (SI).

Kilogram-force per square inch (kgf/in²) and gigapascal (GPa) are units of pressure that have a place with various estimation frameworks. Be that as it may, it is feasible to change over between them utilizing a transformation factor.

1 kgf/in² is equivalent to 6.89475729 × [tex]10^(-3)[/tex]GPa.

In this manner, to change over a tension worth from kgf/in² to GPa, you can duplicate the worth by 6.89475729 × 10^-3. On the other hand, to change over a tension worth from GPa to kgf/in², you can separate the worth by this transformation factor.

For instance, in the event that you have a tension of 100 kgf/in², you can change it over completely to GPa as follows:

100 kgf/in² * 6.89475729 ×[tex]10^-3[/tex] GPa/kgf/in² = 0.689475729 GPa

Likewise, on the off chance that you have a tension of 2 GPa, you can change it over completely to kgf/in² as follows:

2 GPa/6.89475729 × 10^-3 GPa/kgf/in² = 290077.6509 kgf/in²

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The complete question is:

how much kg force per square in gigapascal?

What determines colloid osmotic pressure?

Answers

Colloid osmotic pressure is determined by protein concentration gradient across blood vessel walls.

Colloid osmotic strain (COP) is a sort of osmotic tension not set in stone by the centralization of proteins in an answer. These proteins, regularly egg whites and globulin, are too huge to even consider going through the walls of veins, and thus, they stay in the plasma (the fluid piece of blood) and make a fixation slope across the vein walls. This fixation slope prompts a net development of water into the veins, which assists with keeping up with blood volume and forestall liquid collection in the tissues.

The COP of an answer is relative to the convergence of proteins in the arrangement, with higher centralizations of protein bringing about higher COP. COP is significant in various physiological cycles, including the guideline of circulatory strain, the support of liquid equilibrium, and the anticipation of edema (expanding brought about by liquid gathering in the tissues).

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A 16-g ball at the end of a 1. 4-m string is swung in a horizontal circle. It revolves once every 1. 09 s. What is the magnitude of the string's tension?.

Answers

The stress exerted on the string as it swings in a horizontal circle is 6.56 Newton. frequency is 1/1.09 = 0.92 Hz, and f is 1. (2L) × √T/m\s0.92 = 1/2(1.4) (1.4) (T)/4 multiply everything by 4 ((T/16) 0.92 = 0.36)

3.68 = 1.44 × √T \s √T = 3.68/1.44 = 2.56 \s T = 2.56² = 6.56

Describe a magnitude example.

"How much of a quantity" is how the word "magnitude" is defined. The magnitude, for instance, can be used to describe a comparison of the speeds of a car and a bicycle. Additionally, it can be used to describe how far an object has traveled or how much of an object is represented by its magnitude.

Are size advantages?

The energy released at the earthquake's epicenter is measured in magnitude. Seismograph readings are used to calculate magnitude. The magnitude of the shaking caused by an earthquake is measured by its intensity. The impact on humans is used to gauge intensity.

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The fact that we always see the same face of the Moon tells us that (a) the Moon does not rotate. (b) the Moon's rotation period is the same as its orbital period. (c) the Moon looks the same on both sides.

Answers

The fact that we always see the same face of the Moon tells us that (b) the Moon's rotation period is the same as its orbital period.

What do you call it when everyone's face looks the same?

Every face appears to be identical to every other face. Face blindness, or prosopagnosia, is the medical term for this condition.

Because the period of rotation of the moon on its axis is equal to the period of its revolution around the earth, we always see the same side of the moon, and this side always faces us.

The speed at which it rotates is the same for both rotations. Because of this same speed, one always sees the same side of the moon.

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Which lists the major steps of solar system formation in the correct order? collapse, accretion, condensation collapse, condensation, accretion accretion, condensation, collapse

Answers

The three main phases of the development of the solar system are collapse, condensation, and accretion.

What is the process of accretion?

The process whereby solids accumulate to become progressively larger structures until planets are established is known as accumulation throughout the study of planets. A disc of coarser solid materials mixed with gas at the beginning has a large extent based of around 1% of the volume of the hydrocarbons.

What causes accretion to form?

Small particles are pulled together by attraction forces to form bigger masses during the process of accretion. Gravity draws these particles together, where they combine to form comets and asteroid bodies. Protoplanets are created by collisions between planetesimals.

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What is the walking ghost phase of radiation?

Answers

The "walking ghost phase" of radiation is a term that refers to a short period of time after exposure to a high dose of ionizing radiation, during which the individual may appear to be unaffected by the exposure.

The term originated during the Manhattan Project, when scientists observed that individuals who had received a high dose of radiation would often feel relatively normal for a short period of time before experiencing severe symptoms. During the walking ghost phase, the individual may experience few or no symptoms of radiation exposure, even though their body is sustaining significant damage from the radiation. This is because the initial effects of radiation exposure are often delayed, and the damage to the body's cells and tissues takes time to manifest as symptoms. After the walking ghost phase, the individual may begin to experience symptoms such as nausea, vomiting, diarrhea, fever, and weakness. The severity and duration of these symptoms depend on the dose of radiation and other factors such as the individual's age, health, and medical treatment. It is important to note that the walking ghost phase is a term used primarily in historical contexts, as modern radiation exposure scenarios generally do not involve such high doses of radiation that would produce this effect. Nonetheless, it serves as a reminder of the dangers of ionizing radiation and the importance of taking measures to minimize exposure.

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Psychological perspectives exist:
A. to enforce one particular way of looking at problems.
O B. so that there can be different ways of looking at psychological
questions.
O
C. to address the physical properties of the brain.
D. to explain the science of behavior.

Answers

Psychological perspectives exist to explain the science of behavior, it deals with studying the science of cognitive behavior, hence option D is correct.

What are psychological perspectives?

The five major psychological perspectives are biological, psychodynamic, behavioral, cognitive, and humanistic.

It generally suggests the behavior of humans both consciously and unconsciously and deals with the humans way of thinking and their behavior so it is the science of behavior.

Therefore, psychological perspectives are to explain the science of behavior.

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what is equation for molality?

Answers

Molality (m) is a measure of the concentration of a solute in a solution, and is defined as the number of moles of solute per kilogram of solvent.

The equation for molality is:

m = moles of solute / mass of solvent in kg

Concentration is the ability to focus one's attention and mental effort on a specific task or activity. It involves filtering out distractions and staying attentive to the task at hand. The level of concentration can vary depending on the person, the task, and the environment.

Concentration is an important aspect of productivity and can help individuals achieve their goals more efficiently. A lack of concentration can lead to procrastination, errors, and reduced performance. There are many techniques that can help improve concentration, such as creating a quiet and organized workspace, breaking tasks into smaller manageable parts, taking breaks, and avoiding multitasking. Additionally, engaging in activities that promote mindfulness, such as meditation and yoga, can also improve concentration.

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an electron beam is aimed at two closely spaced slits. the beam is attenuated to produce only 1 electron per minute.

Answers

When an electron beam is aimed at two closely spaced slits, the electrons passing through the slits will interfere with each other, producing an interference pattern on a screen behind the slits. The interference pattern will be a series of bright and dark bands, where the bright bands correspond to constructive interference and the dark bands correspond to destructive interference.

When a beam of electrons is passed through two closely spaced slits, it creates an interference pattern on a screen behind the slits. This pattern results from the wave-like behavior of electrons and the interference between the electrons passing through the two slits. The pattern appears as a series of bright and dark bands, where the position and intensity of the bands are determined by the relative phase of the electrons.

The interference pattern only becomes noticeable with a large number of electrons passing through the slits at the same time. If only one electron is passing through the slits per minute, the pattern will not be easily observable.

"

Complete question

Indicate the result of this experiment:

an electron beam is aimed at two closely spaced slits. the beam is attenuated to produce only 1 electron per minute.

"

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Crane takes 2. 0 minutes to lift a load to the top of a building. The change in gravitati potential energy of the load is 720 kj. What is the useful power output of the crane?.

Answers

6kW is the useful power output of the crane.

Define power.

Energy consumption per second is measured as power. The amount of force necessary to create a unit displacement is another way to quantify power. Power, a scalar quantity, is represented by the letter P. For instance, a light bulb with 100 W of electricity will provide more light than one with 10 W.

The power in a circuit is measured using electrical power, which is given in watts. Electrical and mechanical-electrical techniques are used to measure electrical power in centrifugal pump applications. A watt, which represents power, is equivalent to one joule every second.

Power = Work done /Time taken

Time = 2 minutes = 120 seconds.

Work = 720kJ = 720000J

Power =  720000/120 = 6000W

P = 6kW

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why do higher temperatures often result in greater precipitation

Answers

The higher temperatures often result in greater precipitation because warm air holds more water vapor.

A warmer planet means more precipitation will fall in regions of the world where water vapor is the factor that is currently limiting the amount of precipitation that occurs. This is the condition across a significant portion of the middle and upper latitudes across the Earth.

To put it simply, the amount of precipitation that falls is increasing as temperatures rise because warm air can carry more water vapor. A temperature increase of 1 degree Fahrenheit is equivalent to as much as a 4 percent increase in the amount of water vapor in the atmosphere. Other elements, such as El Nino and La Nina, may also play a role in the amount of rainfall.

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A ferris wheel starts at rest and builds up to a final angular speed of 0. 70 rad/s while rotating through an angular displacement of 2. 5 rad. What is its average angular acceleration?.

Answers

According to the question: the average angular acceleration is 0.70/2.5 is 0.28 rad/s^2.

What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is the angular equivalent of linear acceleration, which is the rate of change of linear velocity over time. Angular acceleration is a vector quantity, having both magnitude and direction. It is usually denoted by the symbol alpha (α).

The average angular acceleration is equal to the change in angular velocity divided by the change in angular displacement. In this case, the change in angular velocity is 0.70 rad/s and the change in angular displacement is 2.5 rad.
Therefore, the average angular acceleration is 0.70/2.5 = 0.28 rad/s^2.

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A man walking at 3. 56 m/s accelerates at 2. 50 m/s2 for 9. 28 s. How far does he get?.

Answers

The total distance traveled by the car when accelerating at a rate of 3. [tex]56 m/s^3[/tex] is 11.2 meters.

What is acceleration?

Acceleration is the rate at which an object's velocity with respect to time changes. Acceleration is defined as a change in velocity over time. It is the pace at which the speed or direction of an item changes. It is determined using the formula a = (vf - vi)/t, where vf is the end velocity, vi is the beginning velocity, and t is the time period. Acceleration can be induced by a force such as gravity or by the motion of an item itself, such as when an automobile accelerates.

In the given question, the man will get a total distance of 40.1 meters.

This is calculated by using the equation d = v0t + 1/2[tex]at^{2}[/tex],

where v0 is the initial velocity (3.56 m/s), a is the acceleration (2.50 m/[tex]s^{2}[/tex]), and t is the time (9.28 s).

Plugging in these values, we get d = 3.56*9.28 + 0.5*2.50*[tex](9.28)^{2}[/tex] = 40.1 meters.

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how is positive feedback supplied in a colpitts oscillator?

Answers

In a Colpitts oscillator, positive feedback is supplied by the capacitive divider formed by two capacitors connected in series between the collector and the emitter of the transistor.

What is the capacitors ?

A capacitor is an electrical component that consists of two conductive plates separated by an insulating material known as a dielectric. The capacitor stores electrical energy in the form of an electrostatic field between the two plates. When a potential difference is applied between the plates, it creates an electric field which can store energy.

The output of the oscillator (the collector voltage) is fed back to the base of the transistor via the capacitive divider. As the collector voltage increases, the voltage across the two capacitors increases, which increases the base current of the transistor, further increasing the collector voltage and thus providing positive feedback.

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What is the derivative of acceleration?

Answers

The derivative of acceleration is also known as jolt or surge. Jolt is defined as the price of alternate acceleration with appreciation to time.

Mathematically, it can be expressed as the second derivative of position with respect to time, or the third derivative of distance with respect to time:

j(t) = a'(t) = d^2v(t)/dt^2 = d^3x(t)/dt^3

Acceleration is a fundamental concept in physics that describes how quickly an object changes its velocity. Velocity is a vector quantity that includes both speed and direction, while the acceleration is the rate of change of velocity with respect to time.

In other words, acceleration measures how much an object's speed or direction changes over time. If an object is moving in a straight line and its velocity is increasing, its acceleration is said to be positive. Conversely, if its velocity is decreasing, its acceleration is negative.

The standard unit of acceleration is meters per second squared (m/s^2). A positive acceleration of 1 m/s^2 means that an object is increasing its speed by 1 meter per second every second.

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