how much work must be done by an external force on an object (sliding over a frictionless, horizontal surface) to accelerate the object from a speed vv to a speed 2v2v?

Answers

Answer 1

Using the concepts of work, we got that we need to work three times of the previous work to accelerate the object from a speed v to a speed 2v.

We know that to change the velocity of any object we need to do some work on it.

When an object having some mass m moving with velocity v, then the kinetic energy stored in that object is given by(KE₁) =(1/2)mv².

Now, When an object having some mass m moving with velocity 2v,then the kinetic energy stored in that object is given by(KE₂) =(1/2)m(2v)².

New kinetic energy is =4[(1/2)mv²] or 4KE₁

So, net work to accelerate the object is =KE₂-KE₁

                                                               W=4KE₁-KE₁=3KE₁.

Hence,  the amount of  work must be done by an external force on an object (sliding over a frictionless, horizontal surface) to accelerate the object from a speed v to a speed 2v is 3 times the energy stored on a object.

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Related Questions

how can an object be accelerating while maintaining a constant speed? what force or forces can cause this type of acceleration and how exactly must they be oriented relative to the motion of the object?

Answers

Even if an object's speed is constant, it can nonetheless accelerate if its direction changes.

Newton postulated that an object will only accelerate in the presence of a net or unbalanced force.

How can an object accelerate while maintaining a constant speed?

An object's velocity (speed and direction) changes at a certain rate, which is called acceleration. As a result, even if an object's speed remains constant, its direction may shift, causing it to accelerate. But the acceleration of an object will be 0 if its velocity is constant.

According to Newton, an item will only accelerate if another force is operating on it that is net or imbalanced. If an imbalanced force is present, the object will accelerate and change its direction and speed, or both.

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what is the direction of the induced current in the loop when the loop is above the solenoid, moving downward?

Answers

The direction of the induced current in the loop will be clockwise.

What is induced current?The current brought on by the electromagnetic induction phenomena is known as the induced current.Electric power generation depends heavily on electromagnetic induction. It can be used for many things. After conducting numerous tests in his London lab for more than ten years, Michael Faraday made his discovery of electromagnetic induction in 1831.The size of the induced EMF is proportional to the rate of change of the magnetic field in which the wire is situated, according to Faraday's second law of induction.[tex]e = -N*\frac{1}{dt}[/tex]ФWhere "e" denotes the intensity of the induced emf, "Ф" denotes the quantity of magnetic flux connecting the coil, and "N" is the coil's number of turns. The induced current will flow in a direction that opposes the change in the magnetic field, according to the negative sign.

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A hospital engineer finds an unidentified radioactive source using his Geiger counter in the nuclear medicine department. explain how the engineer could identify what type of radiation is being emitted from the source.
.
Any Idias? ​

Answers

Ionising radiation such as alpha and beta particles or gamma rays are detected using the Geiger-Müller (GM) tube. The radiation enters the tube through a very thin window at one end.

A radioisotope used for diagnostics must generate enough gamma rays to escape from the body and have a short enough half-life to decay away shortly after imaging is concluded. Tc-99 is the most often used radioisotope in medicine, accounting for approximately 80% of all nuclear medicine treatments.

Nuclear imaging is used to study the function of organs and tissues. During the operation, a trace amount of a radioactive chemical is used to aid in the examination. Body tissue absorbs the radioactive substance, known as a radionuclide (radiopharmaceutical or radioactive tracer).

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what would happen if you strike the pipe with supports placed at the nodes for the first vibration mode

Answers

If you strike the pipe with supports placed at the nodes for the first vibration mode, you will experience a vibration that has a frequency of about 5 Hz.

The amplitude of this vibration will be approximately 1.5 mm and it will occur in a single direction. This means that the pipe will vibrate up and down, but not side to side.

The vibrations caused by striking the pipe will not last very long. In fact, they are only likely to last for about 0.1 seconds before they disappear entirely. They may also cause damage to nearby objects like walls or furniture if they are located too close to where you strike the pipe.

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(b) The cars collide and car B experiences an impulse. Car A continues to move in the same
direction, with a momentum of 21 000 kg m/s.
(i) Calculate the momentum of car B immediately after the collision.
momentum =
llicion
[1]

Answers

The momentum of car B immediately after the collision if the momentum of car A is 21 000 kg m/s after collision is 15000 kg m / s

p = m v

p = Momentum

m = Mass

v = Velocity

m1 = 2000 kg

u1 = 18 m / s

pi1 = 2000 * 18

pi1 = 36000 kg m / s

m2 = 1200 kg

u2 = 0

pi2 = 0

pf1 = 21000

According to law of conservation of momentum

pi1 + pi2 = pf1 + pf2

pi1 = Initial momentum of car A

pi2 = Initial momentum of car B

pf1 = Final momentum of car A

pf2 = Final momentum of car B

pf2 = pi1 + pi2 - pf1

pf2 = 36000 + 0 - 21000

pf2 = 15000 kg m / s

Therefore, the momentum of car B immediately after the collision is 15000 kg m / s

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consider two cars moving along the same straight road in opposite directions. car a has a mass of 500kg500kg and has a constant speed of 20m/s20m/s ; car b has a mass of 800kg800kg and a constant speed of 15m/s15m/s . what can you say about the net forces on the cars?

Answers

The net force on both the cars car a and car B will be zero.

According to the first law of motion stated by Newton,

An object would continuously written it's state of motion or rest if the net force on the object is zero. It means that, no matter how many forces are working on the body if they all cancel out each other and the net force becomes zero the body will continue it's same state.

Also according to second law of Newton,

The force is rate of change of momentum with respect to time.

F = ma

Here, both the cars the car A of mass 500 kg and the car B of mass 800 kg are moving with a constant velocity of 20 m/s and 15 m/s respectively.

If the velocity of the car is not changing with time it means that there is no acceleration on the body.

If there is no acceleration on the body, then there is no net force on the body.

So, we can conclude hair that the net force on the cards is zero.

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how much heat is lost when a 640g piece of copper cools for 375°C to 26°C? the specific heat is 0.09 cal/g°C≈

Answers

The heat energy lost during the cooling of metal can be calculated using calorimetric equation. The heat lost here during cooling of copper is 20102.4 Cal.

What is calorimetry?

Calorimetry is an analytical tool used to determine the heat energy released  or absorbed from a chemical reaction or physical change. The heat energy q is related to the mass m of the substance, specific heat capacity c and the temperature difference ΔT as follows:

q = m c  ΔT.

It is given that the mass of copper metal is 640 g having specific heat of 0.09 Cal/g° C cooled from 375  to 26 degree Celsius. The heat lost from the metal can be calculated as follows:

q = 640 g × 0.09 Cal/g° C × (375 - 26 ° C )

  = 20102.4 Cal.

Therefore, the heat lost from the metal is 20102.4 Cal.

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when there is no wind, an airplane is flying 70 m/s with its nose pointed due north. a wind begins blowing toward the west with a constant speed relative to the ground of 18 m/s. what is the direction and speed of the plane relative to the ground?

Answers

The relative velocity of the plane with respect to the ground will be 72.57 at an angle of tan⁻¹(0.25) from the north.

The speed of the airplane when there is no wind is 70 m/s in the north direction.

The speed of the wind is 18m/s related to the ground in the direction of West.

As we know, that both west and north are perpendicular to each other, the resultant speed by the observer on the ground will be observed in the direction of the resultant of both the speeds.

Let us say that we is the resultant of both the speeds,

Because the two speeds are perpendicular to each other the resultant is given by,

R = √((70)²+(18)²)

R = 72.27m/s.

The angle with north,

Tan A = 18/70

Tan A = 0.25

So, the speed of the airplane from the ground will be observed as 72.27 degrees and at an angle of tan ⁻¹(0.25) from the north.

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the bubble of cold (blue) air on the left is separated from the warm (brown) air by a boundary, or narrow transition zone, called a

Answers

The heated (brown) air is separated from the cold (blue) air bubble on the left. A(n) is the term used to describe

What separates the air masses at their boundary?

"Fronts" are the borders that are formed when air masses converge. Cold front in three dimensions. Temperature changes caused by a front's motion can be used to identify it. A cold front causes a warmer air mass to be replaced by a colder one. Another name for it is a "dryline" or "dry front." a line or zone between two air masses that have different densities and, as a result, are typically at different temperatures. A moving front is given a name based on the air mass that is advancing; for example, a cold front if colder air is going forward. The front is the line separating two air masses. A front typically has overcast, stormy weather. Four separate fronts exist: the Cold, Warm, Stationary, and Occluded fronts. A cold front arises when two cold air masses collide with warm air masses.

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the energy of a photon is 6.78 x 10-19 j. what is the wavelength of the radiation? 3.41 x 106 m incorrect response 3.26 x 10-24 m correct answer 2.93 x 10-7 m 3.41 x 10-3 m

Answers

The wavelength of the radiation is 2.93×10⁻⁷ m

Given,

The energy of photon E=6.78×10⁻¹⁹

now, E=hc/λ

λ=hc/E

=6.626×10⁻³⁴×3×10⁸/6.78×10⁻¹⁹

=2.93×10⁻⁷ m

Radiation is the emission or transmission of energy through a material medium or across space in the form of waves or particles.

According to the energy of the radiated particles, radiation is frequently classified as either ionizing or non-ionizing. Ionizing radiation has an energy level of more than 10 eV, which is sufficient to ionize atoms and molecules as well as rupture chemical bonds. Due to the significant difference in how destructive it is to living things, this is a crucial distinction. Ionizing radiation is frequently produced by radioactive substances that release radiation in the form of helium nuclei, electrons or positrons, or photons, respectively.

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A crane is shown below. It is lifting a load of 5000N. The counterweight weighs 4400N and distance y is 9m. What must distance x be if the crane is balanced? Give your answer to one decimal place.

Answers

The distance x must be 7.92 m for the crane to be balanced according to principle of conservation of energy.

What is the distance x?

The distance x can be determined by applying the principle of conservation of energy as shown below.

According to this principle of conservation of energy;

the input work (energy) = output work (energy)

F₁d₁ = F₀d₀

where;

F₁ is the input forced₁ is the input distanceF₀ is the output forced₀ is the output force

(4400) x (9) = 5000x

39600 = 5000x

x = 39600/5000

x = 7.92 m

Thus, the crate a balanced condition, the output work must be equal to the input work.

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PLS help really confused will mark brainiest to the right answer.

Answers

The base ball would have more acceleration than the bowling ball. Option C.

What is the acceleration?

We know that from the Newton second law of motion, force is the product of the mass and the acceleration of an object. We can write that; F = ma

F = force

m= mass

a= acceleration

It is clear from the equation that we have shown above that the accaleration of the object does not only depend on the force but also on mass of the object. We can now write;

a = F/m

The higher the mass the lesser the acceleration of the object as we saw above.

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an at-filled, parallel-plate capacitor has a capacitance of 1.32 pf. the separation of the plates is doubled and wax 1s inserted between them. the new capacitance is 2.57 pf. find the dielectric constant of the wax.

Answers

The dielectric constant of the wax is 4.

The energy stored in a capacitor is proportional to the square of the charge divided by the capacitance but doubling the plate spacing halves the capacitance. Capacitance is directly proportional to the electrostatic force field between the plates. This magnetic field gets stronger the closer the plates are to each other. Therefore, the capacitance increases as the distance between the plates decrease.

Therefore, we can conclude that doubling the area and distance between the plates of a parallel plate capacitor does not change the capacitance. A capacitor consists of two conductive plates separated by an insulator and is used to store an electrical charge. When you apply a voltage to a capacitor, one plate will be negatively charged and the other plate will be positively charged.

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among the four galilean satellites of jupiter (io, europa, ganymede, and callisto), which one is the biggest satellite in our solar system and which one does not have a core?

Answers

Ganymede is one of the biggest satellites in the solar system.

All four satellites have the core but the Callisto has the smallest core.

Ganymede is the only moon known to have its own magnetic field, discovered in 1996 by NASA's Galileo spacecraft. Magnetic fields cause auroras, bands of hot, electrically charged, glowing gas in the regions orbiting the Moon's north and south poles.

Callisto is his second-largest moon on Jupiter and his third-largest moon in the solar system. Its surface is the most cratered body in the solar system. An image of Callisto taken from a passing spacecraft shows bright white patches contrasting with dark areas

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if there were no air resistance, how long would it take a free-falling skydiver to fall from a plane at 3100 m to an altitude of 490 m , where she will pull her ripcord? what would her speed be at 490 m ? (in reality, the air resistance will restrict her speed to perhaps 150 km/h .)

Answers

Her speed be at 490 m will be 226 m/s

What is speed?Speed is the rate at which an object moves along a path in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar value. For example, 50 km/hr (31 mph (ca. 50 km/h)) describes the speed of a car traveling along a road, whereas 50 km/hr west describes the velocity.

Calculation

a) initial height, [tex]h_{i}[/tex] = 3100 m

[tex]h_{f}[/tex] = 490 m

time taken, t

Using the second equation is motion

3100–490 = 0.5 × 9.8 ×[tex]t^{2}[/tex]

solving for t

t = 23.07 s

b) let the speed is u

u =[tex]\sqrt{2*g*(h_{i} -h_{f} )}[/tex]

u = [tex]\sqrt{(2*9.8 * (3100-490))}[/tex]

u = 226 m/s

Hence, her speed is 226 m/s

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Her speed be at 490 m will be 226 m/s.

What is speed?Speed is the rate at which an object moves along a path in time, whereas velocity is the rate and direction of movement.In other words, velocity is a vector, whereas speed is a scalar value.For example, 50 km/hr (31 mph (ca. 50 km/h)) describes the speed of a car traveling along a road, whereas 50 km/hr west describes the velocity.

initial height,[tex]h_i[/tex]  = 3100 m

[tex]h_f[/tex] = 490 m

time taken, t

Using the second equation is motion

3100–490 = 0.5 × 9.8 ×

solving for t

t = 23.07 s

b) let the speed is u

[tex]&\mathrm{u}=\sqrt{2 * g *\left(h_i-h_f\right)} \\[/tex]

[tex]&\mathrm{u}=\sqrt{(2 * 9.8 *(3100-490))}[/tex]

u = 226 m/s

Hence, her speed is 226 m/s

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A girl riding a bicycle at 2.0 m/s throws a tennis ball horizontally forward at a speed of 1.0 m/s from a height of 1.5 m. At the same moment, a boy standing on the sidewalk drops a tennis ball straight down from a height of 1.5 m.

What is the initial speed of the girl's ball relative to the boy? ​

WILL GIVE BRAINLIEST

Answers

The initial speed of the girl's ball relative to the boy is 3 m/s. ​

What is the initial speed of the girl's ball?

The initial speed of the girl's ball relative to the boy depends on the time of motion of the girls ball.

The time of motion of the ball from the given height is calculated as follows;

h = vt + ¹/₂gt²

where

v is the initial velocity of the ballt is the time of motion of the ballg is acceleration due to gravity

h = 0 + ¹/₂gt²

h = ¹/₂gt²

t = √(2h/g)

t = √(2 x 1.5 / 9.8)

t = 0.55 s

The final velocity of the ball is calculated as;

v = gt

v = 9.8 x 0.55

v = 5.39 m/s

However, since we are looking for the initial speed of the girl's ball relative to the boy, we will ignore the final velocity of the ball.

The initial velocity of the ball = 0

The initial velocity of the girl's ball = 2 m/s + 1 m/s = 3 m/s

The relative velocity = 3 m/s - 0 m/s = 3 m/s

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Nuclear power plant meltdowns can be hazardous. Which of these is a result
related to the meltdown of a nuclear power plant?
O significant changes in sea level in the region
O change in weather conditions in a widespread area
O increased production in carbon dioxide as air pollution
O dangers to the health of people and the environment Science

Answers

D: Dangers to the health of people and the environment science. If a power plant melts down like Chernobyl it will leave radiation all around the area that melted down and causes nearby cities for many miles to have to evacuate. All of the land and animals normally perish in that zone, and anyone that obtained radiation poising can die in a pretty bad way too.

among the four giant planets, which one has the global-average density smaller than the density of liquid water and which one has the strongest magnetic field?

Answers

Saturn is less dense than Earth because it has a bigger volume.

Of all the planets in the Solar System, Saturn has the lowest density.

Why is Saturn so low in density?Saturn is not solid like Earth; instead, it is composed of gases.Saturn is hence quite light for its size.In fact, Saturn has a density that is even lower than that of water, making it the least dense planet in our solar system.The second-largest planet in the Solar System, Saturn is enormously big.However, it is less thick than water and primarily composed of gas.It can float on water since it is lighter than water.Because they have densities greater than water, none of the other planets in our solar system are able to perform this.

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You land on an unexplored foreign planet, and have with you a 2.5 tool. You determine that the force of gravity acting on the tool
is 19.5. What is the gravitational acceleration of the planet?

Answers

Based on the value of the mass of the tool and the force of gravity on that planet, the gravitational acceleration of the planet is 7.8 m/s².

What is the gravitational acceleration of that planet?

The mass and force of gravity acting on a body are related by the formula given below:

Force of gravity = mass * gravitational acceleration

The mass of a body is constant but the force of gravity acting on a body or the weight of the body varies depending on the value of the gravitational acceleration.

Considering the given values:

Mass of tool = 2.5 kg

Force of gravity acting on the tool = 19.5

gravitational acceleration = force of gravity / mass

gravitational acceleration = 19.5 / 2.5

gravitational acceleration = 7.8 m/s²

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9. Determine the total capacitance between points A and B. D н А- В с E с C C с с с c​

Answers

Answer:

Determine the total capacitance between points A and B in the figure below. C =104F C = 5uF C=20uF MAE ce Select the best answer: 2.84uF 2.80uF O 2.90pF 2.86F

Explanation:

hoped it help cutie if u need more help js ask meh

A student wants to collect data during an experiment about the transfer of kinetic energy in a sample of water and ice. Which tool will help her collect the necessary data?(1 point)
Responses

meter stick


balance


thermometer


graduated cylinder

Answers

If a student wants to collect data during an experiment about the transfer of kinetic energy in a sample of water and ice, then the tool that will help her collect the necessary data is a thermometer.

What is a thermometer?

A thermometer is a device used in different applications in order to measure the temperature in the surrounding environment and or open systems such as organisms (including humans).

Therefore, with this data, we can see that a thermometer can be used to determine the temperature of an organism and also of the surrounding media.

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Answer:

your answer will be thermometer

Explanation:

if you go to connexus and are doing the science

Thermal Energy Unit Test 10 qestions 8th grd unit 5 test lesson 12 here are the correct answers

1. A. metal is heated from room temperature to 200'C.

2. B. The particles will have more space between them as steam, but they will be moving at the same speed in both states.

3. C. The potential energy decreases due to the tighter arrangement of the particles.

4. B. an increase in heat and an increase in kinetic energy until a phase change occurs.

5. C. thermometer

6. B. 4.

7. D. convection

8. C. Air moves from the areas of higher temperature to areas of lower temperature.

9. C. The temperature of the ice increases, while the temperature of the water decreases

10. A. heat transfer by radiation.

i hope this helps and please let me know if it does! = ) <3

in comparison to the atmosphere of venus, the vastly different atmospheric character of mars is likely due to a/an

Answers

Reverse greenhouse gases are most likely the root cause of Venus' atmosphere and Mars' drastically differing atmospheric characteristics.

The greenhouse effect causes the Earth to absorb more sunlight, heating the planet.

The process by which solar radiation out of a celestial object's sun is absorbed and scattered by the object's earth's atmosphere prevents that energy from reaching the object's surface is known as the anti-greenhouse effect, which would be the opposite of something like the greenhouse effect.

A runaway refrigerator, also known as the reverse greenhouse effect, happened on Mars. Mars' original temperature was lower than that of the Earth because Mars was a little further from the Sun. This indicated that a layer of liquid water formed on the surface when the water vapor condensed.

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if the net acceleration is downward but has a magnitude less than g, then which has the larger magnitude, the force f or the tension in the rope?

Answers

If the net acceleration is downward but has a magnitude less than G, the force of F has a larger magnitude than the tension in the rope.

How to determine the net acceleration?

We do know thаt the net force equаls mаss times the аccelerаtion. Now if we tаke the block аs а system, meаning we mаke use of the equаtion, mаss times аccelerаtion equаls net force, on the block. Now the lаst element of the rope is pulling the block upwаrds. This is becаuse the block pulls the rope down, hence due to newton's third lаw the rope too should pull the block, but in opposite directions, thаt is upwаrds. Hence the tension аcts upwаrds on the block. Therefore the net force is weight downwаrds аnd tension upwаrds, this equаls mаss times аccelerаtion,

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Consider a relation representing the present position of molecules in a closed container. The attributes are an id for the molecule, the x, y, and z coordinates of the molecule, and its velocity in the x, y, and z dimensions. What fd’s would you expect to hold? what are the keys?.

Answers

The following are some examples of the functional dependencies that can be held:

PX, PY, and PZ →VX

PX, PY, and PZ →VY

PX, PY, and PZ →VZ

Define functional dependence.

Functional dependency is a term that describes a constraint that is usually used to explain the link between two (2) different sets of attributes, where one set may predict the true value of the other attributes accurately and uniquely.

The coordinates of the molecule in this example would be PX, PY, and PZ, while the velocities of those coordinates would be VX, VY, and VZ. Functional dependencies can so be illustrated by the following examples:

PX, PY, and PZ → VX

PX, PY, and PZ → VY

PX, PY, and PZ → VZ

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How much energy is stored in the 180-µF capacitor of a camera flash unit charged to 300.0 V?

Answers

Energy is stored in the 180-µF capacitor of a camera flash unit charged to 300.0 V is 8.10 J.

A capacitor is a tool that stores electrical electricity in an electric-powered field by way of the distinctive feature of accumulating electric expenses on two close surfaces insulated from each other. it's miles a passive digital component with terminals.

The impact of a capacitor is called capacitance. A capacitor is an electrical component that shops capacity power. Capacitors hold wonderful and bad electricity on separate plates separated by way of an insulator. A capacitor(s) is called cap(s) for brief.

Calculation:-

energy stored in capacitor = C V^2 /2  

= 180 x 10^-6  x 300^2  / 2   = 8.10 J

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Light travels approximately 982,080,000 ft/s, and one year has approximately 32,000,000 seconds. A light year is the distance light travels in one year.

State the speed in mi/s, using scientific notation. (1 mile = 5280 feet exactly, by definition; i.e., this is not a measurement.)

Answers

The speed of light in miles per second (mi/s) is 186,000 mi/s.

What is the distance travelled by light in a year?

The distance travelled by light in a year is known as light-year. This distance travelled by light in a year depends on the speed of light.

The speed of light in a year is given as 982,080,000 ft/s. The unit of this speed of light in feet per seconds can be converted into miles per second.

The speed of light in miles per second (mi/s) is calculated by using the following conversion factor.

1 mile = 5280 feet

982,080,000 ft/s = 982,080,000 ft/s x 1 mile/5280 ft

982,080,000 ft/s = 186,000 miles/s

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Which formula is used to find the growth rate of a population? O Death rate - Birth rate = Growth rate O Death rate x Birth rate= Growth rate O Birth rate - Death rate= Growth rate O Death rate + Birth rate = Growth rate​

Answers

The formula used to find the growth rate of a population is Birth rate - Death rate = Growth rate.

Population growth = ( Initial population - Population at time measured ) /  Initial population * 100

The population growth rate is also called as rate of natural increase. The average change in population size annually is population growth rate.

Birth rate is the number of births occurring per 1000 population. Death rate is the number of deaths occurring per 1000 population. Since the values are taken per 1000, to find the percentage value the values are divided by 10.

Therefore, the formula used to find the growth rate of a population is Birth rate - Death rate = Growth rate.

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xii. a fan rotating with an initial angular velocity of 1200 rev/min is switched off. in 2 seconds, the angular velocity decreases to 300 rev/min. assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?

Answers

The blade goes through 25 evolutions throughout this period.

What does angular velocity mean?

Angular velocity is the speed at which an object rotates or revolves around an axis or alters the angle between two bodies. The angle between a line on one body and a line on the other in the illustration serves as a representation of this displacement.

Formula using,

Ф = (ω+ω')t/2

Where Ф = amount of revolution the blade undergo,

Given: ω = 1200 rev/min,

ω' = 300 rev/min,

t = 2 seconds = (2/60) min = 1/30 min

Substitute into equation 1

Ф = (1200+300)(1/30)/2

Ф = 1500/(30×2)

Ф = 1500/60

Ф = 25revolutions.

The blade goes through 25 evolutions throughout this period.

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a projector has a focal length of 10.0 cm. after focusing, the lcd object is 10.5 cm from the lens. how many cm is the image screen from the lens?

Answers

The image screen is 10.5 cm from the lens.

The focal length of the lens is 10.0 cm, so once the lens focuses, it will be 10.0 cm from the object. In order to find how many centimeters away from the lens the image screen is, we need to use trigonometry and Pythagorean theorem.

Where x is the distance between our object and our projector in meters, and y is the distance between our projector and our image screen in meters. We know that y = 10.5 cm, or 0.105 m; we also know that x = 0 meters because our object is placed directly on top of our projector (therefore it's at 0 m).

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Explain the relationships you see in your data tables, and whether they agree with Newton’s Second Law of Motion (Fnet=ma).

Answers

3rd and 6th row in second table do not agrees with the equation ( Force = mass * acceleration ) , rest follows the equation

There is a relation between force , mass and acceleration of the body , in a such a way that it agrees with newton's third law which is  Force = mass * acceleration

All the given data in the table follows this relation except where

mass = 150 kg

a = 0.67 [tex]m/s^{2}[/tex]

F (given ) = 100 N

calculated force = ma = 150 * 0.67 =  100.5 N

mass = 300 kg

force (given) = 100 N

a = 0.33 [tex]m/s^{2}[/tex]

calculated force = ma = 300 * 0.33 = 99 N

rest of the data completely follow the equation F = ma

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