One type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.700 s for a 0.0225 kg mass?

The value of the linear coefficient of thermal expansion is : α= 2.841 * 10⁻⁶ (ºC)⁻¹

Li = 0.4m

ΔL = 0.1 mm = 0.0001m

T1 = 30ºC

T2 = 118ºC

ΔT = 88ºC

α =ΔL/(Li*ΔT)

α =0.0001m /(0.4m * 88ºC)

α = 2.841 * 10⁻⁶  (ºC)⁻¹

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Scale factor is found by estimating the pixel and data of geometry or image.

[tex]scale. factor=\frac{x}{y} \\\\x=dim. new-shape\\y=dim.original-shape[/tex][tex]Scale factor = \frac{x}{y} \\\\x= new -shape\\y=original- shape[/tex]

Example -

Strain Scale 2: The center of strain in the coordinate plane is the origin (0, 0).

Let ABC be a triangle on the coordinate plane. The points in the coordinate plane are A(0, 2), B(2, 1), C(-2, -2).

If the scale factor is 2, each coordinate point of the original triangle is multiplied by a scale factor of 2.

So the triangle drawn is A'B'C' and the resulting coordinate points are A'(0 , 4), B'(4, 2), C'(-4, -4).

Stretch by a factor of 2, then multiply by 2.

(x,y) → (2x,2y)

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Work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.00s is 12,640 Joules

The following equation is used to calculate the net work necessary to accelerate a merry-go-round from resting to a rotational speeds with one rotation every 7.00 secs:

Work is calculated as (mass x radius x angular acceleration) / 2.

In which: 1440 kg in mass

R = 7.50 meters

Angle acceleration is equal to 2/7.00s times 0.89 rad/s2.

Hence, this mathematical methodology is used to compute the net work needed:

Work is equal to (1440 kg x 7.50m2 x 0.89 rad/s2) / (2 x 7.50m x 1440 kg x 1 revolution/7.00s) / 2 = 5,524,000 J or 5.52 MJ.

Acceleration was its term for the variation in velocity. Generally speaking, and sometimes not, acceleration denotes a shift in speed. Regardless of whether an object is moving in a circle, its velocity route is still changing, therefore it keeps gaining speed.

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[tex]1.24 * 10^{-10} m[/tex] is the minimum wavelength of photon.

The potential difference is ΔV = [tex]10 * 10^{3} V[/tex]

The charge on an electron is q = [tex]-1.6 * 10^{-19} C[/tex]

The change in the potential energy of a charged particle when it moves through a potential difference, ΔV, is

ΔU = qΔV

Here,

ΔU is the change in the potential energy.

q is the charge.

ΔV is the potential difference between the initial and the final position of the charge.

The change in the potential energy of the electron is:

ΔU = [tex]-1.6 * 10^{-19} * 10^{4} = -0.16 * 10^{-15} J[/tex]

According to the law of conservation of energy, the sun of the change in the kinetic and potential energy of the charge should be zero, since the electric field is conservative, and there are no other external forces.

ΔU + ΔK = 0

⇒ΔK = [tex]1.6 * 10^{-15} J[/tex]

Therefore, the kinetic energy acquired by the electron is:

Now when such an electron suddenly stops, it produces x-ray to compensate for the sudden release of energy. The maximum energy of this x-ray is equal to the kinetic energy of the electron.

K = [tex]1.6 * 10^{-15} J[/tex]

E = K

Also, the energy of an electromagnetic wave depends on its wavelength,

λ , by the following equation:

E = hc / λ

here;

h = [tex]6.626 * 10^{-34} J[/tex] is the planks constant

c = [tex]3 * 10^{8} m/s the speed of light[/tex]

Therefore, the minimum wavelength corresponds to the maximum possible energy,

E = K

hc / λ = [tex]1.6 * 10^{-15}[/tex]

λ = [tex]6.626 * 10^{-34} * 3 * 10^{8} / 1.6 * 10^{-15[/tex]

  = [tex]19.878 * 10^{-26} / 1.6 * 10^{-15}[/tex]

  = [tex]1.24 * 10^{-10} m[/tex]

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Population II stars can be detected to be present in the halos of different spiral galaxies and in the huge globular clusters of the milky way galaxy.

It is known to us that -

There are populations I and II stars and stellar collections

These stars can be differentiated on the basis of their age from creation time, chemical constitution, and their location in the galaxy systems

Since, we want to identify the place where a sizeable collection of population II stars can be found in the milky way galaxy, let us first learn a bit about the population II stars.

Population II stars constitute of the oldest identified stars and clusters. These stars were created nearly 1,000,000,000 - 15,000,000,000 years ago.

These population II stars can be detected to be present in the halos of different spiral galaxies and in the huge globular clusters of the milky way galaxy.

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The velocity of a vehicle is typically expressed relative to ground.

Velocity is the speed of something that is given direction.

velocity is the measurement  to a  body's "pace of change of  the displacement in relation to time" whenever the main  body is traveling through along a straight route.

It is common knowledge of  that the word "linear" refers to be something that is totally straight; therefore,  when the body moves in a straight path, it is said to be linear velocity .

Alternatively, velocity is the  distance traveled by a body traveling in a specified to the direction during of a predetermined period of time. Thus, the fundamental idea of linear velocity is the  provided by the union of these two quantities.

Because it always has the direction of velocity is a vector.

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The frequency of the voltage across the coil is 60 Hz.

The tendency of a coil to resist internal current fluctuations is known as self-inductance. Every time a coil's current varies, an EMF is produced that is inversely proportional to the rate of change of the coil's current.

Given the self-inductance (L) is 16 mH and resistance is 6.0 Ω.

L = 16×10⁻³ H

The frequency can be calculated using the inductive resistance formula, [tex]f=\frac{X_L}{2\pi L}[/tex] where, XL is inductive resistance and L is inductance.

First, we have to find inductive resistance using the phase angle formula.

[tex]\begin{aligned}\tan\phi&= \frac{X_L-X_C}{R}\\X_L&=R\tan\phi\\&=6\times \tan 45^{\circ}\\&=6\times1\\&=\mathrm{6\;\Omega}\end{aligned}[/tex]

Then, frequency is

[tex]\begin{aligned}f&=\frac{6}{2\pi \times 16\times 10^{-3}}\\&=\mathrm{60\;Hz}\end{aligned}[/tex]

The answer is 60 Hz.

The complete question is -

A coil with a self-inductance of 16 mH and a resistance of 6.0 Ω is connected to an ac source whose frequency can be varied. At what frequency will the voltage across the coil lead the current through the coil by 45°?

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The wheels on a bicycle have a 10 inch radius. If the bike must travel exactly 2000 inches, the number of revolutions the wheel would make will be 31.85 revolutions.

The perimeter of the circle is called the circumference of circle.

Given, radius of the wheel = 10 inches

Diameter of the wheel = 20 inches

Length required to cover = 2000 inches

For one revolution, distance equal to the circumference moved.

1 rev = π D

1 rev = π * 20

1 rev = 62.8 inches

Number of revolutions to travel 2000 inches is 2000/62.8 = 31.85 rev

Thus, the number of revolutions required are 31.85 rev.

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In order to fill the pool to an average depth of 4.8 ft., the water needed is 483,101 gallons

The formula for the volume of rectangular cuboid is:

V = l x w x h

Where:

l = length

w = width

h = height

Parameters given in the problem:

l = 50 m

w = 25 m

h = 4.8 ft. = 1.463 m

Plug these parameters into the formula:

V = 50 x 25 x 1.463

V = 1,828.75 m³

1 m³ = 264.17 gallons

Hence,

V = 1,828.75 m³ = 1,828.75 x  264.17 gallons

V = 483,101 gallons

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There are 4 questions here that need to be solved.

a. The velocity of the astronaut & book system after the collision (using conservation of momentum) is 0.19 m/s

b. The initial kinetic energy of the system is 24J

c. The final kinetic energy of the system is 1.14J

d. The impulse exerted by the book on the astronaut is 11.43 kg.m/s

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during acceleration, the body maintains this kinetic energy unless its speed changes.

Now, let's answer the question.

a.

m1 book = 3kg

m2 astronaut = 60kg

vi1 = 4m/s

vi2 = 0m/s

Vf = final speed after collision

Now, let calculate using conservation of momentum formula

ρi = ρf

m1 * vi1 + m2 * v2 = (m1 + m2) * vf

3 * 4 + 60 * 0 = (3 + 60) * vf

12 = 63vf

vf = 0.19 m/s (rounded)

So, the velocity of the astronaut-book system after the collision is 0.19 m/s.

b. Initial kinetic energy will be calculated using kinetic energy formula

KEi = 1/2 * m1 * Vi1^2

= 1/2 * 3 * 4^2

= 24J

So, the initial kinetic energy of the system is 24J

c. Final kinetic energy will be calculated as follows

KEf = 1/2 * (m1 + m2) * vf^2

= 1/2 * (3 + 60) * 0.19^2

= 1.137J

So, the final kinetic energy of the system is 1.137J

d. To calculate the impulse, it is basically the change in momentum of the book, calculated as follows

I (impulse) = m1 * (Vi1 - Vf)

= 3 * (4-0.19)

= 11.43 Kg.m/s

Therefore, the impulse exerted by the book on the astronaut is 11.43 Kg.m/s

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The volume of the gold with given specs is 1.610 cm³.

Density of the gold as given in the question : 19300 kg/m³

Density of the gold in changed units i.e g/cm³ : 19.3 g/cm³

The measure of how densely a material is packed together is called density. As the mass per unit volume, it has that definition. Density Formula: = m/V, m is the object's mass, and V is its volume.

Density = Mass / volume

=> Volume = Mass / density

Substituting the values :

Volume = (31.103)/(19.3)

Volume = 1.610 cm³

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Gravitational force between objects gets weaker as objects move farther apart, and it is stronger between objects that are closer together.

The gravitational force between two objects is given by:

F = G x M x m / r²

Where:

G = constant of gravity

M = mass of object 1

m = mass of object 2

r = distance between two objects

If the masses are constant, then the gravitational force is inversely proportional to the square of distance between those objects, or mathematically:

F  ∝  1/r²

By inversely proportional means if the distance between two objects decreases, the gravitational force increases or gets stronger; and if the distance between two objects increases, the gravitational force decreases or gets weaker.

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In order for the law of conservation of momentum to be true there should not be any external forces acting on the system.

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Because of the size and variety of galaxies in the Local group, I would anticipate finding large elliptical galaxies there. There isn't a huge elliptical galaxy right now, but that could change when other galaxies develop and give rise to one.

A galaxy type known as an elliptical galaxies has an appearance that is smooth and almost featureless, and it has a roughly ellipsoidal form. These galaxies, along with spiral and lenticular galaxies, are one of the four primary kinds of galaxy that Edwin Hubble described in his 1936 book The Realm of the Nebulae and Hubble sequence. Elliptical (E) galaxies, lenticular (S0) galaxies with their large-scale disks, and ES galaxies with their intermediate-scale disks are all parts of the "early-type" galaxy population.

Most elliptical galaxies are made up of older, low-mass stars with scarce interstellar space and little star formation, and they frequently have a dense globular cluster population surrounding them. According to estimates, the Virgo Supercluster contains between 10% and 15% elliptical galaxies.

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The velocity of a non-relativistic electron whose de broglie wavelength is 3.637 nm is 5.82 x 10^6 m/s.

The velocity of a non-relativistic electron can be calculated using the formula v = h / mλ,  where h  = Planck's constant, m  = the mass of the electron, and λ  = the de Broglie wavelength of the electron.

Assuming the mass of the electron is 9.11 x 10^-31 kg, the velocity of the electron can be calculated as follows:

v = (6.63 x 10^-34 m^2 kg / s) / (9.11 x 10^-31 kg * 3.637 x 10^-9 m)

This works out to be approximately 5.82 x 10^6 m/s.

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67.51 rpm is angular speed for a 500 g ball swinging in a 20 cm radius circle at the end of a 1.0 m long string

A net external torque is required for rigid bodies in order for there to be an angular acceleration. This is not true for non-rigid bodies, though: As an illustration, a figure skater may accelerate her spin without the need for an external force by merely squeezing her arms and legs inward.

Given that,

mass of ball (m) = 500 gm = 0.5 kg

radius of ball (R) = 20 cm = 0.2 m

length of string = 1 m

Let, θ be the angle formed by the string with vertical.

T cos θ = mg ........(i)

T sin θ = mω²r ..........(ii)

Now, (ii) ÷ (i)

T sin θ/ T cos θ = mω²r/ mg

or, tan θ = ω²r/ g

or,  ω = [tex]\sqrt{g/r}[/tex] tanθ

By Pythagoras theorem,

h² + R² = l²

or, h = [tex]\sqrt{(1)^2 - (0.2)^2}[/tex]

or, h = 0.98 m

Next,

tan θ = R/h

tan θ = 1 m/0.98 m

Now, ω = [tex]\sqrt{g/r}[/tex] tanθ

or, ω = [tex]\sqrt{9.8/0.2}[/tex] 1 m/0.98 m

or, ω =  7.07 rad/sec

So, putting the values:

ω = 2πN/60

or, 7.07 = 2πN/60

or, N = 67.51 rpm.

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The value of 0.000000041712 N written in standard notations can be expressed as 41.712 × [tex]10^{-9}[/tex] N in scientific notation.

This is a way of expressing large and small quantity as a simple number. The number will be multiply by a power of ten which is known as multiplying factor

Given that the value of force each object applies on the other is the same which is 0.000000041712 newtons, but in the opposite direction. This value is written in standard notations.

This number can be expressed as

0.000000041712 N = 41.712 nN

That is, 41.712 nano Newton

The multiplying factor of nano is [tex]10^{-9}[/tex]

To express this value in scientific notation, multiply the number 41.712 by the multiplying factor. That is,

0.000000041712 N = 41.712 ×  [tex]10^{-9}[/tex] Newtons

Therefore, the value of 0.000000041712 N of force each object in scientific notation is 41.712 × [tex]10^{-9}[/tex] N

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When two objects collide, they exert forces on each other that can cause one or both of them to move in a certain direction and with a certain quantity of energy.

These forces can be calculated by considering the mass of each object, the velocity of each object, and the distance between them. Depending on the type of collision, the forces exerted on each object will differ.

Inelastic collisions occur when the objects stick together or the kinetic energy of the objects is not conserved. In this type of collision, the forces exerted on each object are equal in magnitude but opposite in direction. This means that one object is pushing the other in one direction, while the other object is pushing in the other direction. As a result, the objects will move in a combined direction with a decreased kinetic energy.

Elastic collisions occur when the objects bounce off one another and the kinetic energy of the objects is conserved. In this type of collision, the forces exerted on each object are still equal in magnitude but opposite in direction. However, the objects will move in opposite directions with the same kinetic energy as before.

The forces exerted on objects in a collision can also be affected by external factors such as friction, air resistance, and gravity. In a collision with friction, the forces exerted on each object will be in the same direction and the kinetic energy of the objects will be decreased due to the energy lost to heat. In a collision with air resistance, the forces exerted on each object will be in the same direction and the kinetic energy of the objects will be decreased due to the energy lost to air drag. In a collision with gravity, the forces exerted on each object will be in the same direction and the kinetic energy of the objects will be decreased due to the energy lost to gravity.

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The adaptive behavior that is beneficial to the animals that live in the extreme cold climates was found to be Lots of tissues, like fat, with low thermal conductivity.

define thermal conductivity ?

A material's thermal conductivity is a measure of its ability to conduct heat.

Heat transfer occurs at a slower rate in low thermal conductivity materials than in high thermal conductivity materials. Metals, for example, have high thermal conductivity and are particularly effective at transferring heat, whereas insulating materials like Rockwool or Styrofoam are the reverse. Materials with high thermal conductivity are commonly used in heat sink applications, while materials with low thermal conductivity are used as thermal insulation. Thermal resistivity is the counterpart of thermal conductivity.

Lots of tissues, such as fat, with low heat conductivity were discovered to be useful to animals living in extreme cold climates.

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Answer:Magnitude of the car's acceleration is 3.5 m/s²

Given:

Mass of car = 1,000 kg

Net force applied by car = 3,500 N

Find:

Magnitude of the car's acceleration

Computation:

Net force = Mass × Acceleration

So,

3,500 = 1,000 × Acceleration

Acceleration = 3,500 / 1,000

Acceleration = 3.5 m/s²

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Angular speed = 0.4 rad/s , when a 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg m2 is rotating freely with an angular speed of 1.0 rad/s.

radius = 5 m

moment of inertia = 2000 kg-m²

angular speed = 1.0 rad/s

mass = 60 kg

to find out

angular speed

solution

Rotational momentum of merry-go-round = I?

The momentum we experience here is expressed as

momentum = 2000 × 1

momentum = 2000 kg-m²/s

and  

Inertia of people will be here as

Inertia of people = mr² = 60 × 5²

Inertia of people = 1500 kg-m²

so Inertia of people for two people  

1500 × 2 = 3000

and

Currently, angular momentum conservation

(Momentum + People's Inertia) = Moment of Inertia Angular Speed angular velocity

2000 ×  1 = (2000 + 3000 ) ω

solve we get now  

ω = 0.4 rad/s

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Nutritionists express energy in calories, which are in fact 1000 real calories. one real calorie is equivalent to 4.18 joules, the universal energy unit. thus, one nutrition calorie is equivalent to 4.18 kilojoules.

Joule is the fundamental energy unit of the metric system, or the International System of Units in a later, more thorough version (SI). In the end, the meter, kilogram, and second are used to characterize it.

Calorie: In the past, the definition of a calorie included the heating of water. Consequently, according to a conventional definition, one calorie is the quantity of heat needed to raise the temperature of one gram of water by one degree Celsius, from 14.5 to 15.5 degrees.

The "calorie" measured for other temperature ranges differs slightly from this, which is frequently referred to as the 15 °C calorie. The calorie has more recently been defined in terms of the joule; historically, the calorie and joule have been equivalent to mechanical heat.

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Buy quality and consume less

Repurpose our clothes

Buy Second Hand  Swap, & Rent Clothing

Change our attitudes toward fast fashion

Shop and drop for charity

Choose organic cotton

Rent or borrow clothes

Watch your washing

Even the greenest garment uses resources for production and transport to your home, creating some environmental impact.More and more fashion brands take into account the environmental and social impact of their production.Don’t throw your clothes in the normal bins! Most of them consist of synthetic, non-biodegradable fiber and will just pile up in the landfill.

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Answer:

6.3 m/min

Explanation:

Circumference of a circle = 2πr

r = D/2 = 40m/2 = 20m

C = 2π(20m) = 125.7 m

speed = distance/time = (125.7 m) / (20  min)  = 6.3 m/min

When 1 kg of water (specific heat 4200 j/(kg c)) and 1 kg of a mystery substance are combined, the mystery substance has a heat capacity of 8400 J/kg C. Initial water temperature is 35 c.

The quantity of heat that must be applied to an object in order to cause a unit change in temperature is known as the specific heat  or thermal capacity of that object. Joules per kelvin (J/K) is the SI unit for heat capacity. An extensive property is heat capacity. The unidentified compound was discovered to be extremely similar to the drug fluoxetine but not exactly the same. In actuality, the two compounds are isomers, which are atoms that are bound to one another in distinct ways despite having the same number and type of atoms.

1*4200(35-25) = 1*C(25-20)

C = (1*4200*10)/5

C = 8400J/kg C

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Potential energy stored in spring is calculated by multiplying force with displacement.

Elastic potential energy is considered as the potential energy stored in spring when it is stretched or deformed. It is calculated as force multiplied by displacement. This energy is the energy stored in the spring by virtue of its position. It is the work done to stretch the spring.

When spring is stretched, it is displaced. It comes to its equilibrium position after the removal of the force. So, it exerts an equal and opposite force When it is stretched. Work is done by this force that is stored in the form of potential energy.

Since potential energy = force × displacement

and, force = spring constant × displacement

So, potential energy = spring constant × [tex](displacement)^{2}[/tex]

P.E. = k ×[tex]x^{2}[/tex]

Where,

k = spring constant

x = displacement caused due to stretching

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(A) The distance from point A to point B to the nearest tenth of a foot will be 3.4 ft.

(B)  The value of 0 to the nearest tenth of a degree will be 54.8°

SOH, CAH, and TOA are the trigonometry ratios that need to be solved in order to find necessary measures or angles in a right triangle.

A) Reference angle  = 28 degrees

Distance  A-B = ?

Adjacent = 3 ft

We will calculate the distance between A-B by using the trigonometry function, CAH, that is:

    Cos ∅ = adj ÷ hyp

    Cos 28° = 3 ÷ A-B

    A-B = 3 ÷ Cos 28°

    A-B = 3.4 ft

B) Reference angle  = ?

Distance  A-B = 5.2 ft

Adjacent = 3 ft

We will calculate the distance between A-B by using the trigonometry function, CAH, that is:

    Cos ∅ = adj ÷ hyp

Put the values

    Cos ∅ = 3 ÷ 5.2

    ∅ = Cos⁻¹ (3 ÷ 5.2)

    ∅ = 54.8°

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The majority of the energy emitted by stars with temperatures above 30,000 K is in the form of short wavelengths, which is why they appear blue. That is revealed by the blue.

Given that blue light has a higher frequency than red, it denotes a greater level of energy. As stars are dynamic beings that can have a variety of photospheric energies depending on their mass and stage of life, there are undoubtedly some limitations to this. The basic rule, in my opinion, is that blue light has a larger energy level (is hotter) than red light. The red giant Betelgeuse has a lower surface temperature but a higher core temperature than the Sun because the heat produced by fusion in the core is distributed across a larger area. Because the temperature in the center depends more on mass,  over a much larger surface.

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The relation between acceleration and mass is inversely proportional, according to Newton's second law, and there is a direct relationship between acceleration and net external force.

One of the most significant laws in all physics is Newton's second law. F = ma, where F (force) and a (acceleration) are both vector values, can be used to represent a body whose mass m is constant. A body is accelerated according to the equation if there is a net force acting on it.

Therefore, An object will remain at rest or move in a straight path at constant speed in the absence of acceleration. A force that is not balanced causes an object to accelerate.

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2.6496 J has the potential to reach its maximum point, according to the statement.

Speed is the rate at which the position of an item shifts in any direction. Speed is defined as the proportion of the distance traveled to the time required to cover that distance. Speed is a scalar quantity because it has a velocity and no quantity. Galileo Galilei, an Italian physicist, is recognized with becoming the first to calculate speed by dividing it by the distance traveled and the time required. Galileo defined speed as the distance covered in a predetermined period of time.

Potential energy becomes kinetic energy in this situation;

K.E. = ½ mv²

= ½ x 0.23 x (4.8)²

= 2.6496 J(joule)

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