A car moves along a straight line whose equation of motion is given by s = 12t + 3t^2 − 2t^3, where s is in meters and t in seconds. The velocity of car at start will be
a. 7m/s
b. 9m/s
c. 12 m/s
d. 16m/s

The speed of the box when it slid off the table is 9.47 m/s².

What is Projectile Motion?

A particle that is flung obliquely toward the surface of the earth travels along a curved route with constant acceleration that is pointed in the direction of the planet's center. Such a particle's motion and trajectory are both referred to as projectile motion.

The only force acting on a particle when it is launched into the air at some speed is the acceleration due to gravity (g). The downward motion of this acceleration is vertical. The horizontal direction does not experience any acceleration, hence the particle's horizontal velocity stays constant.

It is given that a box is knocked off a 1.4 m high table and then strikes the floor 2.7 m from the edge of the table.

[tex]\implies \triangle x_{y}=-1.4m[/tex] and [tex]\triangle x_{x}=2.7m[/tex]

Here, the acceleration of gravity, g = a = -9.81 m/s²

Under projectile motion, the vertical motion equations corresponding to the given problem is:

[tex]\triangle x_{y}=\frac{1}{2}at^{2}+V_{iy}t[/tex]

Since, [tex]V_{iy}=0[/tex], we get t as

[tex]t=\sqrt{\frac{2 \triangle x_{y} }{a} }[/tex]

Substituting the given values, we get

[tex]t=\sqrt{\frac{2(-1.4)}{-9.81} } \\\implies t=\sqrt{\frac{-2.8}{-9.81} }\\\implies t=0.285s[/tex]

Also, we know that, [tex]\triangle x_{x}=V_{ix} \times t[/tex]

Now, calculating the speed, we get

[tex]V_{ix}=\frac{\triangle x_{x} }{t} \\\implies V_{ix} =\frac{2.7}{0.285} \\[/tex]

[tex]\implies V_{ix}=9.47 m/s^{2}[/tex]

Hence, the speed of the box when it slid off the table is 9.47 m/s².

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The acceleration with which a 50 kg person can slide down a rope without the rope breaking if the maximum tension the rope can withstand as the person slides down is 400 N is 2m/s².

The maximum tension that the rope can withstand, is T= 400N. The mass of the person,m= 50kg. So the upward force on the rope is 400N. And the downward force is 50g N and an acceleration also acts downwards as the person climbs down the rope. So, the net force downwards is 50(g+a). Now the acceleration of the person which the rope can withstand is, a=( 50g-400)/50 = (50×10 -400)/50= (500-400)/50 =100/50=2 m/s². So, the acceleration with which a 50 kg person can slide down a rope without the rope breaking is 2m/s².

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The jogger's velocity at t = 35 s is  [tex]v=-5m/s[/tex]

For [tex]t=35s[/tex]

consider the following:[tex](t_{1} ,x_{1})=(30,50)[/tex] and [tex](t_{2} ,x_{2})=(40,0)[/tex]

Speed is the rate at which something is moving, usually expressed in terms of distance travelled per unit of time. The average jogger typically runs at a velocity of 5 to 8 miles per hour. This is equivalent to 8 to 12 kilometers per hour.Velocity is the rate and direction of something's movement. It is the speed of an object in a particular direction.The speed of the jogger at that particular position is determined by the graph's slope.

[tex]v=\frac{x_{2}-x_{1}}{t_{2}-t_{1}}\\\\[/tex]

   [tex]=\frac{0-50}{40-30}\\\\=-5m/s[/tex]

Consequently, the jogger's speed at time [tex]t=35s[/tex]  the velocity is [tex]v=-5m/s[/tex]

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The concept of radioactive decay was discovered in the late 1800s.

The process through which an unstable atomic nucleus loses energy by generating particles and/or electromagnetic radiation is referred to as radioactive decay. This happens when the nucleus has an excess of energy, which can be created by having more neutrons than protons. The extra energy is released as the nucleus decays to generate a more stable nucleus.

In their research of the elements uranium and radium in 1898, Marie and Pierre Curie discovered the phenomena of radioactive decay. Other scientists, like Ernest Rutherford and Marie Curie's daughter, Irene Joliot-Curie, continued to investigate and experiment with radioactive decay during the following decades, providing a better knowledge of the process and its applications.

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The speaker's power output is 392022.72W  if the sound intensity level is 108 dB at a distance of 17m.

Power output or acoustic power is the rate at which sound energy is radiated, reflected, communicated or got, per unit time.[1] It is defined[2] as "through a surface, the result of the power output , and the part of the molecule speed, at a guide on a superficial level toward the path typical toward the surface, coordinated over that surface."

The SI unit of Power output is the watt (W).[1] It connects with the force of the sound power on a surface encasing a sound source, in air. For a sound source, dissimilar to sound strain, Power output  is neither room-subordinate nor distance-subordinate.Power output  is a property of the field at a point in space, while sound power is a property of a sound source, equivalent to the complete power radiated by that source every which way. Power output going through an area is some of the time called sound motion or acoustic transition through that area.

We know that power output of sound waves is calculated by the formula=4πIr² where I is the sound intensity level and r is the distance.

Since,we have I=108dB and r=17m.Therefore,

P=4×3.14×108×17×17

=>P=1356.48×289

=>P=392022.72W

Hence,speaker's power output is 392022.72W.

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729 in^3 is the volume, in cubic inches, of a cube with surface area 486 in^2.

What is volume?

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

A solid object's surface area is a measurement of the overall space that the object's surface takes up. In comparison to the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is significantly more complex. A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

A = 6V^(2/3)

486 = 6V^(2/3)

81 = V^(2/3)

81^(3/2) = V

729 = V

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In physics, the final speed of an object in freefall (with no friction) depends only on the initial height from which it falls and the acceleration due to gravity, not on its mass.

According to the equation of motion, the final velocity of an object in freefall is given by v = sqrt(2gh), where v is the final velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2 on the Earth's surface), and h is the initial height.

In this scenario, all objects, regardless of their mass, will reach the same final velocity if they are dropped from the same height. This is because the force of gravity acting on an object is proportional to its mass, but the acceleration due to gravity is the same for all objects. So, the final velocity of an object in freefall is not affected by its mass.

It's important to note that this is true only in the absence of friction and air resistance. In real-world scenarios, friction and air resistance can affect the final velocity of an object, and the mass of an object can affect its final velocity to some extent through air resistance

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Star a is approximately 10 times brighter than star b.

The relationship between temperature and brightness of stars is complex and depends on various factors, including the size and composition of the star.

However, a rough estimate can be made using the Stefan-Boltzmann law, which states that the luminosity of a star is proportional to the fourth power of its surface temperature.

If star A is 3.2 times hotter than star B, its luminosity is proportional to the fourth power of 3.2, which is approximately 10. Thus, star A is approximately 10 times brighter than star B.

However, this estimate is a rough approximation and the actual brightness ratio can be different, depending on the specific stars in question and their properties.

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Answer:

The displacement can be represented as vectors in the x and y direction.

The displacement 3.62 m south can be represented as a vector of magnitude 3.62 m and direction -90°.

The displacement 8.10 m northeast can be represented as a vector of magnitude 8.10 m and direction 45°.

The displacement 14.6 m west can be represented as a vector of magnitude 14.6 m and direction -180°.

We can find the x and y components of each displacement vector, and then add those components to find the x and y components of the resultant displacement.

x component of the first displacement: 3.62 * cos(-90°) = 0 m

y component of the first displacement: 3.62 * sin(-90°) = -3.62 m

x component of the second displacement: 8.10 * cos(45°) = 5.65 m

y component of the second displacement: 8.10 * sin(45°) = 5.65 m

x component of the third displacement: 14.6 * cos(-180°) = -14.6 m

y component of the third displacement: 14.6 * sin(-180°) = 0 m

The x and y components of the resultant displacement are the sum of the x and y components of each individual displacement:

x component of the resultant displacement: 0 + 5.65 - 14.6 = -8.95 m

y component of the resultant displacement: -3.62 + 5.65 + 0 = 2.03 m

We can use the Pythagorean theorem to find the magnitude and direction of the resultant displacement:

resultant displacement = √(x^2 + y^2) = √(-8.95^2 + 2.03^2) = 9.06 m

direction = tan^-1(y/x) = tan^-1(2.03/-8.95) = 125.3°

So, the resultant displacement is 9.06 m at an angle of 125.3° with respect to the x-axis (east).

Explanation:

Calculate the slope of the graph at a particular moment in time to determine the velocity of an item moving in one dimension from its location against time graph.

The slope reflects the rate of change of the object's location and consequently its velocity. If the object's location is shown on the y-axis and time is drawn on the x-axis, the velocity may be determined as the position's derivative with respect to time.For example, if the object's location is provided by a mathematical function p(t), its velocity at each moment t may be determined as follows: v(t) = dp(t)/dt The velocity units would be the location units divided by the velocity units. the units of time, which in this case is meters per second (m/s).

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The equivalent of 8 CELSIUS in F is 46.4 F. In 8 C, the majority of individuals dress warmly and wore jackets. You are one of those folks who can endure the cold without the need of a jacket. Freezing is 8 C.

MetaPlus®, a patented mixture found in CELSIUS, activates thermogenesis to quicken metabolism and raise caloric burn. Your metabolic rate is increased by Green Tea, EGCG, Tadalafil, Guarana Seed Extract, Taurine, and Ginger Root Extract in combination with other nutrients in CELSIUS.

The Celsius scale is often used to measure the temperature  The Celsius scale was developed by Swedish astronomer Anders Celsius. The water temperature (°C) on a thermometer is the melting point liquid clear water at standard pressure and sea level.

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The observed speed of the ball is (2.92 ± 0.02) cm/s

Speed is calculated as follows: speed = distance/time.The most often used measure of speed in daily life is the kilometre per hour (km/h), or miles per hour in the US and the UK. The SI's unit of speed is the metre per second (m/s) (mph). We may determine the ball's actual speed using the values provided by computing the following:

[tex]distance = 33.6 ± 0.2 cm[/tex]

[tex]time = 11.49 ± 0.02 s[/tex]

speed = distance / time

          [tex]=\frac{ (33.6 ± 0.2) cm } {(11.49 ± 0.02) s}[/tex]

We may calculate the speed calculation's uncertainty as follows by using the most likely uncertainty (0.5 times the smallest uncertainty):

distance uncertainty = 0.2 cm

uncertainty in time = 0.02 s

Speed uncertainty is equal to (distance uncertainty) / (time uncertainty) 0.5 * (smallest uncertainty)

     [tex]=\frac{{ (0.2) }} {(11.49) }}{± 0.5 * (0.02)}[/tex]      

      [tex]=0.01744 ± 0.01 cm/s[/tex]

Therefore, the observed speed of the ball is (2.92 ± 0.02) cm/s.

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Because the wave function's square has its maximum value at x = 0, that location is also the most likely place to detect a particle.

This depends on the type of particle. Generally, a particle is most likely to be found where its wave function is largest in magnitude. For example, an electron would be most likely to be found in regions of space where its wave function has the highest probability of being found. In other words, a positive and a positive wave function produce a bonding orbital where the likelihood of finding an electron is added, but a positive and a negative wave function produce an anti-bonding orbital where the probability of finding an electron is lower, resulting in repulsion.

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Increasing the size of a sea in a computer model of a weather system is likely to affect temperatures along the coast of that sea. In general, larger bodies of water can have a moderating effect on temperatures, leading to more stable and milder temperatures compared to areas further away from the water. This happens because water has a higher specific heat capacity than land, which means it takes longer to heat up and cool down. As a result, coastal areas near a large sea may experience less extreme temperature fluctuations and a more moderate overall climate compared to areas further inland.

The vector that results when one vector is divided into two additional vectors, known as component vectors, is referred to as a vector projection. Additionally, one will be perpendicular to the second vector, and one will be parallel to it.

projection of u on v=

[tex]\frac{u.v}{|v|} \\\\=\frac{-i+j+\pi .[5i+j-6\pi ]}{\sqrt{25+1+36} } \\\\ =\frac{-5+1-6}{\sqrt{62} } \\=\frac{-10}{\sqrt{62} }[/tex]

The component of u with regard to v is the distance we cover when traversing u and is indicated by the letters v u. The projection of u onto v is known as the vector parallel to v. A unit vector in the direction of v is multiplied by the scalar comp v u to produce the vector known as proj v u, which represents the projection of u onto v. Proj v u is the vector obtained by drawing an arrow instead of the blue line segment that represents comp v u.

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The electric field at x=5.00 cm in Figure 18.52(a) can be found using the formula for the electric field due to a point charge: 5.62 x 10⁵ N/C

E = k × q / x²,

where k is the Coulomb constant, q is the charge, and x is the distance from the charge. Substituting the given values, we get: E = (8.99 x 10⁹N m²/C²) ×(1.57 x 10⁻⁶ C) / (0.05 m)² = 5.62 x 10⁵ N/C

When charge is present in any form, a point in space has an electric field that is connected to it. The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the strength and direction of the electric field. Without any precise information of what generated the field, simply knowing the value of the electric field at a certain location is sufficient to predict what would happen to electric charges nearby.

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Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter.

The application, a single parameter is often labeled t; however, parameters can represent other physical quantities (such as geometric variables) or can be selected arbitrarily for convenience.

Parameterizations are non-unique; more than one set of parametric equations can specify the same curve.

The same curve can be specified by more than one set of parametric equations because parameterizations are not unique.

Therefore, Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter.

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Its speed when its height was half that of its starting point is 28.28 m/s

v = 36 m/s is the roller coaster's final speed.

applying the fundamental motion equation;

V² = U² + 2gh

where;

V is the roller coaster's final speed.

U is the roller coaster's starting speed, which is 0

h is the height achieved at a specific speed.

40² = 0 + (2 x 9.8)h

1600 = 19.6 h

h = 1296/19.6

h = 81.63 m

h₂ = 1/2 h when its height was half that of its beginning point.

h₂ = ¹/₂(81.63 m) = 40.81 m

At h = 40.81 m, V = ?

V² = U² + 2gh

V² = 0 + 2 x 9.8 x 40.81

V² = 800

V = √800

V = 28.28 m/s

As a result, it moved at a speed of 28.28 m/s when its height was half that of its starting point.

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The correct option D .Any one of (i), (ii) and (iii): Any of them might be the trajectory of a positively charged particle that enters a uniform magnetic field at uniform velocity.

We are aware that: F=q(vB) describes the magnetic force acting on such a moving charge in such a magnetic field.

The magnetic field's strength, velocity, and direction all affect the particle's course. Given the direction of all these values, there are three possible scenarios.

Case I: Equation holds true when the particle travels in the magnetic field's direction.

(1) changes to F=0.

As a result, the particle travels along the into because in a straight line.

Case ii. The force develops perpendicular towards the direction of magnetic field when the particle travels perpendicular to it.

As a result, the particle's route is circular.

Case iii) The parallel component of the velocity direction tends to drive the particle all along direction of the magnetic field when the velocity direction has both parallel as well as perpendicular components to it. The particle is moved in a circular motion by the perpendicular component.

As a result, the particle's route is helix-shaped.

Consequently, a positively charged particle's trajectory can be a straight line, a circle, or a helix when it enters a uniform magnetic field having uniform velocity.

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0.8 μC is the final charge on the third sphere

Define electric charge

The physical quality of matter—its electric charge—is what causes it to feel a force when exposed to an electromagnetic field. You can have a positive or negative electric charge (commonly carried by protons and electrons respectively, by convention). Unlike charges attract one another while like charges repel one another. Neutral refers to an object that carries no net charge.

Since the 3 objects are similar and conductors, charge can move freely among them. Since the four objects are identical, the overall charge disperses among them as equally as possible.

q1, q2, q3 are same

Q/3 will be value of q

Q is 7.8-1.4-4.0 i.e. 2.4 μC

q will be 2.4/3 i.e. 0.8 μC

The charge q is positive so we have defecit of electrons

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The relation among energy ,density,strain and stress is that Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation.

This is a term which is referred to as the mass per unit volume of a substance.

We should note that he strain energy per unit volume is known as strain energy density and the the area under the stress-strain means that deformation will occur if the object is continually subjected to the force.

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The stopping distance is 8.33.

Let's use the equation s = v0t + 1/2at^2 to solve for the stopping distance.

s = 8.33t + 0.5(0)(t^2)

s = 8.33t

Since the acceleration is 0, the stopping distance is equal to the total distance the car traveled while its velocity was 8.33.

What is distance?

Distance is the amount of space between two points. It can be measured in various units such as miles, kilometers, feet, and meters. Distance can also be used to describe the length of time or amount of effort it takes to reach a certain point. Distance can be used in reference to physical space or to abstract concepts.

Therefore, The stopping distance is 8.33.

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A study that uses two sets of variables and a scientific methodology is called experimental research. You use the first set as a reference point to calculate the differences between the second set. For instance, quantitative research techniques involve experimentation. You can specify and set your own experimental parameters. The highest temperature to which a solution can be heated, for instance. Although classification factors cannot be defined or set, they can be recognized, and your samples can be chosen in accordance with them. such as a person's gender or age. True experiments must include manipulation, control, random assignment, and random selection. The most important aspects are the manipulation and control of these elements. The Experimental Psychology Method by Using an experimental strategy, one variable is changed to see if it has an impact on another. In order to test a hypothesis, this strategy employs controlled research methods and random subject selection.  T Therefore, any variable in a research project that is actually kept constant is referred to be a control variable. Despite not being a study-relevant variable, it is controlled anyway because it might have an impact on the results. 01-Mar-2021

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An experimental factor (also known as an independent variable) is a variable that is manipulated by the experimenter in order to observe its effect on the outcome of the experiment.

Experimental factors are variables that are controlled and manipulated by a researcher during an experiment. These factors can be either independent variables, which are the conditions the researcher changes, or dependent variables, which are the behaviors or outcomes that are observed and measured as a result of changing the independent variables. Experimental factors are important in determining the results of an experiment, and it is important for researchers to have an understanding of the potential effects of different combinations of factors.

It is the variable that the researcher changes or controls in order to measure the effect it has on the dependent variable, which is the variable being measured.

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The acceleration of the ball is - 25764.47 m/s.

What is velocity?

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

Given that sabine lisicki recorded a serve of 131 mi/h (211 km/h ) in 2014.

Now convert the unit 211 km/h into m/s

211 km/h

= 211km/ 1 h

= (211×1000)m/ 3600s

= 1055/12 m/s

The initial velocity of the ball is 1055/12 m/s. The final velocity of the ball is 0 m/s. The ball covers 0.15 m.

The formula of motion is v² - u² = 2as

0² - (1055/12)² = 2 × a × 0.15

0.30 a = - (1055/12)²

a = -1113025/(144 × 0.30)

a = -25764m/s

The negative sign indicates that it is deceleration.

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Multiply the frequency by the conversion ratio is the formula to convert revolutions per minute (rpm) to radians per second (rad/s) .

What is radian ?

A radian is a unit of measurement used to represent angles in mathematics and physics. It is defined as the ratio of the length of an arc to the radius of the circle it encloses. One radian equals approximately 57.3 degrees. Radians are a more convenient and natural way to represent angles in certain math and physics applications.

Unlike degrees, which are divided into 360 equal parts, radians allow a continuous representation of angles that can be used to describe rotations in a more natural and intuitive way. For example, in trigonometry, the relationship between side lengths and angles in a right triangle can be more accurately and easily expressed using radians.

Radians are used in a variety of fields where describing rotations and angles is important, such as engineering, physics, and computer graphics.

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If you disconnect a circuit from its positive terminal, the electrons stop flowing, and the current stops. The power source would no longer provide a flow of electrons.

The flow of electrons and current ceases if the positive terminal of a circuit is cut off. The flow of electrons would stop coming from the power source. It is safer for you if the negative is eliminated first, which is why they advise doing so. In all contemporary automobiles, the negative cable is fastened to the chassis. Therefore, if you use a wrench to loosen the negative post and the wrench impacts the chassis, nothing happens.

After removing the negative cable, you can proceed with the positive without any concerns. Because the battery is already disconnected, nothing happens if the wrench strikes the chassis once more.

A large spark, and possibly more, will occur if you remove the positive first and then touch the chassis with your wrench. Since there is currently no fuse in the system, a wrench handle can draw a significant amount of electricity. The sparks could be hot enough to throw molten metal fragments, possibly even weld the wrench to the automobile, and cause a dead short to kill the battery. As a result, doing the negative first is significantly safer. However, if you took the positive first without the wrench striking and there were no sparks, everything was OK.

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Lightning is an electrostatic discharge which occurs naturally within the storm. The electrostatic discharge is due to electrically charged regions in the storm.

Lightning can be defined as the naturally occurring electrostatic discharge during which two electrically charged regions positive and negative, both in the same atmosphere or with one on the ground, and other at a certain distance which temporarily neutralize each other, causing the instantaneous release of an average of about one gigajoule of energy from the effect.

The electric field within the storm is not the only field which develops. Below the negatively charged storm base in this region, positive charge begins to pool within the surface of the earth. This positive charge will then shadow the storm whichever direction it goes, and is responsible for the cloud-to-ground lightning.

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Scalar is the measurement of a unit strictly in magnitude. Vector is a measurement that refers to both the magnitude of the unit and the direction of the movement the unit has taken.

Classify each measurement as a scaled or vector a 20 books on a shelf?

a-scalar

b-vectot

c-scalar

d-vector

e-vector

f-scalar

g-scalar

h-scalar

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Permeability is a measure of a material's ability to: transmit the fluids.

Measure of the ease of flow of a fluid through a porous solid is known as permeability. Rock may be extremely porous, but if pores are not connected, it will not have permeability.

Permeability is determined by applying head and determining depth of penetration or the amount of liquid or gas passing through sample.

Widely used are permeability μ = B0/H0 (B0 is the magnetic flux density B at the point P and H0 is the magnetic field H ) and differential permeability μd = dB/dH.

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Answer:

Kinetic energy is turned into potential energy on the way up.

Explanation:

Kinetic energy is proportional to the square of speed. As the baseball slows down, kinetic energy of the baseball decreases.

If [tex]g[/tex] is constant, the gain in gravitational potential energy would be proportional to the change in height. As the height of the baseball increases, the baseball gains gravitational potential energy.

As the baseball rises, its speed gradually decreases while its height increases. Kinetic energy of the baseball is turned into potential energy.

As the baseball falls back to the ground, its speed increases while its height decreases. Potential energy is turned back into kinetic energy.