marathon runner keep track of speed using units of pace - minutes/mile. olivia has a pace of 7 min/mile what is her speed in feet/ sec

Sir Isaac Newton was one of the most influential scientists of all time. His work in physics, optics, calculus, and astronomy had a profound impact on the development of modern science.

One of Newton's most significant contributions was the development of calculus. Calculus allowed for the mathematical treatment of motion, which was essential for the development of Newtonian mechanics. Newton's calculus provided the mathematical groundwork for the development of modern physics, which relies heavily on mathematical models. Newton's calculus also allowed for the development of the mathematical tools necessary for understanding the motion of bodies in space, which is essential for the development of astronomy.

Without Newton's discoveries, modern science would be drastically different. The development of modern physics and astronomy would be severely hindered without the mathematical tools provided by calculus. Additionally, the development of mathematical models and the advancement of scientific understanding of the physical world would be significantly delayed.

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The electric field of a long line charge at a radical distance  is 29.55V/m

Any sort of charge causes an electric field to be associated to a location in space. The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the magnitude and direction of the electric field.Knowing the value of the electric field at a certain area alone is sufficient to forecast what will happen to neighboring electric charges without any specific knowledge of what caused the field.

For Infinite length

Electric field = [tex]E=\frac{2K\lambda}{r}[/tex]

Where ,K=[tex]\frac{1}{4\pi \epsilon}[/tex]

[tex]\lambda[/tex]= charge per unit length

potential difference :

[tex]V_{2} -V_{1} =-{2K\lambda}ln\frac{r_{2} }{r_{1}}[/tex]

E = [tex]4(\frac{V}{M} )[/tex] = [tex]\frac{2K\lambda}{r_{1} }[/tex] at r=3

[tex]2K\lambda[/tex]=12V    [tex]\rightarrow(1)[/tex]

[tex]V_{2} -V_{1} =-{2K\lambda}ln\frac{r_{2} }{r_{1}}[/tex]= -24

From (1)

24=-12[tex]ln\frac{r_{2} }{r_{1}}[/tex]

[tex]ln\frac{r_{2} }{r_{1}}[/tex]=-2

[tex]\frac{r_{2} }{r_{1}}[/tex]=[tex]e^-2[/tex]

[tex]r_{2} =r_{1}e^-2[/tex]

Electric field at [tex]r_{2}[/tex] = [tex]\frac{2K\lambda}{r_{2} }[/tex]

[tex]\frac{12}{r_{1}e^-2 } =\frac{12e^2}{3}[/tex]

E=[tex]4e^2[/tex]=29.55 V/m

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The focal length of the glasses for a far-sighted student that has a near point of 196 cm would be 22.17

Lenses with a focal length defined as the distance between a lens's center and the point at which objects come into clear focus. A lens equation, also known as a lens formula, is an equation that links the focal length, image distance, and object distance of a spherical mirror. It is written as:

                                                   1/u + 1/v = 1/f

Where:

v = distance of the image from the lens

u = distance of the object from the lens

f = focal length of the lens

Thus, the focal length for a far-sighted student that has a near point of 196 cm would be:

(1/25) + (1/196) = 1/f

f = 4900/221

f = 22.17 cm

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The type of noise pollution that escalated rapidly in the late 1990s was electronic noise pollution.

The late 1990s saw an alarming increase in electronic noise pollution, which is any unwanted or undesired sound caused by electronic devices and appliances. This type of noise pollution can range from the humming of air conditioning units to the buzzing of computer servers, and is one of the leading causes of environmental degradation.

As such, it is important for individuals, businesses, and government organizations to take proactive steps to reduce this type of noise pollution. By investing in sound-proofing measures and noise-canceling technology, we can ensure that our environment remains free of unwanted electronic noise pollution.

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Answer:

The speed of the marble can be found using the equation for kinetic energy, KE = (1/2)mv^2, where m is the mass of the marble and v is its velocity. Since the marble is being launched by the spring, we can use the equation for potential energy, PE = (1/2)kx^2, to find its velocity.

The potential energy of the spring is (1/2)kx^2 = (1/2)(3000 N/m)(0.2 m)^2 = 600 J

The kinetic energy of the marble is KE = (1/2)mv^2, where m = 1kg, so KE = (1/2)(1 kg)(v^2).

So 600 J = (1/2)(1 kg)(v^2)

Solving for v, we get:

v = sqrt(1200 J/ 1kg)

v = sqrt(1200 m^2/s^2/ 1kg)

v = 34.64 m/s.

Explanation:

Explained above

Speed: According to the problem the cliff is 680 m high

Speed is a measure of the rate at which an object or person moves. It is a scalar quantity, meaning it has only magnitude, not direction. Common units of speed include kilometres per hour (km/h), miles per hour (mph), metres per second (m/s), and feet per second (ft/s). Speed is related to velocity, which is a measure of the rate of change of an object's position. Speed is an important property of any moving object, and can be used to measure the motion of an object relative to another object.

The speed of sound is 340 m/s, which means that it takes 1 second for sound to travel 340 m. Since we know that the sound of the rock striking the ocean was heard 4.0 seconds after it was dropped, then the rock must have fallen for a distance of 4 times 340 m, or 1360 m.
To calculate the height of the cliff, we need to use the formula:
Height = Distance/2
Plugging in 1360 m for the distance, we get:
Height = 1360/2 = 680 m
Therefore, the cliff is 680 m high.

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(i) period of the flashes is,  1/60 minute/flash

(ii) frequency of the flashing is, 60 Hertz

The frequency of a repeated event is the number of occurrences per unit of time. The common unit of expression is Hertz (Hz), which stands for cycles per second. For instance, a wave has a frequency of 1 Hz if it completes one cycle in one second. A wave moves faster and completes more cycles in a given period of time as its frequency increases.

Given that,

A flasher generates 60° regular flashes in one minutes

(i) The period of the flashes is the time it takes for one complete cycle of the flashing, or the time between two consecutive flashes. In this case, the flasher generates 60 flashes in one minute, so the period of each flash is given by:

Period = 1 minute / 60 flashes

           = 1/60 minute

           = 1/60 minute/flash

(ii) The frequency of the flashing is the number of flashes that occur in one unit of time, typically measured in Hertz (Hz), where 1 Hz = 1 cycle per second. To convert the period to frequency, we simply take the reciprocal of the period:

Frequency = 1 / Period

                  = 1 / (1/60 minute/flash)

                  = 60 flashes/minute

                  = 60 Hz

So the frequency of the flashing is 60 Hertz.

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The Uranus have 13 faint rings and 27 small moons in the solar system.

Uranus, the third-largest planet in our solar system and the seventh from the Sun, is incredibly chilly and windy. The ice giant spins at a nearly 90-degree angle from the axis of its orbit, encircled by 13 foggy rings and 27 tiny moons. One of the two frost giants in the outer solar system is Uranus (the other is Neptune). A heated, dense fluid comprised of the "icy" substances water, methane, and ammonia made up the vast majority (80% or more) of the planet's mass.

The age of Uranus' rings is predicted to be less than 600 million years, considering them extremely juvenile. The collisional fragmentation of several former moons that ringed the planets resulted to the Uranian ring system.

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The correct statement is that a body's rotation cannot change if the net torque acting on it is zero. This means that if there is no net torque acting on a body, its angular velocity will remain the same and it will not be able to rotate.

This is because when the net torque acting on a body is zero, the sum of all external torques is also zero. This means that the body's angular momentum is conserved, meaning that the body's angular velocity remains the same over time and it is unable to change its rotation. This can be demonstrated through Newton's second law of motion, which states that the rate of change of angular momentum is equal to the net torque acting on the body.

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If you are in a speedboat which has a top speed of 22 m/s.  the time you travel for the northerly part of the trip is 20.6 s. The velocity of the boat relative to the shore is: 18.5m/s.

The time for the northerly part of the trip can be calculated by using the equation for displacement:

displacement = velocity * time

Rearranging for time:

time = displacement / velocity

Plugging in the given values:

time = 325 m / 15.8 m/s = 20.6 s

To find the velocity of the boat relative to the shore, we need to find the total displacement of the boat and divide it by the total time.

The displacement in the westward direction is 22 m/s * 13.6 s = 304.2 m

The total displacement is the sum of the displacement in the two directions, so:

displacement = 304.2 m + 325 m

displacement = 629.2 m

The total time is the sum of the times for the two parts of the trip, so:

time = 13.6 s + 20.5 s
time  = 34.2 s

The velocity of the boat relative to the shore can be calculated as:

velocity = displacement / time

velocity = 629.2 m / 34.2s

velocity  = 18.4 m/s

Therefore  the time you travel for the northerly part of the trip is 20.6 s. The velocity of the boat relative to the shore is: 18.4m/s.

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D. Solidification. The process of solidification occurs when the kinetic energy of the particles of matter decreases to the point at which attractive forces pull the particles into fixed positions.

More kinetic energy causes particles to travel more quickly and widely apart. Less energetic particles move more slowly and maintain their proximity.

Kinetic energy is used to drive the vibrational motion of particles in solids. Heat causes a solid's particles to vibrate more rapidly, giving them more kinetic energy. Faster vibrating particles collide more frequently and more forcefully. The particles are separated farther as a result.

Solution: Because matter particles7 are constantly moving, they produce kinetic energy by doing so.

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The measurement device that he should use is B. a voltmeter

A voltmeter is used for measuring the potential differences. A voltmeter is an instrument used for measuring the potential difference between two points in an electrical circuit.

Hence, it can be seen that because Kentucky fried chicken is asked to measure the difference in electric potential at two different points, they should make use of a voltmeter

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Connecting a system of vessels with different diameters in parallel reduces the total effective resistance.

The resistance of a vessel depends on its diameter and length; as the diameter of the vessel increases, its resistance decreases. In parallel connections, blood flow is split between different vessels, with the largest vessels carrying the most blood flow and the smallest vessels less.

As a result, the overall resistance of the system decreases as the total cross-sectional area available for blood flow increases. This reduces the total effective resistance and reduces resistance to blood flow.

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True. The points where the potential is the same in three dimensional space lie on a surface known as an equipotential surface. This is a surface in which the electric potential is constant and equal to a specific value.

Potential is the capacity to become or develop into something in the future. It is the ability to do something, or the likelihood of achieving a certain outcome. Potential is something that can be realized or achieved given the right circumstances, actions, or resources. It is the possibility of growth, success, or development. Potential is the latent capacity for accomplishment that exists in any individual, group, or organization. Potential can also refer to the amount of energy that can be produced from a given source. Potential is the promise of something greater, yet to be achieved.

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The block swings to a height of approximately 2894 m.

The momentum of the system of bullet and block before the collision is equal to the momentum of the system after the collision. So conservation of momentum can be used in solving this problem.

Before the collision, the momentum of the bullet is:

p_bullet = m_bullet * v = 15 g * 380 m/s = 5700 g * m/s

After the collision, the momentum of the bullet and the block is:

p_total = m_block * v_block = (3 kg) * v_block

where v_block is the velocity of the block after the collision.

Using the conservation of momentum equation, we can find the velocity of the block:

5700 g * m/s = (3 kg) * v_block

v_block = 5700 g * m/s / (3 kg) = 1900 m/s

Now, we can use this velocity to find the height that the block swings. The height of the block swings can be found using the following equation:

h = (v_[tex]block^2[/tex]) / (2 * g)

where g is the acceleration due to gravity (9.8 [tex]m/s^2[/tex]).

[tex]h = (1900 m/s)^2 / (2 * 9.8 m/s^2) = 56875 m^2 / (19.6 m/s^2)[/tex] = 2894 m

So, the block swings to a height of approximately 2894 m.

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All of the objects will hit the ground at the same time, when released from the same height, if there is no air resistance.

The free fall velocity of the object is determined by the formula, v = √(2gh). Where g is acceleration due to gravity and h is the height of the freefall. We  can see that downward velocity depends on the height which is same for every object. Also all objects fall under the same acceleration of gravity irrespective of their mass.

So if we neglect the air resistance which depends on the exposed surface area of object, then all the object will hit the ground at the same time.

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The force generated by a 2.25 bar pressure on an area of 3cm^2 is 67.5N where Force applied directly relates to pressure.

Given the pressure (P) = 2.25bar

The area  (A) = 3cm^2 = 3 x 10^-4m

We know that pressure (P) = Force(F) per unit area = P = F/A

The amount of force acting on a given area is measured by its pressure. As a result, a force exerted across a smaller area will result in more pressure. Area and pressure are inversely related. Both pounds per square inch (psi) and newtons per square meter (N/m2) are acceptable units of measurement for this pressure.

Then, 1bar pressure = 10^5Pascals

F = 2.25 x 10^5 x 3 x 10^-4 = 67.5N

Hence the force required generated by a 2.25 bar pressure on an area of 3 cm2 is 67.5N

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It will take 8.42 seconds by the basketball to complete 16 dribbles.

Frequency is defined as the number of oscillation, cycles completed by the wave or any object in one second. If the object is exhibiting periodic motion. Its SI unit is hertz or sec⁻¹. In the question frequency is the number of time, the ball dribbles in one second.

The frequency of the dribble, n = 1.9 hz. It means ball dibbles 1.9 times in a second.

So time taken to complete 1 dribble, T = 1/1.9 = 0.526 sec

Total time taken to complete 16 dribbles, T₁₆ = 16 × 0.526

T₁₆ = 8.42 seconds

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Answer:

The kinetic energy of the same amount of water would be greater at the bottom of the drop of river A (waterfall) than in river B (hydroelectric dam.)

Explanation:

In a uniform gravitational field, the gravitational potential energy of an object is proportional to height relative to the ground. It is given that the top of the two drops are of the same height. As a result, the same amount of water at the top of the drops would have the same amount of gravitational potential energy.

When water moves from the top of the drop to the bottom, gravitational potential energy is converted into kinetic energy.

In the waterfall of river A, the change in potential energy is nearly entirely converted into kinetic energy. However, in river B, some of that potential energy is converted into the mechanical energy of the hydroelectric generators. Since energy is conserved, the same amount water at the bottom of the river B drop would have less kinetic energy.

The quantity of matter in a fluid or an object is measured by its mass. The kilogram (kg) is the SI unit of mass, while lower masses can also be defined in grams (g). A balance is what you would use to gauge mass.

The Internacional Numbering Systems, often known as the Units of Measurement (si) and sometimes SI in all language families, has become the most widely used system of measurement in the world. It is the most recent metric measurement system.

We require the Transnational System of Units in order to keep numbers in use on a global scale comparable and consistent. Standardizing such measurements supports society's confidence in data by preserving uniformity and precision.

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The fundamental concepts in physics, chemistry, and mathematics that are the foundation for more specific disciplines of study are gained through an understanding of astronomy.

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To measure an object's mass using Newton's version of Kepler's third law, we need to know the object's distance from the center of a gravitational field and the time it takes to complete one orbit around that center.

Newton's version of Kepler's third law states that the square of the period of a planet's orbit (the time it takes to complete one orbit) is proportional to the cube of its average distance from the center of the gravitational field. Mathematically, this can be expressed as T^2 = k * r^3, where T is the period, k is a constant of proportionality, and r is the average distance from the center of the gravitational field.

To use this equation to measure an object's mass, we need to first determine the value of T and r for the object. This can be done by observing the object as it orbits around a known mass (such as a planet or a star) and measuring the time it takes to complete one orbit and the average distance from the center of the gravitational field.

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When a balloon and sweater are rubbed against each other, one of them becomes negative charged while the other becomes positive charged. Both are equal and oppositely charged.

The sweater may become positively charged and the balloon negatively charged if electrons moved from the sweater to the balloon.

Friction is one method of creating charges. Electrons are transported from one thing to another when they come into contact. While the other object acquires a negative charge, one gets positively charged.

It's possible that electrons will transfer from the sweater to the balloon when it is rubbed against it. The balloon acquires a negative charge, whereas the sweater gains a positive charge.

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During this time charlotte traveled a distance of: 395.36 ft

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this problem is:

v= x/t

Where:

Information about the problem:

Converting the velocity from (mi/h) to (ft/s) we have:

v = 57.5 mi/h * 5280 ft/ 1 mi * 1 h/3600 s

v= 84.3 ft/s

Applying the velocity and isolating the distance we have:

x = 84.3 ft/s * 4.69 s

x = 395.36 ft

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About 3.2 TJ energy is liberated when two moles of 126C atoms are formed from their individual protons, neutrons and electrons.

The energy released when two moles of 126C atoms are formed from their individual protons, neutrons, and electrons can be calculated using the equation for nuclear binding energy:

[tex]B = Z * BE/A + (A - Z) * BE/A - m_n * c^2[/tex]

where Z is the number of protons, BE/A is the binding energy per nucleon, A is the total number of nucleons, m_n is the mass of a neutron, and c is the speed of light.

For carbon-12 (12C), the binding energy per nucleon is about 8.49 MeV, and for carbon-126 (126C), it's about 8.70 MeV.

The energy released when two moles of 126C atoms are formed can then be calculated as:

[tex]2 moles * Avogadro's number * 8.70 MeV = (2 * 6.022 * 10^23 atoms) * 8.70 MeV[/tex] = 3.2 TJ

This calculation gives an estimate of the amount of energy released when two moles of 126C atoms are formed from their individual protons, neutrons, and electrons. However, this is a simplified calculation, and there are many other factors that can affect the actual energy released, including the formation of intermediate isotopes and the production of gamma radiation and other particles.

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A spherical black body 1115 cm in diameter at a temperature of 800 K will radiate approximately 5085798.666 W.

The total power radiated from a black body can be calculated using the Stefan-Boltzmann law, which states that the power per unit area (P) emitted from a black body at temperature T is given by:

P = σ x T^4

where σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4).

The total power radiated from a sphere with diameter D can be calculated as:

P = 4 x π x (D/2)^2 x σ x T^4

Plugging in the values D = 1115 cm, T = 800 K, we get:

P = 4 x π x (1115/2 cm)^2 x 5.67 x 10^-8 W/m^2K^4 x (800 K)^4

P = (4 x π x (1115/2 cm)^2) x (5.67 x 10^-8 W/m^2K^4) x (800^4 K^4)

P = (4 x π x (0.1115 m)^2) x (5.67 x 10^-8 W/m^2K^4) x (800^4 K^4)

Converting the units to watts, we get:

P = 4 x π x (0.1115 m)^2 x 5.67 x 10^-8 W/m^2K^4 x 800^4 K^4

P = 4 x π x 0.0126225 m^2 x 5.67 x 10^-8 W/m^2K^4 x 64000000 K^4

P = 4 x π x 0.0126225 m^2 x 5.67 x 10^-8 x 64000000 W

P = 4 x 3.14 x 0.0126225 m^2 x 5.67 x 10^-8 x 64000000 W

P = 5085798.666 W

So, a spherical black body 1115 cm in diameter at a temperature of 800 K will radiate approximately 5085798.666 W.

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Approximately 12 tires of volume 1.2 ft³ can be inflated to 28 psig using the given conditions.

To calculate the number of tires that can be inflated, we need to compare the initial and final conditions of the air in the tank and the desired pressure in the tires. Use the ideal gas law to solve this problem.

Given:

Tank volume (V₁) = 3 ft³

Tank pressure (P₁) = 120 psig

Tank temperature (T₁) = 80°F

Tire volume (V₂) = 1.2 ft³

Tire pressure (P₂) = 28 psig

First, let's convert the temperature from Fahrenheit to Rankine:

T₁ = 80°F + 459.67 = 539.67 °R

Next, let's convert the tank pressure from psig to absolute pressure (psi):

P₁ = 120 psig + 14.7 psia = 134.7 psia

Since the volume and pressure of the tire are given directly, we don't need to convert them.

Now, let's apply the ideal gas law to the initial and final conditions:

For the tank:

PV = nRT

For the tire:

PV = nRT

Since the moles of air (n) remains constant, we can equate the two expressions:

(P₁ x V₁) / T₁ = (P₂ x V₂) / T₂

Now, we need to solve for the unknown value, which is the number of tires (n).

Rearranging the equation:

n = (P₁ x  V₁ x T₂) / (P₂ x V₂ x T₁)

Substituting the given values:

n = (134.7 x 3 xT₂) / (28 x 1.2 x 539.67 °R)

Now, let's calculate the value of n:

n = (134.7 x 3 x T2) / (28 x 1.2 x 539.67)

To find the number of tires, we need to know the value of T₂, which represents the temperature of the tire.

If the temperature is not specified, we'll assume it remains the same as the initial temperature (T₁ = 539.67 °R).

Substituting T₂ = T₁:

n = (134.7 x 3 x 539.67) / (28 x 1.2 x 539.67)

n = 12.308

Therefore, approximately 12 tires of volume 1.2 ft³ can be inflated to 28 psig using the given conditions.

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A uniform rod is a linear object with a constant linear density whose centre of gravity is located at its midpoint. A uniform rod, as shown in the diagram above, would be perfectly balanced at its midpoint.

Define  frictionless?

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Option C is correct. The consumer price index is 100 in 2009, 109 in 2010, and 115 in 2011 if 2010 is the base year.

Divide nominal GDP by real GDP, multiply by 100 to express as an index number, and you get the implicit GDP deflator.  services produced by an economy in a given year at current prices to that of prices prevailing at the time. A statistical tool for determining the amount of changes in a group of connected variables is an index number. It is derived from diverging ratios, from which it depicts the overall trend. It is a measurement of the typical shift between two different situations in a set of connected variables.

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