How do you calculate the speed of an object rolling down a ramp?

Answer:

Explanation:

a.speed with direction associated

b.the ability to resist motion

c.The rate of change of position of an object

e.any influence object's motion

f.forces cancel out, create equilibrium

g.total force acting on an object

h. change in position of an object (total distance from starting point)

Answer:

(a)

[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex] --- velocity

[tex]x(t) = \frac{At^3}{6} -\frac{Bt^4}{12} + x(0)[/tex] --- position

(b) The maximum velocity is: 39.0625m/s

Explanation:

Given

[tex]a_x(t) =At -Bt^2[/tex]

[tex]A = 1.5m/s^3[/tex]

[tex]B = 0.120m/s^4[/tex]

Solving (a): The position and velocity as a function

To calculate the change in velocity, we integrate the given acceleration

i.e.

[tex]\int\limits^{v(t)}_{v(0)} {dv} = \int\limits^t_0 {a(t)} \, dt[/tex]

Integrate

[tex]v|\limits^{v(t)}_{v(0)} = \int\limits^t_0 {a(t)} \, dt[/tex]

Substitute v(t) and v(0) for v

[tex]v(t) - v(0) = \int\limits^t_0 {a(t)} \, dt[/tex]

[tex]v(0) = 0[/tex] ---- The initial velocity.

So, we have:

[tex]v(t) - 0 = \int\limits^t_0 {a(t)} \, dt[/tex]

[tex]v(t) = \int\limits^t_0 {a(t)} \, dt[/tex]

Substitute: [tex]a_x(t) =At -Bt^2[/tex]

[tex]v(t) = \int\limits^t_0 {[At -Bt^2]} \, dt[/tex]

Integrate

[tex]v(t) = {\frac{At^2}{2} -\frac{Bt^3}{3}}|\limits^t_0[/tex]

Substitute 0 and t for t

[tex]v(t) = [\frac{At^2}{2} -\frac{Bt^3}{3}] - [\frac{A*0^2}{2} -\frac{B*0^3}{3}][/tex]

[tex]v(t) = [\frac{At^2}{2} -\frac{Bt^3}{3}] - 0[/tex]

[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]

To calculate the change in position, we integrate the calculated velocity

i.e.

[tex]\int\limits^{x(t)}_{x(0)} {dx} = \int\limits^t_0 {v(t)} \, dt[/tex]

Integrate

[tex]x(t)|\limits^{x(t)}_{x(0)} = \int\limits^t_0 {v(t)} \, dt[/tex]

Substitute x(t) and x(0) for x(t)

[tex]x(t) - x(0) = \int\limits^t_0 {v(t)} \, dt[/tex]

Substitute: [tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]

[tex]x(t) - x(0) = \int\limits^t_0 {\frac{At^2}{2} -\frac{Bt^3}{3}} \, dt[/tex]

Integrate

[tex]x(t) - x(0) = \frac{At^3}{6} -\frac{Bt^4}{12}}|\limits^t_0[/tex]

Substitute t and 0 for t

[tex]x(t) - x(0) = [\frac{At^3}{6} -\frac{Bt^4}{12}] - [\frac{A*0^3}{6} -\frac{B*0^4}{12}][/tex]

[tex]x(t) - x(0) = [\frac{At^3}{6} -\frac{Bt^4}{12}] - [0][/tex]

[tex]x(t) - x(0) = \frac{At^3}{6} -\frac{Bt^4}{12}[/tex]

Make x(t) the subject

[tex]x(t) = \frac{At^3}{6} -\frac{Bt^4}{12} + x(0)[/tex]

Where x(0) represents the initial position

Solving (b): The maximum velocity

First, we calculate the time at which it attains the maximum height

Set acceleration to 0

[tex]a_x(t) =At -Bt^2[/tex]

[tex]At - Bt^2 = 0[/tex]

Factorize

[tex]t(A - Bt) = 0[/tex]

Split

[tex]t = 0\ or\ A - Bt = 0[/tex]

t can't be 0.

So, we have:

[tex]A - Bt = 0[/tex]

Solve for t

[tex]-Bt = -A[/tex]

[tex]t = \frac{-A}{-B}[/tex]

[tex]t = \frac{A}{B}[/tex]

Substitute: [tex]A = 1.5m/s^3[/tex] and [tex]B = 0.120m/s^4[/tex]

[tex]t = \frac{1.5m/s^3}{0.120m/s^4}[/tex]

[tex]t = \frac{1.5}{0.120}s[/tex]

[tex]t = 12.5s[/tex]

Substitute [tex]t = 12.5s[/tex] in v(t) to get the maximum velocity

[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]

[tex]v(t) = \frac{A*12.5^2}{2} -\frac{B*12.5^3}{3}[/tex]

[tex]v(t) = \frac{156.25A}{2} -\frac{1953.125B}{3}[/tex]

Substitute: [tex]A = 1.5m/s^3[/tex] and [tex]B = 0.120m/s^4[/tex]

[tex]vmax = (156.25*1.5)/2 -(1953.125*0.120)/3[/tex]

[tex]v_{max} = 117.1875 - 78.125[/tex]

[tex]v_{max} = 39.0625[/tex]

The difference between active flexibility and passive flexibility is that in active flexibility, we rely on our own muscle power to reach the end range, but in passive flexibility, we rely on an external push to reach the end range.

According to the findings of recent studies, active flexibility has a stronger connection to a person's level of sporting performance than passive flexibility does. The ability to build active flexibility is more difficult to achieve than passive flexibility. Active flexibility involves passive flexibility in addition to muscle strength in order to be able to retain and maintain the initial extended position.

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A lengthy string is simple to stretch. The string's two designated spots, A and B, should be at an angle of 90 degrees with the same magnitude, and B should be at an angle of 270 degrees with the same magnitude.

Angle magnitude definition

This is referred to as the amount of rotation that is believed to have been applied to one of the arms' vertex in order to produce a specific position for the other.

It is well known that equal vectors have the same magnitude and direction. When the magnitude and direction of two vectors are the same, they are said to be equal.

|v|=a2+b2 yields the magnitude. Depending on the application, the direction is equal to the angle made with the x-axis or the y-axis.

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Endothermic Reactions

Answer:

Chemical reactions that release energy are called exothermic. ... Chemical reactions that absorb (or use) energy are called endothermic. In endothermic reactions, more energy is absorbed when the bonds in the reactants are broken than is released when new bonds are formed in the products.

Explanation:

Endothermic reactions are ones that absorb heat energy. The excess heat absorbed in the reaction is being used to break bonds in the products. One of the most obvious types of endothermic reaction is the melting of ice. Endothermic Processes

These examples could be written as chemical reactions, but are more generally considered to be endothermic or heat-absorbing processes: Melting ice cubes. Melting solid salts. Evaporating liquid water

Answer: The distance between the objects

Explanation:

Answer:

11. True  

12. False (air pressure)

13. False (nitrogen)

14. False (stratosphere)

Explanation:

Dynamic flexibility tests are not used as often as static flexibility tests because dynamic flexibility tests involve more subjective measurements.

Static flexibility tests are more common in comparison to dynamic tests because static flexibility tests are easier to replicate. It is difficult to standardize motion-based tests such as dynamic flexibility tests between various subjects, while static flexibility tests are simple and easy to standardize it is because the metrics are fixed and not open to interpretation.

Since, dynamic flexibility tests are hard to perform because they measure the amount of stress on a muscle that is in motion. And it is difficult to assess this among multiple people and to get an accurate picture. That is why these tests are not used as often as static flexibility tests.

"

Complete question

Why are dynamic flexibility tests not used as often as static flexibility tests?

"

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Correct option is C)  the acceleration of gravity at that altitude is 9.75m/s².

The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s2.

The following formula is used to determine the acceleration of gravity:

g= GM/r2

What G The general gravitational constant is what it is.

G is equal to 6.674x10⁻¹¹ Nm2/kg2, and M is the earth's mass:

M = 5.972x10²⁴kg

The radius of the earth plus the airplane's altitude, or r, is the distance from the earth's center in this case:

r = 6.37x10⁶ m + 20000 m equals 6.39x10⁶ m

Consequently, the acceleration in g is equal to:

(6.674x10⁻¹¹ Nm²/kg²)(5.972x10²⁴ kg) / (6.39x100m)₂

g = 9.75m/s²

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Complete Question -

You are on an airplane traveling with a constant velocity at an altitude of 20,000m. What is the acceleration of gravity at that altitude? The earth's radius is 6.37 x 10^6m.. . A) 9.81 m/s^2. B) 9.78 m/s^2. C) 9.75 m/s^2. D) 9.72 m/s^2. E) 9.69 m/s^2.

After solving the problem the person's far point is 25 cm

What is myopic person?

A myopic person is someone who is near sighted and is unable to clearly see objects that are far away. This is caused by the eyeball being too long and the cornea having too much curvature. Light entering the eye is focused in front of the retina rather than directly on it, resulting in blurred vision for distant objects. Myopia is a common eye condition and can usually be corrected with glasses or contact lenses. In more severe cases, laser surgery may be necessary. People with myopia may need to wear their glasses or contact lenses all the time in order to see clearly, but they may be able to take them off when they are close to something they want to see clearly.

The far point is the farthest distance at which a person can see clearly without any corrective lenses.
The formula for calculating far point is 1/f = 1/d + 1/p, where f is the far point, d is the distance from the eye to the lens (1.75 cm in this case), and p is the power of the lens (in diopters) which is -4.00 D.
Plugging the values into the formula yields 1/f = 1/1.75 + 1/-4.00, which simplifies to 1/f = 4.00 - 0.5714. Solving for f gives f = 0.2500, or 25 cm.
Therefore, the person's far point is 25 cm.

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In a year, the earth revolves around the sun once in a circular motion. Therefore, the earth will orbit the sun at a 2.95 m/s speed.

Planets in our solar system did not appear out of thin air. Neither did the sun. They were all a part of a large cloud of gas and dust. Gravity accumulated a lot of material in the center to form the sun. As it spun around the forming sun, the extra matter clashed and gathered together. Some would be capable of attracting more gas and dust, eventually forming planets, because to their powerful gravitational forces.

The answer to the query is

v = 2πR / T

2R equals 6.28 * 9.3 * 107 miles.

T = 24 * 3600 * 365 = 3.15 × 10⁷ sec

v = 9.3 / 3.15 = 2.95 m/s.

Hence, the earth's speed of the earth around the sun will be 2.95 m/s.

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Hydroelectric power accounts for between 16 and 17 percent of global electricity production, making it one of the most significant renewable energy sources.

In 2016, hydropower contributed more than twice as much to the grid as the next largest renewable energy source, solar. Hydropower can provide many valuable services to the power grid beyond just energy generation. These include frequency regulation, voltage support, contingency reserves, load following, and black start service, all of which contribute to the reliability and safety of the power system. Hydropower's role in grid-scale energy storage, balancing services for other intermittent renewables like wind and solar power, and water management services by reservoirs are growing.

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1) Any mechanical interactions taking place in the process should be frictionless, to make a process perfectly reversible

What is mechanical interactions?

Mechanical interactions are physical forces that are used to affect the behavior of objects and materials. This can include contact forces such as friction, tension, and compression, as well as non-contact forces such as gravity, magnetism, and electric fields

Mechanical interactions can be used to cause objects to move, change shape, or experience a change in energy. These interactions can also be used to create, store, or transfer energy. Mechanical interactions are studied by engineers and scientists in multiple disciplines, and are used in many different applications, including the design of machinery, medical devices, and consumer products.

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Answer:2.30

Explanation:

The law of reflection, The relationship between the angle of incidence and the angle of reflection is that they are equal.

The angle of incidence is the angle between the incoming light ray and the normal line (a line perpendicular to the surface of the reflecting material), and the angle of reflection is the angle between the reflected light ray and the normal line. When a light ray strikes a reflection surface at a certain angle, it will be reflected back at the same angle. This relationship is represented by the equation.

=> angle of incidence = angle of reflection

This relationship holds true for all types of electromagnetic waves and for all surfaces that are reflective, whether they are smooth or rough, opaque or transparent. It's important to note that this is true for regular reflection, which is defined as the reflection of light off a smooth surface. If the surface is rough, the light rays are reflected in many different directions, this is called diffuse reflection.

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The spring with the higher spring constant (15.0 N/cm) will be more difficult to stretch than the spring with the lower spring constant (10.0 N/cm).

This is because the spring constant is directly related to the amount of force required to stretch the spring. Therefore, the higher the spring constant, the more force that is required to stretch the spring.

The spring constant is a measure of how difficult it is to stretch or compress a spring. It is determined by the stiffness of the spring material, its shape and size, and how much the spring is compressed or stretched.

The higher the spring constant, the more force is required to stretch or compress the spring. The lower the spring constant, the less force is required to stretch or compress the spring.

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The film strip that emerges from the camera is usually a Negative. That is, its color and light values are the opposite of those in the original scene.

One of the three camera settings that affects exposure is the aperture. The shutter speed, aperture, and ISO settings are together referred as as the "exposure triangle." By adjusting the relative amount of light entering a camera lens, an aperture can change the exposure.

A camera's shutter can close or open depending on how much light is required to expose the film at the rear of the device.

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In the given case it can be concluded that-  The two basic tenets of the special theory of relativity were that observers moving at constant speeds should be subject to the same physical rules and that the speed of light is constant for all observers.

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Answer:

metric ruler

Explanation:

it counts legnth

Answer:

1.constant acceleration.

2.0 ms

3. 0 ms

Explanation:

1. (D) uniformly accelerated motion

2. (A) zero

3. (B) -10 m/s

4. (C) -9.8 m/s^2

5. (B) projectile motion

Answer:

a.the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of a body.

b.is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

c.Mass is a physical magnitude and general property of matter that expresses the inertia or resistance to change in motion of a body.

d.Mass is a physical magnitude and general property of matter that expresses the inertia or resistance to change in motion of a body.

e.

Answer:

  d.  600 J

Explanation:

You want to know the work done to lift a box using a lever with a mechanical advantage of 2, if the work required without the lever is 600 J.

A lever trades force for distance. That is raising the box a distance of 6 m requires moving the lever arm a distance of 12 m, but only half the force is required. The product of force and distance is the same.

The total required work is unchanged: 600 J.

__

Additional comment

Actually, more work is required to lift the box using the lever. There is work applied to the box, and there is more work applied to moving the lever. (We have to assume a massless lever with no friction in these problems.)

Answer:

speed will be constant and so no acceleration

Explanation:

the body will move toward the weaker force, but since the forces are constant there will be no acceleration.

An iceberg is formed by the broken part of a large glacier that floats into the sea. The iceberg is composed of fresh water, just like the glaciers or ice in the North Pole. Since, freshwater is less thick than salty seawater, icebergs float in the water.

When chunks of ice break off the end of a glacier that is flowing into ocean, icebergs are created.

Since, seawater has a slightly higher density than ice, the iceberg floats with the majority of its mass below the surface. A cork, on the other hand, floats quite near to the water's surface due to its density, which is around 20% that of water.

As moving icebergs are dangerous, they have never been a main supply of drinking water. Freshwater is released by melting glaciers and icebergs, which also lowers the salinity of the surrounding sea.

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The tides are considered an example of shallow-water waves because the tidal bulges have a wavelength that is on the order of thousands of kilometers.

Complete Response.The tides are caused by the sun and moon's tremendous gravitational pulls on the surface of the planet, which is the right answer.

Response and Justification:Tides are not primarily caused by the gravitational influence of the sun, as is commonly believed.In reality, the Moon's gravitational pull is what mostly causes tides.

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The energy stored in the capacitor is 0.045 mJ. Under DC conditions, the capacitors will be open-circuited.

Energy stored in a capacitor can be calculated by

E = ½ CV²

Where

The picture of circuit in the attached plot is in the attachment.

Find the energy stored in the capacitor under DC conditions!

We have

Under DC (Direct Current) conditions, the capacitors will be open-circuited. It means that there is no current will flow through the 20 Ω resistor. So, I across the 10 Ω resistor is the same as I source.

See the picture below in the attachment!

The voltage across the 10 Ω resistor is

V = IR

V = 3(10)

V = 30 V

The voltage across the capacitor is the same as the voltage across the 10 Ω resistor.

Vc = V = 30 V

The energy stored would be

E = ½ C Vc²

E = ½ (0.1)(10⁻⁶)(30)²

E = ½ (10⁻⁷)(900)

E = 450 × 10⁻⁷

E = 0.045 × 10⁻³

E = 0.045 mJ

Hence, the energy stored in the capacitor under DC conditions is 0.045 mJ. The correct option is (c).

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A coulomb is a measure of electrical charge and has units of amperes times seconds (A⋅s). A faraday is a constant equal to the magnitude of electric charge per mole of electrons of 96,485.3399 Coulombs (C).

What is magnitude?
Magnitude is a measure of the size or scale of an object or event. It is often used to describe the intensity or severity of a phenomenon, such as earthquakes and hurricanes. It is usually expressed as a number on a logarithmic scale. In astronomy, magnitude is used to measure the brightness of stars and other celestial bodies. On Earth, magnitude is often used to measure the size of earthquakes and other seismic events. Magnitudes are typically expressed as a number on a logarithmic scale, with a greater magnitude indicating a larger size or scale of the event. Magnitudes can also be used to measure the intensity of light, sound, and other forms of energy.

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Answer:

it gives off 71.0 kJ of heat.

Explanation:

The magnitude of the centripetal acceleration of the car is 0.0034 km/sec².

Centripetal acceleration is the acceleration of an object moving in a circular path. It is directed towards the center of the circle and is responsible for the change in direction of the object's velocity.

The magnitude of the centripetal acceleration of an object moving in a circle is given by the formula:

a = v² / r

where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circle.

Given that the car goes once around the track in 320 s, we can calculate its velocity by using the formula:

v = d / t

where d is the distance traveled and t is the time.

d = 2pir = 2pi3.0 km = 18.849 km

t = 320 sec

so the velocity of the car is v = 18.849 km / 320 sec = 0.059 km/sec.

We can now use the formula to find the centripetal acceleration of the car

a = v² / r = (0.059 km/sec)²/ 3.0 km = 0.0034 km/sec²

Hence, the magnitude of the centripetal acceleration of the car is 0.0034 km/sec².

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