Is acceleration greater going up or down a ramp?

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]

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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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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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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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)

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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Answer: The distance between the objects

Explanation:

Answer:2.30

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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Answer:

Below

Explanation:

To fall 1.8 m the time will be found with :

 d = 1/2 a t^2

 1.5 = 1/2 ( 9.81) t^2      shows t = .55 s

in this .55 s it travels .8 m horizontally    

     Horizontal velocity = .8 m / .55 s = 1.45 m/s

When it hits the ground , horizontal velocity will still be 1.45 m/s

  vertical velocity will be    v = at = 9.81 m/s^2  * .55 = 5.42 m/s

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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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.

Some harmful environmental factors can change the nucleotide sequence of a gene. UV rays, for example, can harm DNA strands.

Genetic variations arise during meiosis as a result of mutation and recombination. Chemical or biological mutagens frequently result in mutations. The genetic diversity of organisms is also altered by accidental mating.

The length at which you want to wear your hair. Scars – from your own unique accidents. The strength of your muscles depends on how much exercise you get. Piercings, whether you decide to have them or not. Mutations are the primary cause of the emergence of genetic variation.

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Answer:

2 inches

Explanation:

Volume of a sphere = 4/3  pi r^3

   for the EIGHT balls   total volume =   8  *  4/3 pi (1^3) = 32/3 pi

This is the volume of the made-up ONE ball

    4/3 pi r^3  = 32/3 pi

       4/3 r^3 = 32/3

            r^3 = 32/3  * 3/4

             r^3 = 8

              r = 2 inches

Answer:

metric ruler

Explanation:

it counts legnth

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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Answer:

a) The direction of the current in the copper rod that causes the springs to stretch is left-to-right. This is because the magnetic field is oriented perpendicular to the surface of the table and the force exerted on the rod by the magnetic field is given by F = qVB, where F is the force, q is the charge of the particle, V is the velocity of the particle, and B is the strength of the magnetic field. Since the force is perpendicular to the velocity of the particle, the direction of the current that produces this force must be parallel to the magnetic field. In this case, the magnetic field is oriented perpendicular to the surface of the table, so the current must flow in the direction left-to-right to produce a force that stretches the springs.

b) To find by how much each spring stretches, you can use the formula F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the distance the spring stretches. In this case, the force exerted by the spring is given by F = qVB, and the spring constant is k = 76 N/m. The charge of the particle is q = Ie, where I is the current and e is the charge of an electron. The velocity of the particle is V = L / t, where L is the length of the rod and t is the time it takes the particle to travel the length of the rod. Since the current is 14 A and the length of the rod is 0.77 m, the velocity of the particle is V = 0.77 m / (1 / 14 A) = 10.78 m/s. The strength of the magnetic field is 0.14 T, so the force exerted by the spring is F = (14 A)(1.60 x 10^-19 C)(10.78 m/s)(0.14 T) = 2.40 x 10^-17 N. Therefore, the distance each spring stretches is x = F / k = 2.40 x 10^-17 N / 76 N/m = 3.16 x 10^-19 meters.

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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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

Important Formulas:

[tex]v=\dfrac{d}{t}[/tex]

velocity(measured in m/s) = distance(measured in meters) / time(measured in seconds)

__________________________________________________________

Given:

[tex]d=15m[/tex]

[tex]t=3s[/tex]

[tex]v=?[/tex]

__________________________________________________________

Finding velocity:

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{15}{3}[/tex]

__________________________________________________________

[tex]\fbox{v = 5 m/s}[/tex]

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.

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.)

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

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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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 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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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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Answer:

Explanation: