If all planets were the same distance from the sun, which would have the largest gravitational force between itself and the sun? Why? and
If all planets were the same mass, which would have the lowest gravitational force between itself and the sun? Why?

Answer:

Approximately [tex]12.3\; {\rm N}[/tex] at approximately [tex]106^{\circ}[/tex].

Explanation:

Assume the two given directions are measured with respect to the positive [tex]x[/tex] axis.

If a vector of magnitude [tex]\| a\|[/tex] is at an angle of [tex]\theta[/tex] from the positive [tex]x[/tex] axis, this vector can be written in the component form as:

[tex]\begin{aligned}\| a\|\begin{bmatrix}\cos(\theta) \\ \sin(\theta)\end{bmatrix}\end{aligned}[/tex];

Or equivalently:

[tex]\begin{aligned}\begin{bmatrix}\|a\|\, \cos(\theta) \\ \|a\|\, \sin(\theta)\end{bmatrix}\end{aligned}[/tex].

For example, the [tex]7.6\; {\rm N}[/tex] force is a vector with magnitude [tex]7.6\; {\rm N}[/tex] at a direction of [tex]38^{\circ}[/tex] from the positive [tex]x[/tex] axis. This vector can be represented as:

[tex]\begin{aligned} 7.6\, \begin{bmatrix}\cos(38^{\circ}) \\ \sin(38^{\circ})\end{bmatrix} &= \begin{bmatrix}7.6\, \cos(38^{\circ}) \\ 7.6\, \sin(38^{\circ})\end{bmatrix} \approx \begin{bmatrix}5.9889 \\ 4.6790 \end{bmatrix}\end{aligned}[/tex].

Similarly, the [tex]11.8\; {\rm N}[/tex] vector can be represented as:

[tex]\begin{aligned}11.8\, \begin{bmatrix}\cos(143^{\circ}) \\ \sin(143^{\circ})\end{bmatrix} &= \begin{bmatrix}11.8\, \cos(143^{\circ}) \\ 11.8\, \sin(143^{\circ})\end{bmatrix} \approx \begin{bmatrix}-9.4239 \\ 7.1014 \end{bmatrix}\end{aligned}[/tex].

To find the sum of the two vectors, take the sum of each component separately:

[tex]\begin{aligned}& \begin{bmatrix}5.9889 \\ 4.6790 \end{bmatrix} + \begin{bmatrix}-9.4239 \\ 7.1014\end{bmatrix} \\ =\; & \begin{bmatrix}5.9889 + (-9.4239)\\ 4.6790 + 7.1014\end{bmatrix} \\ \approx\; & \begin{bmatrix}-3.4350 \\ 11.780\end{bmatrix} \end{aligned}[/tex].

Apply the Pythagorean Theorem to find the magnitude of this vector sum:

[tex]\displaystyle \sqrt{(-3.4350)^{2} + (11.780)^{2}} \approx 12.271[/tex].

Note that the first component ([tex]x[/tex]-component) of this vector is negative, such that this vector would point to the left of the vertical axis. Since the second component ([tex]y[/tex]-component) of this vector is positive, this vector would point above the horizontal axis. Hence, the direction of this vector (relative to the positive [tex]x\![/tex]-axis) would be an angle between [tex]90^{\circ}[/tex] and [tex]180^{\circ}[/tex].

Divide the [tex]x[/tex]-component of this vector by its magnitude to find the cosine of the angle between this vector and the positive [tex]x\![/tex]-axis. Apply the inverse cosine function to find this angle:

[tex]\begin{aligned}\arccos \left(\frac{-3.4350}{12.271}\right) \approx 106^{\circ}\end{aligned}[/tex].

The frictional force acting on the bullet is 16.08 N. The force produced when two surfaces slide past one another and make contact is known as frictional force.

Friction is a force that prevents two solid objects from rolling or sliding over one another. Although frictional forces, such as the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.

we need to use the equation for work done by friction.

The work done by friction is:

W = F_friction * d

F_friction = W / d

where F_friction is the frictional force.

To find the work done by friction, we need to use the kinetic energy equation:

KE = 1/2 * m * v^2

where KE = kinetic energy of the bullet, m = mass of the bullet, and v = velocity of the bullet.

W = KE

Substituting the values,

KE = 1/2 * m * v^2

KE = 1/2 * 0.00791 kg * (352 m/s)^2

KE = 0.782 J

So, the work done by friction is 0.782 J.

Now, we can use the given depth of penetration to find the distance over which the frictional force acts:

d = 0.0486 m

we can use the equation for the frictional force,

F_friction = W / d

F_friction = 0.782 J / 0.0486 m

F_friction = 16.08 N

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Answer:

If the water in the left side drops .2 m then the water on the right side rises by .2 m

The pressure on the gas is due to the height difference of the water on the two sides.

P = ρ g h

ρ g = 9.8 m/s^2 * 1000 kg / m^3 = 9800 N/m^3      weight density of water

P = 9800 N/m^3 * .4 m = 3920 N / m^2 = 3.92E3 N/m^2

Absolute pressure of gas = 3.92E3 / 1.01E5 = .0388 atmosphere

Between 1980 and 2010, there were significant differences in the average annual ice loss of glacial mass balance between different glaciers and geographical areas. This suggests that ice loss has risen since the 1980s.

The average annual mass balance of reference glaciers globally between 1980 and 1999 was -0.50 m water equivalent (w.e.) per year, while between 2000 and 2017 it was -0.69 m w.e. per year, according to the World Glacier Monitoring Service. This shows a pattern of higher ice loss compared to the 1980s and 1990s in recent years. It's crucial to remember that this figure represents an average across a significant number of glaciers.

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According to the charge that is stored on the positive plate, the order is B, A, C, D, and E, from biggest to smallest.

The charge stored on the positive plate of a capacitor is given by Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. Since the capacitors are connected in parallel, they all have the same voltage V. Therefore, the capacitor with the largest capacitance will have the largest charge stored on its positive plate.

Ranking the capacitors from largest to smallest based on their capacitances, we get:

B) A = 2 cm, C = 8 nF

A) A = 4 cm, C = 8 nF

C) A = 2 cm, C = 4 nF

D) A = 4 cm, C = 2 nF

E) A = 1 cm, C = 1 nF

Therefore, the ranking from largest to smallest based on the charge stored on the positive plate is: B, A, C, D, E.

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The negative terminals of batteries must be connected on the same side of a parallel circuit and positive terminals on the other side to ensure that the voltage across each branch of the circuit is the same and that the batteries share the load equally.

In a parallel circuit, each branch of the circuit provides a separate path for current to flow, and the voltage across each branch is the same. Connecting the negative terminals of the batteries on the same side and the positive terminals on the other side ensures that the voltage across each branch remains the same, as the voltage drop across each battery is identical.

If the batteries were connected with opposite polarity, the voltage across each branch would be different, and the battery with the higher voltage would take on a larger share of the load, leading to unequal discharge and potentially damaging the batteries. It is essential to connect the negative terminals of the batteries on the same side and the positive terminals on the other side to ensure that each battery shares the load equally.

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(a) There is only one degree of freedom in this problem since the collar can move along the shaft but cannot rotate. The constraints are that the distance between the collar and the pivot point is always equal to l, and the collar cannot move perpendicular to the shaft.

(b) The forces acting on the collar are the spring force and the gravitational force. Since the collar is sliding along a frictionless shaft, there is no frictional force. The equation of motion for the collar is given by:

m(d²x/dt²) = -k(x-l) - mg

where x is the displacement of the collar from its equilibrium position.

(c) The normal force between the collar and the shaft is perpendicular to the shaft and balances the component of the gravitational force that is perpendicular to the shaft. As the collar moves away from its equilibrium position, the spring force becomes unbalanced and the normal force changes accordingly. The normal force is given by:

N = mgcos(θ) + k(x-l)sin(θ)

where theta is the angle between the shaft and the vertical axis.

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The initial angular acceleration of the steering wheel is 3.67 rad by s2.

The initial angular acceleration of the steering wheel can be calculated using the formula alpha = (F * R) by I, where F is the applied force, R is the radius of the wheel, and I is the rotational inertia.

In this case, F = 20.0 N, R = 0.18 m, and I = 0.097 kgm2. Substituting these values into the formula gives:

alpha = (20.0 N * 0.18 m) by 0.097 kgm2 = 3.67 rad by s2

Therefore, the initial angular acceleration of the steering wheel is 3.67 rad by s2.

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If ocean water did not move, it would be hot in the equatorial region and frigid in the polar regions.

Ocean currents are responsible for redistributing heat around the planet. Without these currents, the equatorial region would receive more sunlight and heat than it loses, resulting in an accumulation of heat in the water. On the other hand, the polar regions would lose more heat than they receive, resulting in frigid temperatures.

The rotation of the Earth also influences the movement of ocean water through the Coriolis effect. Without this effect, ocean currents would be less predictable, and their impact on climate and temperature distribution would be more severe. Therefore, ocean currents play a crucial role in regulating Earth's climate, and their disruption could have significant consequences for both marine life and global weather patterns.

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500 seconds (or 8 minutes and 20 seconds) for 300 C of electric charge to pass through an aluminum wire if the current through it is 0.6 A.

To answer this question, we need to use the formula:

Q = I × t

where:

Q is the electric charge in Coulombs (C)

I is the current in Amperes (A)

t is the time in seconds (s)

We can rearrange this formula to solve for t:

t = Q / I

Substituting the given values, we get:

t = 300 C / 0.6 A

t = 500 seconds

Therefore, it would take 500 seconds (or 8 minutes and 20 seconds) for 300 C of electric charge to pass through an aluminum wire if the current through it is 0.6 A.

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Discovery Statement:

I discovered that my note-taking skills needed improvement when I attended a lecture by a guest speaker who spoke very quickly and used complex technical terms that were unfamiliar to me. I found it challenging to keep up with the speaker's pace and understand the content at the same time. As a result, I struggled to take accurate and organized notes, and ended up with a confusing and incomplete set of notes. When I reviewed my notes later, I realized that I had missed important points and failed to capture the essence of the lecture. This experience made me realize that I need to improve my note-taking skills, especially in situations where the content is complex and the speaker is fast-paced.

My intention is to implement the following five note-taking strategies immediately to improve my skills:

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See transcribed text below

MINDTAP

try: Transform Your Note-Taking

ms Journal Entry Transform your note taking

3

Q Search this course

0

Q

Question 1 of 1

Think back on the last few lectures you have attended. How would you rate your note-taking skills? As you complete this exercise, think of areas that need improvement.

1. Discovery Statement

First, recall a recent incident in which you had difficulty taking notes. Perhaps you were listening to an instructor who talked fast. Maybe you got confused and stopped taking notes altogether. Or perhaps you went to review your notes after class, only to find that they made no sense at all. Describe this incident in more detail, noting how it was challenging for you.

I discovered that...

X

2. Intention Statement

Now review this chapter to find at least five strategies that you can use right away to help you take better notes. In the space below, sum up each of those strategies in a few words, and note the title of the article where these strategies are explained.

2 Action Statement

Q Search

LM

A-Z

b

بین

9:19 PM

3/3/2023

The fraction of the engine power used to make the airplane climb is 0.14.

The fraction of the engine power used to make the airplane climb can be determined by the equation Pclimb/Pengine = mgh/Pengine, where Pclimb is the power used to climb, m is the mass of the airplane, g is the acceleration due to gravity, and h is the rate of climb. In this case, Pclimb = 75 kW, m = 700 kg, g = 9.81 m/s2, and h = 2.5 m/s. Plugging these numbers in, we get:
Pclimb/Pengine = (700 kg)(9.81 m/s2)(2.5 m/s)/75 kW
Pclimb/Pengine = 0.14
Therefore, the fraction of the engine power used to make the airplane climb is 0.14.

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The ball would be hit if it was hit at an angle of 25° and a velocity of 80 mph, it will travel 1-8m.

The definitiοn οf velοcity is the rate at which a bοdy mοves in a particular directiοn. Velοcity is the rate at which a distance changes in relatiοn tο time. A vectοr quantity with bοth magnitude and directiοn is velοcity.

The amοunt οf matter in a bοdy is referred tο as its mass. The kilοgramme is the kilοgrams, which is the SI unit οf mass (kg). Mass is defined as: Mass = Density/Vοlume.

Therefοre, ball wοuld be hit if it was hit at an angle οf 25° and a velοcity οf 80 mph, it will travel 1-8m.

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The potential energy of the cat is 17.76 joules.

The kinetic energy of the cat just before hitting the ground is 84.59 joules.

Part 1:

The potential energy of the cat can be found using the formula:

potential energy = mass x gravity x height

where the mass of the cat is 3.63 kg, gravity is 9.81 m/s², and height is 0.5 meters.

Substituting these values in the formula, we get:

potential energy = 3.63 kg x 9.81 m/s² x 0.5 m

potential energy = 17.76 joules

Therefore, the potential energy of the cat is 17.76 joules.

Part 2:

The kinetic energy of the cat just before hitting the ground can be found using the formula:

kinetic energy = 0.5 x mass x velocity²

To find the velocity of the cat just before hitting the ground, we can use the equation of motion:

height = (1/2) x acceleration x time² + initial velocity x time

where height is 0.5 meters, acceleration is gravity (9.81 m/s²), time is 2 seconds, and initial velocity is 0 m/s (since the cat starts from rest).

Rearranging this equation to solve for velocity, we get:

velocity = (height - (1/2) x acceleration x time²) / time

velocity = (0.5 - (1/2) x 9.81 x 2²) / 2

velocity = -4.905 m/s (the negative sign indicates that the velocity is downward)

Substituting the mass of the cat (3.63 kg) and the velocity (-4.905 m/s) in the formula for kinetic energy, we get:

kinetic energy = 0.5 x 3.63 kg x (-4.905 m/s)²

kinetic energy = 84.59 joules

Therefore, the kinetic energy of the cat just before hitting the ground is 84.59 joules.

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Speed before the tire popped must have been 35.8 m/s. To calculate your speed before the tire popped, we will use the equation vf = vi + at. In this equation, vf is the final velocity (0 m/s), vi is the initial velocity, a is the acceleration (deceleration in this case), and t is the time.

Since we know the diameter of the roundabout, the time it took to stop, and the acceleration is constant, we can calculate the initial velocity as:

vi = vf + at
vi = 0 m/s + (-1.125 m/s2) * 32 s
vi = -35.8 m/s

So, your speed before the tire popped must have been 35.8 m/s.

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Answer:

Yes you're correct

Explanation:

The Moon's surface is not perfectly smooth but rather has mountains and valleys. Imagine looking at a sponge at a certain angle  and put a dim flashlight behind the sponge. You can see that the grooves make it so its not a perfectly straight shadow.

The fact that the line dividing the dark and bright regions of the Moon is not perfectly straight proves that the Moon's surface is not perfectly smooth but rather has mountains and valleys.This is because the terrain of the Moon is comprised of mountains, craters, and valleys, meaning that the line separating the dark and bright regions will not be completely straight.

The irregularities of the terrain cause the line to appear wavy, and thus not completely straight. This tells us that the surface of the Moon is far from perfectly smooth.

To illustrate this further, a comparison can be drawn between the Moon and a billiard ball. If the Moon's surface were perfectly smooth, the line separating the dark and bright regions would be perfectly straight, just as if a billiard ball had been sliced in half. However, since the surface of the Moon is not perfectly smooth, the line appears wavy due to the irregularities of the terrain.

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The balanced form of the given chemical equation is as follows: 2N₂ + 0₂ → 2N₂0.

A chemical equation in chemistry is a symbolic representation of a chemical reaction where reactants are represented on the left, and products on the right.

A chemical equation results in the formation of new substances called products from substances called reactants.

However, to obey the law of conservation of mass, the atoms of each element on both sides of the equation must be the same. This is referred to as a balanced chemical equation.

The balanced form of the reaction between nitrogen and oxygen gas is given above.

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If the the dolphin produces sound waves of wavelength of 5 cm determine by the means of calculations whether the frequency produced by dolphin can be heard by human ear the speed of sound is water is 1480 m. S-1

To determine whether the frequency produced by the dolphin can be heard by the human ear, we can use the formula:

v = f x λ

where v is the velocity of sound in water, f is the frequency of the sound wave, and λ is the wavelength of the sound wave.

Given v = 1480 m/s, λ = 5 cm = 0.05 m, we can rearrange the formula to solve for f:

f = v / λ

Plugging in the values, we get:

f = 1480 m/s / 0.05 m

f = 29600 Hz

Therefore, the frequency produced by the dolphin is 29600 Hz.

The human ear can typically hear frequencies ranging from 20 Hz to 20,000 Hz, with some variation among individuals. Therefore, the frequency produced by the dolphin is well beyond the range of human hearing.

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The net gravitational force on b due to a and c is 5.338 x 10^-8 N.

The net gravitational force on b due to a and c can be calculated using the formula:

F = G (m1m2) / r^2

where;

First, let's calculate the gravitational force between a and b:

F1 = G (m1m2) / r^2

= 6.67 x 10^-11 * (10.0 x 10.0) / (0.50/2)^2

= 1.067 x 10^-7 N

Next, let's calculate the gravitational force between b and c:

F2 = G(m2m3) / r^2

= 6.67 x 10^-11 (10.0 x  15.0) / (0.50/2)^2

= 1.67 x 10^-7 N

The net gravitational force on b due to a and c is the vector sum of these two forces:

Fnet = F2 - F1

= 1.67 x 10^-7 N - 1.067 x 10^-7 N

= 5.338 x 10^-8 N

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Answer:

The answer is B.

Explanation:

It is clear that the substance will be in liquid state above its melting point and below its boiling point.

A) This is incorrect. The substance is above the melting point but it is also above the boiling point (0 is greater than -183)

B) This is your correct answer. The substance is above the melting point and also below the boiling point.

C) This is incorrect. The substance is below both the melting point and the boiling point.

D) This is incorrect. The substance is drastically below the melting and boiling point.

Therefore , the only correct answer for this question would be B.

For two objects of the same mass and radius, the one with more mass concentrated farther away from the axis of rotation will have a larger moment of inertia. Therefore, the moment of inertia of a solid cylinder is greater than that of a thin hoop of the same mass and radius.

The moment of inertia of a thin hoop of mass m and radius r is given by:

I_{hoop} = mr²

The moment of inertia of a solid cylinder of mass m and radius r is given by:

I_{cylinder} = (1/2)mr²

From these equations, the moment of inertia of a solid cylinder is greater than that of a thin hoop of the same mass and radius.

Therefore, a solid cylinder has a larger moment of inertia compared to a thin hoop.

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The minimum radius of the circle so that the acceleration at this point will not exceed 4.00 is 2304 m, and the apparent weight of the pilot at the lowest point of the pullout is 272.6 N.

The equation for centripetal acceleration is:

a = (v²)/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the circle.

The equation can be rearranged to solve for the radius of the circle,

r = (v²)/a.

Plugging in the given values, we get:

r = (96)² / 4.00g

r = 2304 m.

The equation for the apparent weight of the pilot is

[tex]w_{app}[/tex] = mg - m* [tex]a_{centripetal}[/tex], where [tex]w_{app}[/tex] is the apparent weight, m is the mass of the pilot, g is the acceleration due to gravity, and [tex]a_{centripetal}[/tex] is the centripetal acceleration.

Plugging in the given values, we get [tex]w_{app}[/tex] = (47.0)(9.8) - (47.0)(4) = 272.6 N.

Therefore, the minimum radius of the circle is 2304 m, and the apparent weight of the pilot is 272.6 N.

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a) In a series circuit, the current remains the same throughout, so the current in the ammeter A1 is the same as the current in the ammeter A3. Therefore, the readings of A1 and A3 should be the same.

b) As mentioned in the previously, the readings of A1 and A3 should be the same since they are measuring the same current.

c) To determine the reading of the voltmeter V1, we need to know the current passing through it and the resistance between its two points. Since the circuit contains only resistors, we can apply Ohm's law to calculate the total resistance of the circuit.

The total resistance of the circuit can be calculated as follows:

Total Resistance = 9 x 3Ω (since there are nine 3Ω resistors connected in series)

Total Resistance = 27Ω

Since the current in the ammeter A1 is 1 ampere, the voltage across the voltmeter V1 can be calculated using Ohm's law:

V1 = I x R

V1 = 1 x 27

V1 = 27 volts

Therefore, the reading of the voltmeter V1 should be 27 volts.

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The amount of work done by the force of the rope as it pulled the block through the 6 meters is 9J.

The kinetic energy of the block is given by the formula

K = [tex]\frac{1}{2}[/tex]m[tex]v^{2}[/tex]

where,

m = mass of the block

v = velocity

Initially, the block is at rest. After being pulled by rope for 4 seconds it has an initial velocity of 3 m/s. Therefore, its final initial velocity is

Kf = [tex]\frac{1}{2}[/tex](2 kg)[tex](3 m/s) ^{2}[/tex]= 9 J

change in kinetic energy

ΔK = Kf - Ki = 9 J - 0 J = 9 J

Therefore, The amount of work done by the force of the rope as it pulled the block through the 6 meters is 9J.

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Answer:

d. decomposer

Explanation:

they play a critical role in the flow of energythrough an ecosystem. They break apart dead organisms into simpler inorganic materials, making nutrients available to primary producers

The final speed of an electron accelerated through a potential difference V, starting from rest, is given by the expression [tex]v = 5.93 \times 10^7 \times \sqrt{V}[/tex], where v is in meters per second and V is in volts.

The kinetic energy gained by an electron accelerated through a potential difference V is given by:

K = eV

Where:

K is the kinetic energy gained by the electron (joules)

e is the charge of the electron ([tex]1.6 \times 10^{-19}[/tex]coulombs)

V is the potential difference across which the electron is accelerated (volts)

Since the electron was initially at rest, its initial kinetic energy was zero. Therefore, the final kinetic energy of the electron will be equal to the kinetic energy gained during acceleration:

K = eV

The final velocity of the electron can be calculated using the formula for kinetic energy:

K = (1/2)m[tex]v^2[/tex]

Where:

m is the mass of the electron[tex](9.11 \times 10^{-31} kg)[/tex]

v is the final velocity of the electron

Substituting the expression for K, we get:

eV = (1/2)m[tex]v^2[/tex]

Solving for v, we get:

v = √(2eV/m)

Substituting the values for e, V, and m, we get:

[tex]v =\sqrt{ [(2 \times 1.6 x 10^{-19} C \times V) / 9.11 \times 10^{-31} kg]}[/tex]

Simplifying this expression, we get:

[tex]v = 5.93 \times 10^7 \times \sqrt{V}[/tex]

Therefore, the final speed of an electron accelerated through a potential difference V, starting from rest, is given by the expression [tex]v = 5.93 \times 10^7 \times \sqrt{V}[/tex], where v is in meters per second and V is in volts.

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The biggest state in the United States by land area is Alaska also what the meme

Answer:

The speed of the object is increasing.

F = M a       as long as the magnitude of the acceleration is acting towards the right there will be an acceleration towards the right

The table suggests that the acceleration of the marble increases steadily over time due to the increasing force being applied to it. This is because acceleration is directly proportional to the force applied, according to Newton's second law of motion (F = ma).

Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.

Newton's second law is often stated as F=ma, which means the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a). This means the more mass an object has, the more force you need to accelerate it. And the greater the force, the greater the object's acceleration.

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