Question 1
A) What happens when new evidence is found that contradicts part of a theory?(1 point)

The theory is discarded for a new one.


New pieces are added to the original ideas.


It gets ignored to maintain the original idea.


Science reevaluates the validity of the theory.

Question 2
A) How does a hypothesis differ from a scientific theory?(1 point)

Hypotheses can change with new evidence, but theories remain constant.

Theories always lead to the development of new scientific ideas.


Hypotheses are testable, while theories only exist conditionally.


Theories are well established with lots of evidence to support their claims.

Question 3
A) How is a hypothesis similar to theory?(1 point)

Both a hypothesis and a theory need evidence to support them.


Both a hypothesis and a theory are accepted as true statements.


Both a hypothesis and a theory are statements supported by data.


Both a hypothesis and a theory explain why things happen.

The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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The car is moving at approximately 12.5 meters per second.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 1/2 * m * \(v^2\)

where

KE = kinetic energy,

m =Mass of the object, and

v = velocity.

In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .

Substituting the  values , we have:

125,000 J = 1/2 * 1600 kg *\(v^2\)

Now, we can solve for v by rearranging the equation:

\(v^2\) = (2 * 125,000 J) / 1600 kg

\(v^2\) = 156.25 \(m^2/s^2\)

Taking the square root, we find:

v = √156.25\(m^2/s^2\)

v ≈ 12.5 m/s

Therefore, the car is moving at approximately 12.5 meters per second.

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Use the Ideal Gas Law to find the pressure of the gas under the given conditions:

Where P represents pressure, V represents volume, n represents the amount of substance of the sample, R is the universal gas constant and T represents the temperature.

The volume and the temperature of the sample are given. On the other hand, we can calculate the amount of substance from the given mass of the sample. The molar mass M of a substance is the ratio between the mass of a sample and the amount of substance, and is characteristic of each substance:

A molecule of O₂ is made of two oxygen atoms. The atomic mass of oxygen is approximately 16u, then, the atomic mass of the molecule of O₂ is 32u, which means that its molar mass is 32 grams per mole:

Isolate n from the equation and replace m=1g and M=32g/mol to find the amount of substance of the sample:

Now that we have calculated the value of n, the only unknown for the Ideal Gas Law is the pressure of the gas. Write the universal gas constant using units of liters for the volume:

Isolate P from the ideal gas law and replace V=4.00L, n=0.03125mol, T=293K and the value of R to find the pressure of the gas:

Therefore, the pressure of the container will be approximately 19kPa.

Answer:

p = 60.6N*s

Explanation:

v_f = v_0+a*t

a = (v_f-v_0)/t

a = (1.8m/s)/2.35s

a = 0.77m/s²

F = m*a

F = (25kg+8.5kg)*0.77m/s²

F = 25.8N

^p = F*t

p = 25.8N*2.35s

p = 60.6N*s

The fundamental frequency change when the mass per unit length of a guitar string increases by a factor of 3.50 is, 3.5ⁿ

Frequency definition states that it is the number of complete cycles of waves passing a point in unit time, the SI unit of frequency is Hertz(Hz),

The frequency of a sinusoidal wave as the number of complete oscillations made by any wave element per unit of time.

The frequency of vibration of a string depends on the length L between the nodes,

the tension F in the string and its mass per unit length m.

Frequency,

f ∝ [Lᵃ] ... (1)

f ∝ [Fᵇ]  ...(2)

f ∝ [Mⁿ]  ...(3)

Combining equation (1) (2) and (3) we can say:

f₀ = k[Lᵃ x Fᵇ x Mⁿ]

So, when the mass per unit length increases by a factor of 3.50

Then, the new frequency is,

f = k[Lᵃ x Fᵇ x( 3.5M)ⁿ]

 = 3.5ⁿ x k[Lᵃ x Fᵇ x Mⁿ]

f = 3.5ⁿ f₀

Hence, the frequency will increase by a factor of 3.5ⁿ

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Videos can be streamed from the cloud to a computer with no loss in quality because Digital signals are used to transmit data to and from the cloud.

How do digital signals work?

An established or one that represents data as a step made up of discrete values is known as a digital signal. There is no noise produced by digital signals. Electronic signals sent as pulses are used to transmit digital signals to computers. These signals can be found in things like digital phones and computers.

Because digital signals are used to transport data to and from the cloud, it should be noted that videos are said to stream from the cloud to a computer without quality degradation.

Videos can be streamed from the cloud to a computer with no loss in quality because Digital signals are used to transmit data to and from the cloud.

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Answer:

F = 0.012 N

Explanation:

Given that,

Mass of the object, m = 6 g

Acceleration, a = 2 m/s²

1 kg = 1000 grams

6 g = 0.006 kg

Force, F = ma

So,

\(F=0.006\ kg\times 2\ m/s^2\\F=0.012\ N\)

So, the force is 0.012 N.

Answer:

t = Δa / v

Explanation:

To know which option is not true, we shall fine a relationship between acceleration (a), velocity (v), time (t) and radius (r). This is illustrated below:

Acceleration can simply be defined as the rate of change of velocity with time. Mathematically, it is expressed as shown below:

Acceleration = change in velocity / time

a = Δv / t ..... (1)

But

Δv = v₂ – v₁

Substitute the value of Δv into equation (1)

a = Δv / t

a = v₂ – v₁ / t ....... (2)

From equation (1), make Δv the subject of the equation.

a = Δv / t

Cross multiply

Δv = at .... (3)

From equation (1), make t the subject of the equation.

a = Δv / t

Cross multiply

at = Δv

Divide both side by a

t = Δv /a ...... (4)

From circular motion, centripetal's force is given by:

F = mv²/r

F = ma꜀

Therefore,

ma꜀ = mv²/r

Cancel out m

a꜀ = v²/r

SUMMARY:

a = Δv / t

a = v₂ – v₁ / t

Δv = at

t = Δv /a

a꜀ = v²/r

Considering the options given in question above, t = Δa / v is not a true statement.

Answer:

Option 4

Explanation:

Complete Question

For each of the following scenarios, describe the force providing the centripetal force for the motion:

a. a car making a turn

b. a child swinging around a pole

c. a person sitting on a bench facing the center of a carousel

d. a rock swinging on a string

e. the Earth orbiting the Sun.

Answer:

Considering a

    The force providing the centripetal force is the frictional force on the tires \

          i.e  \(\mu mg = \frac{mv^2}{r}\)

    where \(\mu\) is the coefficient of static friction

Considering b

   The force providing the centripetal force is the force experienced by the boys  hand on the pole

Considering c

     The force providing the centripetal force is the normal from the bench due to the boys weight

Considering d

     The force providing the centripetal force is the tension on the string

Considering e

      The force providing the centripetal force is the force of gravity between the earth and the sun

Explanation:

Answer:

a

Explanation:

AAAA

Answer:

C !! i needed to make this answer  longer lol so hi

Answer: \(0.13m/s^2\)

Explanation:

\(Formula: a=\frac{V_2-V_1}{t}\)

Where;

a = acceleration

V2 = final velocity

V1 = initial velocity

t = time

If John runs 1.0 m/s first, we assume this is V1. He accelerates to 1.6 m/s; this is V2.

\(a=\frac{1.6m/s-1.0m/s}{4.5s}\)

\(a=\frac{0.6m/s}{4.5s}\)

\(a=0.13m/s^2\)

Answer:.13

Explanation:

The magnitude of the power dissipated in resistor R4 is approximately 10,028 watts.

To find the power dissipated in resistor R4, use the formula:

P = I² × R

where P = power, I = current flowing through the resistor, and R = resistance of the resistor.

The total resistance, Rt, can be calculated using the formula:

1/Rt = 1/R1 + 1/R2 + 1/R3

Substituting the given values:

1/Rt = 1/3 + 1/0.8 + 1/2

Simplifying the equation:

1/Rt ≈ 1.6667

Rt ≈ 0.6 Ω

Next, calculate the total voltage, Vt, by summing the individual voltage sources:

Vt = ε1 + ε2 + ε3

Substituting the given values:

Vt = 9 + 6 + 4

Vt = 19 V

Now calculate the current flowing through resistor R4 using Ohm's Law:

I = Vt / Rt

Substituting the calculated values:

I = 19 / 0.6

I ≈ 31.6667 A

Finally, calculate the power dissipated in resistor R4:

P = I² × R4

Substituting the calculated values:

P = (31.6667)² × 10

P ≈ 10,028 W

Therefore, the magnitude of the power dissipated in resistor R4 is approximately 10,028 watts.

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To solve the problem, let's break it down into three parts:

1. Determining the distance covered by cars A and B as a function of time:

For uniformly accelerated rectilinear motion, we can use the following equation to calculate the distance covered:

distance = initial velocity * time + (1/2) * acceleration * time^2

For car A:

The initial velocity is 0 m/s, and the acceleration is 4 m/s².

So, the distance covered by car A at time t is:

d¹(t) = 0.5 * 4 * t^2 = 2t^2

For car B:

The initial velocity is 0 m/s, and the acceleration is -2 m/s² (opposite direction to car A).

So, the distance covered by car B at time t is:

d²(t) = 0.5 * -2 * t^2 = -t^2

2. Deducing the time of meeting for the two cars:

To find the time of meeting, we need to set the distances covered by both cars equal to each other:

2t^2 = -t^2

Simplifying the equation:

2t^2 + t^2 = 0

3t^2 = 0

Since the equation equals zero, the only solution is t = 0. This means that the two cars meet at the starting point at t = 0.

3. Considering car B in uniform rectilinear motion with a speed of 10 m/s:

If car B is moving at a constant speed of 10 m/s, it means its acceleration is 0 m/s². Therefore, the equation for car B's distance covered becomes:

d²(t) = initial velocity * time = 10 * t = 10t

Now, we can answer the preceding questions using this new equation for car B.

1. The distance covered by car A at time t is still d¹(t) = 2t^2.

The distance covered by car B at time t is now d²(t) = 10t.

2. The time of meeting for the two cars can be found by setting the distances equal to each other:

2t^2 = 10t

Simplifying the equation:

2t^2 - 10t = 0

2t(t - 5) = 0

From this equation, we have two solutions:

t = 0 (the initial meeting point)

t = 5 seconds (when the two cars meet again after 5 seconds)

Therefore, the cars meet again after 5 seconds.

Please note that the distances calculated above are in terms of t, the time elapsed since t = 0.

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The force between these charges, according to Coulomb's law would be -54 N.

We can solve this problem applying "Coulomb's Law" which states-

\(\qquad\:\sf \underline{F_{(air)} = K\times \dfrac{ q_1 q_2}{r^2}} \\ \)

\( \qquad\sf\underline{F_{(air)} = \dfrac{1}{4\pi \epsilon_{0} } \dfrac{q_1q_2}{r^2} }\\ \)

Where-

According to the given parameters -

Now that required values are given, so we can plug the values into the formula and solve for Force -

\(\qquad\qquad \:\sf\underline{Force = \dfrac{1}{4\pi \epsilon_{0} } \dfrac{q_1q_2}{r^2} }\\ \)

\( \longrightarrow \sf Force = 9\times 10^9 \times \dfrac{ 3\times 10^{-6}\times -5 \times 10^{-6}}{\bigg(5\times 10^{-2}\bigg)^2}\\ \)

\( \longrightarrow \sf Force = -\dfrac{9\times 5\times 3\times 10^{9} \times 10^{-12}}{25\times 10^{-4}}\\ \)

\( \qquad\longrightarrow \sf Force =- \dfrac{135 \times 10^{9-12+4}}{25}\\ \)

\( \qquad\longrightarrow \sf Force = - \dfrac{\cancel{135}}{\cancel{25}}\times 10\\ \)

\( \qquad\longrightarrow \sf Force = -5.4 \times 10\\ \)

\( \qquad\qquad\longrightarrow \sf \underline{Force = \boxed{\sf{-54 N}}} \\ \)

The length of the pendulum is measured from the lower part of the wooden clamp, because the center of gravity is at the center of the bob.

The simple pendulum's length, l is determined by measuring it from the point of suspension to the center of gravity (center of the bob), which is the place where all of this sphere's mass is concentrated.

The center of the mass will exactly reside in the center of the bob when we take the bob's dimensions into account.

As a result, the total length is now equal to the length of the string plus the bob's radius. The length is thus measured from the lower part of the wooden clamp.

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Answer:

176.38 rpm

Explanation:

mass percentage of arms and legs = 13%

mass percentage of legs and trunk = 80%

mass percentage of head = 7%

Total mass of the skater = 74.0 kg

length of arms = 70 cm = 0.7 m

height of skater = 1.8 m

diameter of trunk = 35 cm = 0.35 m

Initial angular momentum = 68 rpm

We assume:

We split her body into two systems, the spinning hands as spinning rods

1. Each rod has moment of inertia = \(\frac{1}{3} mL^{2}\)

mass m of the arms is 13% of 74 kg = 0.13 x 74 = 9.62 kg

mass of each side will be assumed to be 9.62/2 = 4.81 kg

L = length of each arm

therefore,

I =  \(\frac{1}{3}\) x 4.81 x \(0.7^{2}\) = 0.79 kg-m   for each arm

2. Her body as a cylinder has moment of inertia =  \(\frac{1}{2} mr^{2}\)

r = radius of her body = diameter/2 = 0.35/2 = 0.175 m

mass of body trunk = (80% + 7%) of 74 kg = 0.87 x 74 = 64.38 kg

I = \(\frac{1}{2}\) x 64.38 x \(0.175^{2}\) = 0.99 kg-m

We consider each case

case 1: Body spinning with arm outstretched

Total moment of inertia = sum of moments of inertia of both arms and moment of inertia of body trunk

I = (0.79 x 2) +  0.99 = 2.57 kg-m

angular momentum = Iω

where ω = angular speed = 68.0 rpm = \(\frac{2\pi }{60}\) x 68 = 7.12 rad/s

angular momentum = 2.57 x 7.12 = 18.29 kg-rad/m-s

case 2: Arms pulled down parallel to trunk

The momentum of inertia will be due to her body trunk alone which is 0.91 kg-m

angular momentum =  Iω

=  0.99 x ω = 0.91ω

according to conservation of angular momentum, both angular momentum must be equal, therefore,

18.29 = 0.99ω

ω = 18.29/0.99 = 18.47 rad/s

18.47 ÷ \(\frac{2\pi }{60}\)  = 176.38 rpm

The potential energy of a 2-kg object dropped from a height of 10 meters can be calculated by using the formula mgh

The potential energy is calculated as 200 Joules

If the object strikes the ground with a speed of 5 m/s, then using the formula ¹/₂mv², the kinetic energy is 100 joules.

This requires that some of the energy is turned into sound and eventually released to its surroundings.

Potential energy is the energy that an object has as a result of its position or height above the ground.

An object that is on the ground has zero potential irrespective of its mass. However, an object of mass m. that is at a height, h, above the ground, has potential energy that can be calculated as follows;

Potential energy = mgh

where;

The Potential energy of the 2 kg object = 2 * 10 * 10

Potential energy =  200 J

Kinetic energy is energy due to motion and is calculated using the formula /₂mv².

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Answer:

In an ionic bond the valence electrons are transferred from the metal

Explanation:

The amount of compression this bone can withstand before breaking is 4.56 mm.

A solid material's tensile or compressive stiffness when a force is applied longitudinally is measured by the mechanical property known as Young's modulus in tension or compression.

Mathematically, Young’s modulus can be expressed as:

Young’s modulus = Longitudinal stress ÷ Longitudinal strain

Y = P ÷ (Δl/l)

Y = Pl/Δl

Δl = Pl/Y

= (1.52 × 10⁸ × 0.54) ÷  (1.8 × 10¹⁰)

= 0.00456 meter

= 4.56 mm.

Hence, the amount of compression this bone can withstand before breaking is 4.56 mm.

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Answer:

3.5 s

Explanation:

Given

\(Initial\ Velocity (u) = 0m/s\) --- because it starts from rest

\(Height\ (S) = 60\ m\)

Required

Determine time (t) to hit the ground

This can be solved using the following motion equation

\(S = ut + \frac{1}{2}gt^2\)

Substitute values for S and u and take g as 9.8m/s^2

\(60 = 0 * t + \frac{1}{2} * 9.8 * t^2\)

\(60 = 0 + \frac{1}{2} * 9.8 * t^2\)

\(60 = \frac{1}{2} * 9.8 * t^2\)

Multiply through by 2

\(2 * 60 = 2 * \frac{1}{2} * 9.8 * t^2\)

\(120 = 9.8 * t^2\)

Solve for t^2

\(t^2 = \frac{120}{9.8}\)

\(t^2 = 12.2448979592\)

Take square roots

\(t = \sqrt{12.2448979592\)

\(t = 3.49927106112\)

\(t=3.5\ s\) ---- approximated

It would take a stone released from a height of 60m, 3.5s to hit the ground.

EQUATION OF MOTION:

Where;

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Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.

To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.

In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.

To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.

Total cost covered by the five friends = Total cost - Cost of one person's meal

= (£12 x 6) - £12

= £72 - £12

= £60

Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).

Amount each friend needs to pay = Total cost covered by the five friends / Number of friends

= £60 / 5

= £12

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The plate that feels colder is likely a better conductor of heat compared to the other plate.

Compared to the other plate, the one that feels cooler is probably a greater heat conductor. The capacity of a material to transfer heat is known as conductivity. A colder feeling will result from the plate's ability to more efficiently absorb heat from our skin if its thermal conductivity is higher.

The two plates may truly be at the same temperature, but our perception of that temperature is affected by the rate of heat transmission, it is crucial to note.

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The frequency of f3 is approximately 716 Hz.

The frequency of a repeated event is its number of instances per unit of time. Hertz (Hz), which stands for the number of cycles per second, is a popular unit of measurement.

a. Given two frequencies, f1 and f2, the frequency ratio is as follows:

frequency ratio= \(\frac{f2}{f1}\)

Inputting the values provided yields:

frequency ratio = \(\frac{576}{320Hz}\) =1.8.

As a result, the difference in frequency between f1 = 320 Hz and f2 = 576 Hz is 1.8.

b. Since there are 12 half-steps in an octave and a fourth is a distance of 5 half-steps, going down a fourth requires dividing the frequency by \(2^{(4/12)}\). Hence, once a fourth is subtracted, the frequency ratio between f and f1 is:

frequency ratio= \(\frac{f}{ (f1 /f2 ) }\)=  \(\frac{f}{ (f1 / 1.3348) }\)

By dividing the numerator and denominator by 1.3348, we may make this more straightforward:

frequency ratio= (f × 1.33348)/f1

As a result, (f × 1.3348) / f1 is the frequency ratio between f and f1 after descending a fourth.

c. (c) To find the frequency of f3, we need to know the interval between f1 and f3. Let's assume that f3 is a fifth above f2. The frequency ratio for a fifth is given by: \(2^{(7/12)}\) = 1.49831

Therefore, the frequency of f3 is:

f3 = f1 × (\(2^{(7/12)}\)) × (\(2^{(7/12)}\)) = 320 Hz × 1.49831 ×1.49831 = 716 Hz

Therefore, the frequency of f3 is approximately 716 Hz.

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Answer:

The ratio of the displacement amplitudes of two sound waves is 1.16.

Explanation:

Given that,

Frequency = 5.0 kHz

Intensity level difference = 3.0 dB

We know that,

The sound intensity is inversely proportional to the square of distance.

\(I\propto\dfrac{1}{r^2}\)

The sound intensity for first wave is

\(\beta_{1}=10\log\dfrac{I_{1}}{I_{0}}\)...(I)

The sound intensity for second wave is

\(\beta_{2}=10\log\dfrac{I_{2}}{I_{0}}\)...(II)

We need to calculate the ratio of intensity

From equation (I) and (II)

\(\beta_{2}-\beta_{1}=10\log\dfrac{I_{2}}{I_{0}}-10\log\dfrac{I_{1}}{I_{0}}\)

\(\Delta \beta=10\log(\dfrac{I_{2}}{I_{1}})\)

Put the value into the formula

\(3.0=10\log(\dfrac{I_{2}}{I_{1}})\)

\(\dfrac{I_{2}}{I_{1}}=e^{\dfrac{3.0}{10}}\)

\(\dfrac{I_{2}}{I_{1}}=1.34\)

We need to calculate the ratio of the displacement

Using formula of displacement

\(\dfrac{r_{1}}{r_{2}}=\sqrt{\dfrac{I_{2}}{I_{1}}}\)

Put the value into the formula

\(\dfrac{r_{1}}{r_{2}}=\sqrt{1.34}\)

\(\dfrac{r_{1}}{r_{2}}=1.16\)

Hence, The ratio of the displacement amplitudes of two sound waves is 1.16.

Answer:

The x and y components of the 500 N-force are 321.394 newtons and 383.023 newtons, respectively.

Explanation:

At first we present a figure describing the situation explained on statement, the x and y components of the force are determined by the following trigonometric expressions:

\(F_{x} = F\cdot \cos \alpha\) (1)

\(F_{y} = F\cdot \sin \alpha\) (2)

Where:

\(F\) - Magnitude of the force, measured in newtons.

\(\alpha\) - Direction of the force above the horizontal surface, measured in sexagesimal degrees.

If we know that \(F = 500\,N\) and \(\theta = 50^{\circ}\), then the components of the force is:

\(F_{x} = (500\,N)\cdot \cos 50^{\circ}\)

\(F_{x} = 321.394\,N\)

\(F_{y} = (500\,N)\cdot \sin 50^{\circ}\)

\(F_{y} = 383.023\,N\)

The x and y components of the 500 N-force are 321.394 newtons and 383.023 newtons, respectively.

When the pressure (100 N) and weight (40 kg) are entered into the appropriate fields, the gravity is 2 m/s².

Force and acceleration are linked by the equation F=ma. The characters "F," "m," and "a" stand for acceleration, mass, and force, respectively. Force is the ability of one object to exert a pull or force on another. Acceleration is the rate at which an object's speed changes.

Speed increase is the pace of progress of speed. Acceleration typically indicates a change in speed, but not always. Because its velocity is changing in the opposite direction, even if an object moves in a circle at the same speed, it will still accelerate.

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