a car accelerates uniformly from rest and reaches a speed of 21.3 m/s in 9.05 s. assume the diameter of a tire is 57.2 cm. find the number of revolutions the tire makes during this motion, assuming that no slipping occurs.

To find the value of ro, the inner radius of the spiral track on the CD, we need to use the given information and equations provided.

Let's convert this to millimeters, as the units of ro are in millimeters:

1.55 μm = 1.55 × 10^(-3) mm

To calculate the angular acceleration, we'll differentiate the equation of the spiral with respect to time:

dr/dθ = d(ro + 30)/dθ

=> 0 = d(ro)/dθ

Since the angular speed (dθ/dt) is constant, the derivative of ro with respect to time (d(ro)/dt) must be zero.

Given that ro is the inner radius of the track, we can express ro in terms of θ and then differentiate with respect to time:

=> ro = 25.0 mm + 30

ro = 55.0 mm

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The kinetic energy of a car with a mass of 1050kg and a velocity of 5m/s will be 13,125 joules or 13,125 kg⋅m2⋅s−2.

As we know, the formula to find the kinetic energy in a system is \(1/2 m v^{2}\) where m is the mass of the system and v is the given velocity at the moment. So , by putting the given data in the equation, we get :

⇒\(1/2mv^{2}\)

⇒1/2 x 1050 x 5 x 5

⇒525 x 25

⇒13,125

∴ The Kinetic energy of the car will be 13,125 Joules where joule is the SI unit of energy.

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The work required to stretch the spring from 12 cm to 19 cm is 0.91 J

When an object is moved across a specific distance by an external force, work is the quantity of energy that is transmitted to the object.

According to the given information

Natural length = 12 cm

Stretched length = 26 cm

Change in length ( x ) = 26 - 12 = 14 cm = 0.14 m

Force required = 26 N

It is known to us that spring force F = K x

K = \(\frac{F}{x}\)

K = \(\frac{26}{0.14}\)

K = 185.7 N/m

This is the stiffness of the spring

Now the Force that is required to stretch the spring F = K\(x_{1}\)

\(x_{1}\) = change in length of the spring = 19 - 12 = 7 cm = 0.07 m

F = 185.7 × 0.07

F = 13 N

Now the work that is done in stretching the spring W = F × \(x_{1}\)

W = 13 × 0.07

W = 0.91 J

The work required to stretch the spring from 12 cm to 19 cm is 0.91 J

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Newton's 2nd law of motion says:

Net force = (mass) · (acceleration) .

Newton didn't make up this law for his health.

Let's use it to answer this question about the car moving down the road.

Net force on the car = (car's mass) · (car's acceleration).

But the net force on the car is zero.  So we can write:

0 = (car's mass) · (car's acceleration).

Look at the right side of this equation.

Newton's law tells us that the product of the car's mass and the car's acceleration is zero.

That tells us that at least one of three things must be true.

Either 1). the car's mass is zero, or 2). the car's acceleration is zero, or 3). Newton was crazy.

We're pretty sure that 1). and 3). are false. The car's acceleration is zero.

What does this mean ? It means that the car's speed and direction are not changing.

That's exactly what Choice-B says.

An appropriate value for the resistance in parallel with the smoothing capacitor would be 1.59 kΩ.

To ensure good tracking of the AM envelope, the resistance in parallel with the smoothing capacitor should be low enough to discharge the capacitor quickly during the troughs of the modulated signal, but high enough to avoid discharging it too quickly during the peaks of the signal.

The time constant (τ) of the RC circuit formed by the smoothing capacitor and the parallel resistance is given by the formula:

τ = RC

where R is the resistance and C is the capacitance.

To determine an appropriate value for the resistance, we need to calculate the time constant and compare it to the period of the modulated signal.

The period of a 500 kHz signal is T = 1/f = 2 μs. The modulating signal has a bandwidth of 5 kHz, which means its period is 200 μs.

Assuming a small signal approximation, we can use the formula for the time constant to calculate an appropriate value for the resistance:

τ = 20 nF × R = T/2π = 31.8 ns

Solving for R, we get:

R = τ/C = 31.8 ns / 20 nF = 1.59 kΩ

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Complete question is:

The input signal into an envelope detector is an am signal of carrier frequency 500 khz. the envelope detector employs a smoothing capacitor of 20 nf. the modulating signal has a bandwidth of 5 khz. specify an appropriate value for the resistance in parallel with the smoothing capacitor for a good tracking of the am envelope.

The following changes would cause the greatest increase in the rate of flow of charge through a conducting wire is increasing the applied potential difference and decreasing the length of the wire.

In a conducting wire, the rate of flow of charge is determined by the magnitude of the potential difference (PD) across the wire, as well as the resistance offered by the wire. The resistance of a wire, in turn, is directly proportional to its length, and inversely proportional to its cross-sectional area. A higher potential difference will cause more current to flow through the wire, as per Ohm's Law: I = V/R, where I is the current, V is the potential difference, and R is the resistance of the wire.

Decreasing the length of the wire, a shorter wire will offer less resistance to the flow of current, leading to an increase in the rate of flow of charge. Of these two changes, increasing the applied potential difference would cause the greatest increase in the rate of flow of charge through the wire, since it has a direct effect on the current. The exact amount of increase in the current would depend on the resistance of the wire, which could decrease as the wire is shortened. So therefore the following changes would cause the greatest increase in the rate of flow of charge through a conducting wire is increasing the applied potential difference and decreasing the length of the wire.

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The closest answer among the options given is 3.9 x 105 J. . An object can accelerate by increasing its speed, changing its direction, or both.

What is Acceleration?
Acceleration is the rate of change of velocity of an object over time. It is a vector quantity, meaning it has both magnitude and direction, and is expressed in units of meters per second squared (m/s^2) or feet per second squared (ft/s^2)

The work done to accelerate the car can be calculated using the kinetic energy formula:

K = 1/2 mv^2

Substituting the given values, we get:

K = 1/2 (1600 kg) (22 m/s)^2

K = 677,600 J

Therefore, the work done to accelerate the car to this speed is 677,600 J.

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8. The velocity of the electron in this orbit is  4.35 x 10^6 m/s, 9. The meter stick is moving relative to the observer at  7.35 x 10^8 ft/s, and 10. the mass of the electron is 9.11 x 10^-31 kg.

8. The de Broglie equation states that the wavelength (λ) of a particle is equal to Planck's constant (h) divided by the particle's momentum (p): λ = h/p. We can rearrange this equation to solve for the momentum: p = h/λ.

In this problem, we are given the wavelength of an electron in a hydrogen atom (λ = 1.67 x 10^-10 m) and the value of Planck's constant (h = 6.626 x 10^-34 Js). Therefore, we can use the de Broglie equation to find the momentum of the electron:

p = h/λ = (6.626 x 10^-34 Js)/(1.67 x 10^-10 m) ≈ 3.96 x 10^-24 kg m/s

Next, we can use the formula for the momentum of a particle to find its velocity (v): p = mv, where m is the mass of the particle. Solving for v, we get:

v = p/m = (3.96 x 10^-24 kg m/s)/(9.11 x 10^-31 kg) ≈ 4.35 x 10^6 m/s

So, the velocity of the electron in this orbit is approximately 4.35 x 10^6 m/s.

9. We can use the concept of relativistic length contraction to solve this problem. When an object moves at high speeds relative to an observer, its length appears to be shorter in the direction of motion. The formula for the relativistic length contraction factor (γ) is:

γ = 1/√(1 - v^2/c^2)

where v is the speed of the object relative to the observer, and c is the speed of light.

In this problem, the length of the moving meter stick appears to be 1 ft (which is equivalent to 12 inches or 30.48 cm) to the observer. Therefore, we can use the relativistic length contraction formula to solve for the speed of the meter stick:

γ = 1/√(1 - v^2/c^2) = 1/√(1 - (30.48 cm/1 ft)^2/(2.54 cm/in)^2) ≈ 1.002

Squaring both sides of this equation, we get:

1 - v^2/c^2 = 1/γ^2 ≈ 0.998

Solving for v, we get:

v = c√(1 - 1/γ^2) ≈ 2.25 x 10^8 m/s

Converting this speed to feet per second (ft/s), we get:

v ≈ 7.35 x 10^8 ft/s

So, the meter stick is moving relative to the observer at approximately 7.35 x 10^8 ft/s.

10. The charge-to-mass ratio of the electron (e/m) is given as -1.76 x 10^-19 C/kg. We can use this value and the charge of the electron (e = -1.602 x 10^-19 C) to solve for the mass of the electron:

e/m = -1.76 x 10^-19 C/kg

m = e/(-1.76 x 10^-19 C/kg) = (-1.602 x 10^-19 C)/(-1.76 x 10^-19 C/kg) ≈ 9.11 x 10^-31 kg

So, the mass of the electron is approximately 9.11 x 10^-31 kg.

Hence. 8. The velocity of the electron in this orbit is  4.35 x 10^6 m/s, 9. The meter stick is moving relative to the observer at  7.35 x 10^8 ft/s, and 10. the mass of the electron is 9.11 x 10^-31 kg.

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Answer:

The product choices along with its competitive prices were provided to the consumers. Practices such as horizontal collusion and resale price maintenance was declared unlawful in 1984. Prevention of monopoly growth was the aim of the competition policy act.

Explanation:

hope this helps you

Answer with Explanation:

Spain is known to have hot summers, thus, it is very easy for water to evaporate once exposed to direct heat source (such as the sun).

A fountain is being used in order to keep the garden's surrounding air temperature low by allowing the evaporation of water. One factor that speeds up the evaporation of water is the surface area. The water coming out of a fountain is in small quantities; however, it meets up with hot air in a large surface area. This allows faster evaporation, leading to an even greater cooling effect because heat is being transported immediately from the liquid state to the gaseous state. This is the reason why people often meet up in places where there's a fountain. It is not only aesthetically appealing but also provides comfort from the heat.

Answer:

B

Explanation:

Researchers begin their study by identifying the rock type and then dating the meteorite

Explanation:

.

The molarity of solution of NaCl is 2.28 M

The molarity of a solution is the amount in moles of a solute dissolved in a given volume of solvent in liters.

The moles of a substance = mass/ molar mass

Molar mass of NaCl = 58.5 g/mol

Moles of NaCl = 200/58.5

Moles of NaCl = 3.42 moles

Molarity of solution = 3.42/1.5

molarity of solution = 2.28 M

Therefore, the molarity of the solution of NaCl is 2.28 M.

In conclusion, molarity is the ratio of moles of solute and volume of solvent.

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Answer:

Source:

Answer:

The amplitude of the resulting oscillations can be calculated using the formula:

A = F/mω^2

where F is the amplitude of the applied force, m is the mass of the object, and ω is the angular frequency of the applied force.

In this case, F = 4.8 N, m = 2.0 kg, and ω = 3.0 rad/s.

Substituting these values into the formula, we get:

A = 4.8/(2.0 x (3.0)^2) = 0.267 m or 0.27 m (rounded to two significant figures)

Therefore, the amplitude of the resulting oscillations is 0.27 m, which is closest to option A) 0.15 m.

Explanation:

The electric eel's power output is 222.4 Watts

Given voltage (V) = 278 V

Current (I) = 0.8 A

To find the electric eel's power output, we have to use the formula

P = IV,

Where P is the power output, I is current, and V is the voltage.

So, we can calculate the electric eel's power output as follows:

Power Output (P) = IVP

⇒278 × 0.8

Power Output (P) = 222.4 Watts

Hence, The power output of the electric eel is 222.4 Watts.

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Answer:

Tide rising and falling would be different from the moon near the Earth .

(a) A solar panel with an area of approximately 3.86 m2 is needed to supply 9 A at 120 V, assuming a 40% efficiency and 700 W/m2 solar irradiance. (b) such a solar panel can save approximately $0.98 per day in utility costs.

To calculate the required roof area to supply 9 A at 120 V, we need to first calculate the power needed by the load.

Power (P) = Voltage (V) x Current (I) = 120 V x 9 A = 1080 W

Next, we can calculate the power output of the solar panel:

Power output of solar panel = Solar irradiance x Efficiency = 700 W/m2 x 0.4 = 280 W/m2

Now, we can calculate the area of the solar panel needed to produce the required power:

Area = Power required / Power output of solar panel = 1080 W / 280 W/m2 = 3.857 m2 or approximately 3.86 m2 (rounded to three decimal places).

Therefore, a solar panel with an area of approximately 3.86 m2 is needed to supply 9 A at 120 V, assuming a 40% efficiency and 700 W/m2 solar irradiance.

To calculate the savings in utility cost, we need to first calculate the energy produced by the solar panel per day.

Energy produced per day = Power output of solar panel x Hours of sunlight = 280 W/m2 x 8 hours = 2240 Wh or 2.24 kWh

Next, we can calculate the cost savings per day:

Cost savings per day = Energy produced per day x Utility cost per kWh = 2.24 kWh x $0.44/kWh = $0.98

Therefore, such a solar panel can save approximately $0.98 per day in utility costs, assuming an average of 8 hours of sunshine per day and a utility cost of $0.44/kWh. Over the course of a year, this would add up to approximately $357 in savings.

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The radius of the circular path is approximately 0.0251 m. The angle through which the direction of the beam changes is 1.62 × \(10^{-5}\)radians.

The equation for the centripetal force, which is given by F = Bqv

R = mv / Bq

Substituting the given values, we get:

R = (9.10938356 × \(10^{-31}\)kg) × (1.8 × \(10^7\) m/s) / (2 × \(10^{-3}\) T × 1.60217662 × \(10^{-19}\)C)

R = 0.0251 meters or 2.51 centimeters

θ = (qvBt) / m

θ = (1.60217662 × \(10^{-19}\) C) × (1.8 × \(10^7\) m/s) × (2 × \(10^{-3}\) T) × (0.41 × \(10^{-9}\) s) / (9.10938356 × \(10^{-31}\) kg)

θ = 1.62 × \(10^{-5}\) radians

Centripetal force is a type of force that acts on an object moving in a circular path, causing it to continuously change direction. It is directed towards the center of the circle and is responsible for keeping the object moving along the circular path.

According to Newton's laws of motion, an object in motion tends to stay in motion unless acted upon by a net external force. In the case of circular motion, the centripetal force is the net force that acts on the object and keeps it moving in the circular path. The magnitude of the centripetal force depends on the mass, speed, and radius of the circular path. It can be calculated using the formula Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.

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Answer:

Solon,

total mass (kg)= 100kg

height (h)= 25m

acceleration due to gravity = 9.8m/s²

so,

work done =m*g*h

= 100*9.8*25

= 24,500 joule

The work done by the crane in lifting the given mass of concrete to the given vertical height is 24500 Joules.

Work done is simply defined as the energy transfer that takes place when an object is either pushed or pulled over a certain distance by an external force. It is expressed as;

W = F × d

Where f is force applied and d is distance travelled.

Note that, the concrete is lifted upward, Weight of the concrete becomes mass multiply by acceleration due to gravity. g = 9.8m/s²

F = Weight = mg

Given that;

W = F × d

W = (mg) × d

W = ( 100kg × 9.8m/s² ) 25m

W = 980kgm/s² × 25m

W = 24500kgm²/s²

W = 24500J

Therefore, the work done by the crane in lifting the given mass of concrete to the given vertical height is 24500 Joules.

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The wavelength of the light has beam 355 nm.

What is a wavelength?
A wavelength is the measure of a wave's distance from one peak to the next. It is the physical distance between two successive wave crests or troughs, and is usually measured in meters, nanometers, or micrometers. Wavelengths are an important aspect of light, sound, and other types of waves. Wavelengths are often used to describe the properties of these waves such as their color, pitch, and intensity. Wavelengths are also related to the frequency of a wave, with shorter wavelengths associated with higher frequencies and longer wavelengths associated with lower frequencies.

The wavelength of the light beam can be calculated using the equation λ = h/eV, where h is Planck's constant, e is the charge of an electron, and V is the potential difference in volts.
For this question, the wavelength of the light beam is therefore λ = (6.626 x 10-34 Js)/(1.602 x 10-19 C x 1 V) = 4.13 x 10-7 m or 355 nm.

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Answer:

Their deceleration is - 19 \(\frac{m}{s^{2} }\)

Explanation:

Acceleration is a quantity that indicates how the speed of the object changes over time. In other words, acceleration is a vector quantity that relates changes in velocity to the time it takes to occur. It is normally represented by the letter a and its unit of measurement, in the International System it is meters per second squared \(\frac{m}{s^{2} }\).

The mathematical expression for the acceleration is:

\(a=\frac{final speed - initial speed}{final instant - initial instant}\)

In this case:

Replacing:

\(a=\frac{0 \frac{m}{s} - 2.8\frac{m}{s} }{0.15 s - 0s}\)

a= -18. 667 \(\frac{m}{s^{2} }\) ≅ -19 \(\frac{m}{s^{2} }\)

Deceleration is a quantity that expresses the passage of a moving body from one speed to a lower speed. Mathematically it is calculated as the acceleration but the result will be a negative acceleration.

Their deceleration is - 19 \(\frac{m}{s^{2} }\)

The maximum displacement from equilibrium that the mass will attain is 0 meters.

To determine the maximum displacement from equilibrium, we need to consider the properties of the mass-spring-damper system and its response to the given initial conditions.

Given:

Mass of the system, m = 4 kg

Stiffness of the spring, k = 48 N/m

Damping constant, c = 16√3 N·s/m

Initial displacement, x₀ = 10 cm = 0.1 m

Initial velocity, v₀ = 3 m/s

The equation of motion for the mass-spring-damper system is given by:

\(m * d^2x/dt^2 + c * dx/dt + k * x = 0\)

We can rewrite this second-order differential equation as:

\(d^2x/dt^2 + (c/m) * dx/dt + (k/m) * x = 0\)

The general solution to this equation consists of two parts: the complementary solution (representing the transient behavior) and the particular solution (representing the steady-state behavior).

The complementary solution is given by the homogeneous solution:

\(x_c(t) = A * e^(\lambda_1t) + B * e^(\lambda_2t)\)

where A and B are constants determined by the initial conditions, and λ₁ and λ₂ are the roots of the characteristic equation:

\(\lambda^2 + (c/m) * \lambda + (k/m) = 0\)

In this case, the roots of the characteristic equation are complex conjugates since \(c^2 < 4mk\). Let's denote the real part of the roots as α and the imaginary part as β:

λ₁ = α + βi

λ₂ = α - βi

The particular solution, representing the steady-state behavior, is given by:

\(x_p(t) = D * cos(\omega t - \phi)\)

where D is the amplitude of the steady-state response and φ is the phase angle.

To find the maximum displacement, we need to determine the amplitude D, which represents the maximum value of the steady-state response.

The amplitude D can be calculated using the formula:

\(D =\frac{F}{sqrt((k - m*omega^2)^2 + (c\omega)^2)}\)

where F is the amplitude of the driving force (which is zero in this case), ω is the angular frequency, and ω = √(k/m) is the natural angular frequency of the system.

Substituting the given values into the formula, we have:

\(D =\frac{0}{sqrt((k - m*omega^2)^2 + (c\omega)^2)}\)

= 0

Therefore, the maximum displacement from equilibrium that the mass will attain is 0 meters.

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A distributed denial-of-service (DDoS) attack known as a "SYN flood" makes use of the three-way handshake that the Transmission Control Protocol (TCP) uses to link two servers.

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(Complete Question :Which of the following conditions are results of a SYN (synchronize) flood attack? (Select all that apply.) A. Packet filtering. B. Resource exhaustion. C. System instability. D. Denial of service.)

The linear velocity in terms of the angular velocity is,

where,

The angular velocity in terms of the linear frequency is,

Thus, the linear velocity in terms of linear frequency is,

The linear velocity in terms of the displacement and time is,

The relation given in the first option is the expression for centripetal acceleration.

Thus, option a is the correct answer.

Answer: 20,000 seconds

Explanation: there are 1000 miles in a km, so 200km is 200,000 miles

Answer:

have two or more paths

Explanation:

A parallel circuit is one that has two or more paths for the electricity to flow, the loads are parallel to each other.

If the car b travels a distance d before stopping, the car a travelled a distance of 4D.

The third equation of motion can be used to calculate the distance how far the cars drove before coming to a stop:

Vf2 - Vi2 = 2as

(Vf2 - Vi2)/2a = s

where,

s is the distance covered.

Final Speed = 0 m/s for Vf

Initial Speed = Vi

an is the deceleration rate.

We start by thinking about Car B and giving it a subscript 2:

Vf₂ = 0 m/s (As, automobile finally stops) (As, car finally stops)

s₂ = D

a₂ = - a (due to slowdown) (due to deceleration)

D = (0² - Vi₂²) /(-2a) (-2a)

the equation D = Vi22/2a (1)

We now take Car A into consideration and give it a subscript 1:

Vf₁ = 0 m/s (As, automobile finally stops) (As, car finally stops)

s₁ = ?

a₁ = - a (due to slowdown) (due to deceleration)

Vi₁ = 2 Vi₂ (Since, car A was previously moving at twice speed of car B) (Since, car A was initially traveling at twice speed of car B)

s₁ = (0² - Vi₁²) /(-2a) (-2a)

s₁ = (2Vi₂)²/2a

s₁ = 4 (Vi₂²/2a)

Using formula (1), we arrive at:

s₁ = 4D.

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