Given the following velocity time graph of 7kg object what is the impulse during segment c (from35 to 55 seconds)

Solving the equation f(x) = 0 will give us the equilibrium points, the differential equation governing z(t) is \(\frac{dz}{dt} = \frac{dx}{dt} = f(x)\), the system trajectories is negative semidefinite: \(\frac{dV(z)}{dt} \leq 0\) for all z and The solution to the linear differential equation can be written as:

\(z(t) = Ce^(^A^t^)\)

a) To find the equilibrium points of the given scalar nonlinear system, we need to set the derivative of the system with respect to the variable (in this case, x) equal to zero. Let's denote the system as dx/dt = f(x).

So, we have:

\(\frac{dx}{dt} = f(x) = 0\)

Solving the equation f(x) = 0 will give us the equilibrium points.

b) For the positive equilibrium point \(xe^+\), let \(z = x - xe^+\). To find the differential equation governing z(t), we substitute this value of z into the original system equation:

\(\frac{dz}{dt} = \frac{dx}{dt} = f(x)\)

Substituting \(z = x - xe^+\) into f(x), we get:

\(\frac{dz}{dt} = f(x) = f(z + xe^+)\)

c) To show that \(V(z) = (1/2)z^2\) is a Lyapunov function, we need to demonstrate the following properties:

V(z) is positive definite: V(z) > 0 for all z ≠ 0, and V(0) = 0.

V(z) is radially unbounded: V(z) approaches infinity as z approaches infinity.

The derivative of V(z) along the system trajectories is negative semidefinite: \(\frac{dV(z)}{dt} \leq 0\) for all z.

d) For z ≈ 0, we can consider the linearized form of the system around the equilibrium point z = 0. This involves finding the linear differential equation governing z(t), which can be obtained by linearizing the nonlinear system equation around z = 0.

The linearized equation will have the form:

\(\frac{dz}{dt} = Az\)

Where A is the Jacobian matrix evaluated at the equilibrium point z = 0.

The solution to the linear differential equation can be written as:

\(z(t) = Ce^(^A^t^)\)

Where C is a constant determined by the initial conditions.

To argue that the equilibrium point \(ze = 0\) is asymptotically stable, we need to show that all trajectories starting sufficiently close to z = 0 converge to the equilibrium point as t → ∞. This can be inferred by examining the eigenvalues of the matrix A. If all eigenvalues have negative real parts, then the equilibrium point is asymptotically stable.

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Answer:

Explanation:

A) E) When the light hits a square on the CCD charge is produced

B) A) Starting in one corner the charge on each square is moved off the CCD

C) D) The charges on each square are converted into a digital signal

D) B) Light enters the camera

E) C) That signal can be stored or sent to a computer or other device

b. The delay between taking one photograph with a digital camera and taking the next photograph is due to the time it takes to capture the image and process it into a digital signal. This process includes the capturing of the light entering the camera, the conversion of the charges on each square of the CCD into a digital signal, and the storage or sending of the signal to a computer or other device.

1 ) The value of the race constant acceleration = 28.14  m / s²

2 ) Time taken by the car to complete the distance = 5.33 s

s = ( u + v ) t / 2

s = Displacement

u = Initial velocity

v = Final velocity

t = Time

u = 0 m / s

v = 150 m / s

s = 400 m

400 = ( 0 + 150 ) t / 2

t = 800 / 150

t = 5.33 s

v = u + a t

a = Acceleration

150 = 0 + 5.33 a

a = 150 / 5.33

a = 28.14  m / s²

Therefore,

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Answer:

-220 j

Explanation:

The resistance of a conductor rise with temperature because high temperature cause vibration which make difficult the flow of electron.

When electrons move through a conductor, it collide with atoms, electrons or other substances. These collisions cause resistance which leads to generate heat. Heating the metal conductor leads to more vibration of an atoms which in turn makes it more difficult for the electrons to flow through a conductor that leads to increasing resistance.

So we can conclude that the resistance of a conductor rise with temperature because high temperature cause vibration which make difficult the flow of electron.

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Answer:

R = -2500N

Explanation:

Use formula ΣF = Ma. We can split the Net Force into two parts: Fe - Ff  =  Ma.

Fe is the force developed by the engine: 4000N

Ff (R) is the air resistance projected on the vehicle. This is the value we're looking for.

Mass: 1000kg

Acceleration: 1.5m/s^2

Next, just plug in the values and solve.

▪4000N - Ff  =  (1000kg)(1.5m/s^2)

▪Ff = 1500N - 4000N

▪Ff = -2500N

R = -2500N.

The air resistance acting on the car is R = -2500N.

Answer: The moon is said to be in full phase when the illuminated half of the moon is fully in position for us to see it. The "new moon" phase of the lunar cycle happens when the sun, moon, and earth are located in a straight line, with the moon between the earth and the sun. The moon is said to be in a "waxing" phase when it is moving from the new moon phase into the full moon phase. During this time, the amount of visible, illuminated moon will be gradually growing. The moon is said to be in a "waning" phase when it is moving from the full moon phase into the new moon phase. During this time, the visible portion of the moon will appear to be shrinking. A crescent moon occurs close to the new and full moon stages, whether the moon is waxing or waning. At this time, only a small sliver of the illuminated moon is visible to us.

Explanation:

When you move the compass near the north pole of the bar magnet, the north pole of the compass will point towards the south pole of the bar magnet.

This is because opposite poles attract each other, so the north pole of the compass is attracted to the south pole of the magnet. When you move the compass near the south pole of the bar magnet, the north pole of the compass will point towards the north pole of the bar magnet. This is because like poles repel each other, so the north pole of the compass is repelled by the south pole of the magnet and is attracted to the opposite pole.

A north pole and a south pole attract each other, while like poles repel each other. Therefore, the north pole of the bar magnet attracts the south pole of the compass, and the south pole of the bar magnet attracts the north pole of the compass.

Based on the previous answers, the Earth's geographic North Pole is near the Earth's magnetic South Pole. This is because opposite magnetic poles attract each other, and the North Pole of the Earth is attracted to the South Magnetic Pole.

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Each aircraft must be moving at a speed of 85.75 km/hr towards each other to hear a pitch that is 2 times the emitted frequency.

What is frequency ?

Frequency is a physical quantity that describes the number of occurrences of a repeating event per unit of time. It is often measured in Hertz (Hz), which represents the number of cycles or vibrations per second.

In the context of waves, such as sound waves or electromagnetic waves, frequency refers to the number of complete cycles of the wave that occur in one second. A high frequency wave has more cycles per second than a low frequency wave.

Frequency is also an important concept in physics, particularly in the study of oscillations and waves. It is used to describe the behavior of systems that oscillate or vibrate, such as a simple pendulum or a guitar string. In these cases, the frequency of the oscillation is related to the natural frequency of the system, which is determined by its mass, stiffness, and other properties.

When two aircraft are moving towards each other, the sound waves from each aircraft are compressed, leading to a higher pitch than the emitted frequency. The pitch heard by the pilots of the aircraft can be calculated using the following formula:

Pitch heard = Emitted frequency * (Speed of sound + Speed of observer) / (Speed of sound - Speed of source)

Since the two aircraft are flying towards each other at the same speed, we can assume that the speed of one aircraft is x km/hr, and the speed of the other aircraft is also x km/hr. Therefore, the relative speed between the two aircraft is 2x km/hr.

Substituting the values given in the formula, we get:

2 * Emitted frequency = Emitted frequency * (343 + 2x) / (343 - x)

Simplifying this equation, we get:

686 - 2x = 343 + 2x

4x = 343

x = 85.75 km/hr

Therefore, each aircraft must be moving at a speed of 85.75 km/hr towards each other to hear a pitch that is 2 times the emitted frequency.

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Answer:

New Moon - Crescent Moom ---- Full Moon ---- Waning Quarter

Explanation:

The Moon revolves around the Earth in a 28 day period, which is approximately one Earth month, therefore S the student has been recording the movement of the Moon for 4 Earth weeks this is a period of complete revolution of the Moon .

Consequently you must register the following phases

New Moon - Crescent Moom ---- Full Moon ---- Waning Quarter

in the period where it begins, it must go through the cycle in an orderly way to the right.

Answer:

The pressure altitude is \(A = 10\ km\)

The density altitude is \(\rho = 0.429 kg/m^3\)

Explanation:

From the question we are told that

The outside pressure is \(P_o = 2.65*10^{4} N/m^2\)

The outside temperature is \(T_o = 215 \ K\)

Generally the density altitude is mathematically represented as

\(\rho = \frac{P_o }{RT}\)

Here R is the gas constant with value \(R = 287\ J/kg/K\)

So

\(\rho = \frac{2.65 (*10^{4}}{287 * 215}\)

=> \(\rho = 0.429 kg/m^3\)

Generally the altitude at which the pressure in the question is experience is

\(A = 10\ km\)

Thus the pressure altitude is  \(A =  10\ km\)

Answer:

Kinetic Energy = 1/2 mass*velocity^2

K=1/2mv^2

Therefore if you reduce the speed of an object by 1/2, K reduced to 1/4 its value.

Answer:

A.

Explanation:

I remember this one from my science class.

The molecules in the wood are vibrating faster .

During heating, the temperature of any object or substance increases. This cause the particles to move faster as they gain kinetic energy which leads to an increase in the collision rate as well as diffusion.

Heat is the result of the movement of kinetic energy within a material or an item, or from an energy source to a material or an object. Radiation, conduction, and convection are the three mechanisms through which such energy can be transferred.

The International System of Units (SI) defines the calorie (cal) as the standard unit of heat. The cal measures the amount of energy transfer needed to raise the temperature of one gram of pure liquid water by one degree Celsius, provided that the water is above the freezing point and below the boiling point.

Therefore, The molecules in the wood are vibrating faster .

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Answer:

lol can u tell what to help u with. cause I didn't understood

The Solar weather affects the Earth's magnetosphere which is a threat to our magnetic protection and generates auroras.

The effect of Earth's magnetosphere is like widening a hole - suddenly more energy and particles enter the magnetosphere. Auroras intensify, and geomagnetic storms become likely.

For this reason the scientists pay careful attention to not only the strength but also the orientation of incoming magnetic fields from the sun.

As the wind blows from the galaxy towards the earth it carries with it the Sun's magnetic field and moves very fast, then smacks right into the Earth's magnetic field. The blow causes a shock to our magnetic protection thus which can result in turbulence.

So we can conclude that The Solar weather affects the Earth's magnetosphere which is a threat to our magnetic protection and generates auroras.

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The time taken by the box to reach the velocity of 2 m / s will be 4 sec.

Force is defined as the external effort or agent applied to the object in a particular direction to displace it from one position to another position. The force is measured in a Newton.

Given that the force applied is 5 N and the velocity is 2 m / s. The mass of the object is 10 kg.

The time required by the object to get the velocity of 2 m/s will be calculated as:-

Force x Time = m x V

Time = ( m x V ) / F

Time  = ( 10 x 2 ) / 5

Time = 4 sec

Hence, the time will be equal to 4 seconds.

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Hi there!

Recall the equation for torque:
\(\large\boxed{\Sigma \tau = rF}\)

∑τ = Net Torque (Nm)

r = lever arm (m)

F = Force (N)

Rearrange to solve for force:

\(F = \frac{\tau}{r}\)

Plug in the givens:

\(F = \frac{45}{0.21} = \boxed{219.05 N}\)

Answer: the group in an experiment that doesn’t get treatment

Explanation:

First, let's calculate the electric force, using the formula below:

Now, let's use the second law of Newton to find the acceleration:

a = (v - u)

t

v final velocity

u initial velocity

a = (10 - 40)

12

a = -30/12

a = -5/2 m/s²

This will be the deceleration.

Sure! To elaborate further, recursive methods are functions that call themselves with different inputs until a base case is reached. The base case is a condition that stops the recursion and returns a result. In the case of a method that computes the nth Fibonacci number, the base cases are often defined as n == 0 and n == 1, as the Fibonacci sequence starts with 0 and 1.

Here is an example of a recursive method that computes the nth Fibonacci number in Java:

```

public int fibonacci(int n) {

   if (n == 0) {

       return 0;

   } else if (n == 1) {

       return 1;

   } else {

       return fibonacci(n - 1) + fibonacci(n - 2);

   }

}

```

In this implementation, the method checks if n is 0 or 1, and if so, it returns the corresponding value. Otherwise, it recursively calls itself with n-1 and n-2 as inputs and returns the sum of the two results. This process continues until the base cases are reached and the recursion stops.

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The answer is Thermal Pollution .

Pollution is the introduction of pollutants into the natural setting that causes negative changes. Pollution will take the shape of any substance (solid, liquid, or gas) or energy (such as radiation, heat, sound, or light). Pollutants, will be foreign substances/energy or pollution that happens naturally. though pollution will be caused by natural phenomena, the word pollution usually implies that pollution is associated with phylogenesis supply - that's, a supply created by human activities. Pollution is usually viewed as a supply of pollution or pollution of associated indirect supply.

The main sorts of pollution embody pollution, lightweight pollution, garbage, pollution, plastic pollution, soil pollution, radiation pollution, heat pollution, visual pollution, and pollution.

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Compared to a coal power plant that produces , same amount of energy, a nuclear plant generates less CO2, SO2, fly ash, and thermal pollution.

Coal-fired power plants generate electricity by burning coal to produce steam, which is then used to generate electricity. This process releases a variety of pollutants into the air, including CO2, SO2, fly ash, particulates, and thermal pollution. These pollutants contribute to air pollution and can have negative impacts on human health and the environment.

On the other hand, nuclear power plants generate electricity by using nuclear fission to produce heat, which is then used to generate electricity. This process releases significantly less air pollutants than coal-fired power plants. In particular, nuclear power plants generate very low levels of CO2, SO2, fly ash, particulates, and thermal pollution compared to coal-fired power plants.

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Answer:

D. Dylan is incorrect because a 90-degree launch angle results in the largest vertical range​

Explanation:

Projectile is the motion of an object thrown into space. When an object is thrown into space, the only force which acts on it is the acceleration due to gravity.

An object thrown into space would reach maximum height (vertical range) if it is launched at an angle of 90 degrees. For maximum horizontal range, the object needs to be launched at an angle of 45 degrees.

Therefore Dylan is incorrect because a 90-degree launch angle results in the largest vertical range​

The correct statement is

D. Dylan is incorrect because a 90-degree launch angle results in the largest vertical range​

It is the object motion that should be thrown into space. At the time when the object is thrown into space, the only force that should act on it represent the acceleration because of gravity.

Since object thrown into space should have to reach maximum height in the case when it is launched the 90 degrees angle. Due to the above reasons, option D is considered.

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Voyager 2 passed closer to the southern magnetic pole of Uranus.

During its flyby of Uranus in 1986. This was determined by the measurements taken by the spacecraft's instruments, which detected the magnetic field of Uranus and allowed scientists to map its magnetic structure.

The spacecraft's trajectory and the data collected indicated that Voyager 2 passed nearer to the southern magnetic pole than the northern one. This encounter provided valuable insights into the magnetic field and overall magnetosphere of Uranus, contributing to our understanding of the planet's unique characteristics and the dynamics of its magnetic environment.

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Answer:

For liquid at room temperature and pressure, the value of specific heat capacity (Cp) is approximately 4.2 J/g°C.

Explanation: This implies that it takes 4.2 joules of energy to raise 1 gram of water by 1 degree Celsius. This value for Cp is actually quite large. This (1 cal/g.

The smallest sound power output of the airplane motor that can be listened to on the ground is  6.73 × 10^-6 W which has the lowest-intensity sound that is still loud and has an intensity of  10^-12 W/m^2.

The intensity of sound =  10^-12 W/m^2

Altitude =  6,500 m.

Calculate the smallest sound energy output of an aircraft motor that can be heard on the ground is done by using the formula:

I = P/(4πr^2)

Pythagoras' theorem is used for calculating the distance

d = (\(\sqrt{6500^2 + R^2}\))

I = 10^-12 W/m^2

d = \(\sqrt{6500^2 + R^2}\)

d = 6500 m

P/(4πd^2) = I

\(P/(4π(6500)^2) = 10^-12 W/m^2\)

\(P = 4π(6500)^2 × 10^-12 W\)

P = 6.73 × 10^-6 W

Therefore, we can conclude that the smallest sound power output of the aircraft engine that can be heard on the ground is  6.73 × 10^-6 W.

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Starting from rest on a circular track with a radius of 300 m and a constant tangential acceleration of 0.75 m/s², the car will travel a distance of approximately 0.2119 meters or 21.19 centimeters in 0.75 seconds.

To determine the distance traveled and the time elapsed by the car starting from rest on a circular track with a radius of 300 m and a constant tangential acceleration of 0.75 m/s², we can use the equations of circular motion.

The tangential acceleration is the rate of change of tangential velocity. Since the car starts from rest, its initial tangential velocity is zero (v₀ = 0).

Using the equation:

v = v₀ + at

where v is the final tangential velocity, v₀ is the initial tangential velocity, a is the tangential acceleration, and t is the time, we can solve for v:

v = 0 + (0.75 m/s²) * t

v = 0.75t m/s

The tangential velocity is related to the angular velocity (ω) and the radius (r) of the circular track:

v = ωr

Substituting the values:

0.75t = ω * 300

Since the car starts from rest, the initial angular velocity (ω₀) is zero. So, we have:

ω = ω₀ + αt

ω = 0 + (0.75 m/s²) * t

ω = 0.75t rad/s

We can now substitute the value of ω into the equation:

0.75t = (0.75t) * 300

Simplifying the equation gives:

0.75t = 225t

t = 0.75 seconds

The time elapsed is 0.75 seconds.

To calculate the distance traveled (s), we can use the equation:

s = v₀t + (1/2)at²

Since the initial velocity (v₀) is zero, the equation becomes:

s = (1/2)at²

s = (1/2)(0.75 m/s²)(0.75 s)²

s = (1/2)(0.75 m/s²)(0.5625 s²)

s = 0.2119 meters or approximately 21.19 centimeters

Therefore, the car travels a distance of approximately 0.2119 meters or 21.19 centimeters.

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The ratio of the electrostatic to gravitational force between two electrons 4.17×10 42

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The distance the truck travel in given time is 216 m and the final velocity of acceleration at 0.5m/\(s^{2}\) for 30 seconds is 19 m /s

The following question has two parts

For part 1 we need to calculate the distance covered by the truck in 12 seconds

We know that

 s = ut + \(\frac{1}{2}a .t^{2}\) . . . . . . .  . . . . .(1)

where s = distance travelled

           u = initial velocity

           a = acceleration

           t  =  time in seconds

Now , As per the question

u = 6 m/s

a = 2 m/\(s^{2}\)

t  = 12 seconds

Putting the values in the equation (1)

                          s = 6 X 12 + \(\frac{1}{2}\) X 2 X 144

                          s = 72 + 144

                          s = 216 m

Therefore the distance travelled is 216 m

For part 2 we need to calculate the final velocity that Paco was driving

We know that

v = u + at . . . . . . . . . . .  .(2)

where v = final velocity

          u = initial velocity

          a = acceleration

           t = time in seconds

As per the question,

u = 4m/s

a = 0.5 m/\(s^{2}\)

t = 30 seconds

Putting in equation (2)

                                      v = 4 + 0.5 X 30

                                      v  =  4 + 15

                                      v = 19 m/s

Therefore the final velocity is 19 m/s

Therefore , the distance the truck travel in given time is 216 m and the final velocity of acceleration at 0.5m/\(s^{2}\) for 30 seconds is 19 m /s

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The final velocity of the scooter is 19 m/s.

Given:

Initial velocity of truck, u = 6 m/s

Acceleration of truck, a = 2 m/s²

Time taken by the truck, t = 12 s

Formula used:

s = ut + 1/2 at²

Where,

s = Distance travelled

u = Initial velocity

a = Acceleration

t = Time taken

Substituting the given values in the above formula, we get:

s = ut + 1/2 at²

 = 6(12) + 1/2 × 2 × (12)²

 = 72 + 1/2 × 2 × 144

 = 72 + 144

 = 216 m

Therefore, the truck travels 216 m in the given time.

Given:

Initial velocity of scooter, u = 4 m/s

Acceleration of scooter, a = 0.5 m/s²

Time taken by the scooter, t = 30 s

Formula used:

v = u + at

Where,

v = Final velocity

u = Initial velocity

a = Acceleration

t = Time taken

Substituting the given values in the above formula, we get:

v = u + at

 = 4 + 0.5 × 30

 = 4 + 15

 = 19 m/s

Therefore, the final velocity of the scooter is 19 m/s.

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