consider an organ pipe 34.3 cm long that has one open and one closed end. what is the fundamental pitch of this pip?

Velocity of  first ball is -28m/s , and velocity of second ball is -4m/s.

Velocity is a vector quantity that describes the rate of change of an object's position. It is equal to the displacement of an object divided by the time interval over which the displacement occurred. Velocity has both magnitude and direction, and its units are typically meters per second (m/s). The velocity of an object can change over time due to acceleration, and if an object is moving in a circular path, it also has a component of velocity perpendicular to its direction of motion, known as centripetal velocity.

Given : Coefficient of restitution

[tex]$e=\dfrac{2}{3}$Velocity of mass[/tex]

[tex]$$1 \mathrm{~kg}$ after the collision is given by \\\\$V_1=\dfrac{\left(m_1-e m_2\right) u_1+(1+e) m_2 u_2}{m_1+m_2}$\\Or $\quad V_1=\dfrac{\left(1-\frac{2}{3} \times 2\right) \times 12+\left(1+\frac{2}{3}\right) \times 2 \times(-24)}{1+2}=-28 \mathrm{~m} / \mathrm{s}$\\[/tex]

[tex]Velocity of mass $2 \mathrm{~kg}$ after the collision is given by \\$V_2=\dfrac{\left(m-e m_1\right) u_2+(1+e) m_1 u_1}{m_1+m_2}$\\Or $\quad V_2=\dfrac{\left(2-\frac{2}{3} \times 1\right) \times(-24)+\left(1+\frac{2}{3}\right) \times 1 \times(12)}{1+2}=-4 \mathrm{~m} / \mathrm{s}$[/tex]

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Y-component of the electrostatic force on q3 is 9.36 x 10^-5 N.

Electrostatic force is an attractive as well as repulsive force caused by electric charge particles

As F = k * q1 * q2 / r^2

k is Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are  magnitudes of the charges, and r is separation distance between the charges.

F1_y = k * q1 * q3 / r1^2 * sin(θ1)

r1 is separation distance between q1 and q3 and θ1 is angle between r1 and the positive Y-axis.

F2_y = k * q2 * q3 / r2^2 * sin(θ2)

r2 is separation distance between q2 and q3 and θ2 is angle between r2 and the positive Y-axis.

r1 = sqrt((7.0 m)^2 + (0 m)^2) = 7.0 m

θ1 = tan^(-1)(0 / 7.0) = 0 rad

r2 = sqrt((7.0 m)^2 + (6.0 m)^2) = sqrt(65.0) m = 8.06 m

θ2 = tan^(-1)(6.0 / 7.0) = 0.98 rad

F1_y = k * (7.00x10^0 µC) * (6.0000x10^0 µC) / (7.0 m)^2 * sin(0) = 0 N

F2_y = k * (-9.000x10^0 µC) * (6.0000x10^0 µC) / (8.06 m)^2 * sin(0.98 rad) = 9.36 x 10^-5 N

F_y = F1_y + F2_y = 9.36 x 10^-5 N

So, the Y-component of the electrostatic force on q3 is 9.36 x 10^-5 N.

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Answer:  a. (-x, y) = (r, 90° + θ) , b. (−2x, −2y) = (2r, 180° + θ) , c. (3x, −3y) = (3r, 360°- θ)

What are Polar Coordinates?

Suppose we have a point O on the plane called the origin, let's say the axis through that point - x Axis – Called the polar axis.

Then the polar coordinates (r,θ) describes a point at an angle θ to the x-axis and a distance of r units from the origin. The θ value can be specified in degrees or radians.

The conversion from Cartesian to Polar is:

[tex]r= [x2 + y2]^{1/2}[/tex] and θ = tan-1 y/x

a] P = ( - x, y) is a point in the 2nd quadrant.

So, therefore, (-x, y) = (r, 90° + θ)

b] P = (-2x, -2y) is in the 3rd quadrant

=> R' = [(-2x)2 + (-2y)2] = 2R

therefore, (−2x, −2y) = (2r, 180° + θ)

c] P = (3x, - 3y)

Similarly, R' = 3R

and since this point is in the 4th quadrant (3x, −3y) = (3r, 360°- θ)

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The polar coordinates for the points a. (-x, y) = (r, 90° + θ) , b. (−2x, −2y) = (2r, 180° + θ) , c. (3x, −3y) = (3r, 360°- θ)

What are Polar Coordinates?

Polar coordinates are a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point (the pole) and an angle from a reference direction. It is most commonly used to plot points on a two-dimensional graph.

Suppose we have a point O on the plane called the origin, let's say the axis through that point - x Axis – Called the polar axis.

Then the polar coordinates (r,θ) describes a point at an angle θ to the x-axis and a distance of r units from the origin. The θ value can be specified in degrees or radians.

The conversion from Cartesian to Polar is:

[tex]r = [x2+y2]^{1/2}[/tex] and θ = tan-1 y/x

a] P = ( - x, y) is a point in the 2nd quadrant.

So, therefore, (-x, y) = (r, 90° + θ)

b] P = (-2x, -2y) is in the 3rd quadrant

=> R' = [(-2x)2 + (-2y)2] = 2R

therefore, (−2x, −2y) = (2r, 180° + θ)

c] P = (3x, - 3y)

Similarly, R' = 3R

and since this point is in the 4th quadrant (3x, −3y) = (3r, 360°- θ)

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If your automobile tyre needs 30 psi of pressure, it would roughly translate to 2.068427 kg/cm^2.

1 psi is equal to 6.894757 kPa, and 1 kPa is equal to 0.01 kg/cm^2.

So, 30 psi would equal:

30 psi * 6.894757 kPa/psi = 206.8427 kPa

And then:

206.8427 kPa * 0.01 kg/cm^2/kPa = 2.068427 kg/cm^2

The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure. In comparison to the surrounding pressure, gauge pressure is the pressure. Pressure is expressed using a variety of units.

The Imperial method of measuring measures pressure in pounds per square inch (PSI). PSI is frequently used to calculate the pressure of liquids or gases (hydraulic pressure).

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Answer:

To calculate for how long the force of 300 N acts on the object with a mass of 60 kg, you need to calculate the work done by the force using the equation W = F × d, where W is the work done, F is the force and d is the displacement. In this case, the displacement is the difference in velocities (50 m/s - 20 m/s), which is 30 m/s. Therefore, the work done is 300 N × 30 m/s = 9000 Nm. To calculate the time that the force acts, divide the work done by the force: 9000 Nm ÷ 300 N = 30 s. Therefore, the force of 300 N acts on the object for 30 seconds.

For 6 seconds, the force acts on the object.

Speed: The distance traveled by an object per unit time is defined as its speed. Speed is a scalar quantity because it has no direction and only magnitude. The SI unit is meter/second.

Given the following parameters:

F =300N is the resultant force acting on the object.

Object mass: M = 60 kg

As a result,

the object decelerates: a = F/m = 300 N /60kg = 5 m/s2.

Now read

The object's initial speed is u = 50 m/s.

The object's final speed is v = 20 m/s.

Decides the object's speed = u - v = 50 m/s - 20 m/s = 30 m/s.

The deceleration formula is:

deceleration = Decrees in object speed/time taken

Time taken = Decrees in object speed/deceleration

= 30/5 s

= 6s.

As a result, the force acts for 6 seconds.

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No heat is transferred from the system to the surrounding,The local concentration does not change with time.

The term "adiabatic process" refers to a change in a thermodynamic system where there is no heat transfer between the system and its environment. There is no heat exchange between the system and environment during the adiabatic process.

What method doesn't involve heat transfer?

A thermodynamic process known as adiabatic means that no heat is transferred into or out of the system. For an ideal gas, an adiabatic process is a reversible process with constant entropy.

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A negative charge experiences a force opposite to the direction of the electric field.

electric field, an electric property that is connected to every point in space when any kind of charge is present. The electric field strength, intensity, or simply the electric field is expressed by the value of E, which indicates the magnitude and direction of the electric field.

There is never a point where the field lines meet. The charge's surface is perpendicular to the field lines. Both the quantity of field lines and the magnitude of the charge are proportional to one another.

a negative charge that is in an electric field experiences a force that is

A. opposite to the direction of the electric field.

B. same  to the direction of the electric field.

C. vertical to the direction of electric field.

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University Physics A displacement vector is also a vector quantity as well as the total of all vector quantities given a vector. Therefore, the effect of adding two displacement vectors is another displacement.

Written as d = (x2 - x1)i + (y2 - y1)j, the displacement vector d from P1 to P2 can be understood. The displacement, denoted by the symbol d, consists of (x2 - x1) units in the x-direction and (y2 - y1) units in the y-direction. d = (((x2 - x1)2 + (y2 - y1)2)12 represents the displacement's magnitude. The Pythagorean theorem leads to this.

The reason why displacement is a vector

A physical quantity with both directions and magnitude is referred to as a vector quantity. The fact that displacement has both a magnitude and a direction makes it a vector quantity.

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The resistance of R a cell has an emf of 4.0 V and an internal resistance of 2.0 Ω is 0.8 Ω.

This can be calculated using Ohm's law, which states that the voltage (V) across a resistor is equal to the current (I) multiplied by the resistance (R): V = I x R. Since the ideal voltmeter reads 3.2V, rearranging and solving for R gives R = V/I = 3.2V/4.0A = 0.8Ω. Ohm's law states that the voltage (V) across a resistor is equal to the current (I) multiplied by the resistance (R): V = I x R. This means that if you know the voltage and the resistance, then you can calculate the current, and vice versa. Ohm's law is a fundamental law in electrical engineering and is used to calculate resistance, current, and voltage in electrical circuits.

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Finding the area of a velocity-versus-time graph will reveal the displacement because velocity is equal to the product of the displacement and the time. Finding the area of a graph of acceleration vs. time will give you the change in velocity because acceleration is equal to the velocity change divided by the time.

As the word constant denotes steadiness, the graph of velocity vs. time for constant acceleration shows that the acceleration is constant throughout the motion; however, we can determine the change in velocity of a body for a given period by calculating the slope of the plotted curve on the V-T graph. If an item experiences this kind of acceleration, the graph that is drawn will have a linear slope, and these curves are used to calculate only variable velocity.

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The x and y components of vector A are directed along negative X and Y axes respectively having magnitudes 4.330 and 2.5 units respectively.

Let the vector be taken as A.

Magnitude of the vector A = |A| = 5 units

We are aware that the positive X-axis and the negative Y-axis form a 270° anti-clockwise angle.

θ = Angle of vector A with positive X-axis = (270° - 60°) = 210°

So, x component of vector A = A x = |A| × cos 210° = |A| × cos (180° + 30°) = |A| × (- cos 30°) = 5 × (-0.866) = -4.330

And, y component of vector A = Ay = |A| × sin 210° = |A| × sin (180° + 30°) = |A| × (- sin 30°) = 5 × (-0.5) = -2.5

Thus, Ax and Ay both are negative relative to positive X and Y axes respectively. So, the x and y components of vector A are directed along negative X and Y axes respectively with magnitudes 4.330 and 2.5 units respectively.

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A significant source of information used to determine the unidentified sources of the gamma-rays was data from NASA's Hubble and Fermi space telescopes.

Researchers examined data on a variety of galaxies, including their rates of star formation, total masses, physical sizes, and separations from Earth.

Several satellites used to track treaty compliance found a significant rise in the quantity of gamma rays they were counting every second.

Therefore, based on the effects of the freed atomic electrons in gases, crystals, and semiconductors, conventional methods for gamma ray detection are described in radiation measurement and scintillation counter. Atomic nuclei and gamma rays can collaborate.

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A significant source of information used to determine the unidentified sources of the gamma-rays was data from NASA's Hubble and Fermi space telescopes.

Researchers examined data on a variety of galaxies, including their rates of star formation, total masses, physical sizes, and separations from Earth.

Several satellites used to track treaty compliance found a significant rise in the quantity of gamma rays they were counting every second.

Therefore, based on the effects of the freed atomic electrons in gases, crystals, and semiconductors, conventional methods for gamma ray detection are described in radiation measurement and scintillation counter. Atomic nuclei and gamma rays can collaborate.

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187cm will be 6.135ft and 73.5in

What does the measuring unit foot mean?

"Feet" is the plural form of the single unit of measurement known as "foot." The symbol for foot or feet is, and the abbreviation is ft. One foot-long bags, for instance, can be written as either 1 ft or 1'.

Simply measure the length in inches, multiply the result by 12, and then you will have the conversion to feet. The linear footage is the resultant number. Height and width are unimportant for this dimension.

1 inch equals 2.54 cm or 0.0254 m.

1 ft. = 12 in. = 0.3048 m

187cm will be 6.135ft i.e. 73.5in

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Its side measures 2.00 0.02 cm. Find the volume with this uncertainty, then convert it to a percentage. Therefore, the cube's volume is 8.00 cm3 + 3%.

The following is where to find the percent uncertainty:

(Uncertainty / Measurement) * 100% = (0.02 cm / 2.00 cm) * 100% = 1% is the formula for percent uncertainty.

The cube's side length is therefore 2.00 cm + 1%.

Simply raise the side length to the power of three to determine the cube's volume:

Volume = side length * 3 * (2.00 cm * 3 * 8.00 cm * 3 * 3)

The following is where the volume's uncertainty may be found:

Volumetric uncertainty is equal to side length uncertainty times three, or 1% times three, or 3%.

Therefore, the cube's volume is 8.00 cm3 + 3%.

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The third law of thermodynamics will allow by the absolute entropies of the substances to be determined by a reference point by which entropy will changes can be measured and assigned an absolute entropy for the substance.

The entropy of a system approaches a constant value when the temperature approaches absolute zero, according to the third rule of thermodynamics. The entropy of a system at absolute zero is typically zero, and in all the cases it is determined only by the number of different ground states it has.

It defines the sign of the entropy of any of the substance at temperatures above absolute zero as positive, and it provides a fixed reference point that allows us to measure the absolute entropy of any of the substance at any temperature.

The given question is incomplete. The complete question is 'A) It defines a reference point by which entropy changes can be measured and assigned as an absolute entropy for a substance. B) It defines the temperature at which all absolute entropies are measured. C) It requires that all energy in a process be conserved to accurately measure an absolute entropy. D) It provides a reference point for the absolute entropy of the universe. E) It requires that a process be reversible to measure the absolute entropy change.'

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Density is an important property of a material that helps to identify it. In determining the density of an unknown metal, the volume of the metal and the volume of the flask it occupies play a crucial role. Inaccuracies in measuring these parameters can cause errors in the calculated density. In this scenario, two such inaccuracies have been mentioned - less than one quarter of the metal was filled in the flask and the flask was not completely filled with water when determining its volume. In this text, we will discuss the effects of these inaccuracies on the measured density of the unknown liquid and solid.

Effects on Measured Density:

Less than one quarter of metal in the flask:

When the flask was filled less than one quarter with the metal, it means that the volume occupied by the metal in the flask is smaller than what it should have been. This leads to an overestimation of the density of the metal as the numerator in the density equation (mass) remains the same while the denominator (volume) is smaller. This error will be proportional to the extent of the deviation from one quarter - the greater the deviation, the greater the error in the calculated density.

Flask not completely filled with water:

When determining the volume of the flask, it is important to fill it completely with water. The presence of air at the top of the flask results in an underestimation of its volume, leading to an overestimation of the density of the unknown metal. This is because the numerator in the density equation (mass) remains the same, while the denominator (volume) is smaller. The error will be proportional to the volume of the air present in the flask.

In conclusion, these inaccuracies in measuring the volume of the metal and the flask will result in errors in the calculated density of the unknown metal. To minimize these errors, it is important to follow standard procedures when determining density, including filling the flask halfway with the metal and completely with water when measuring its volume.

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In a series circuit current is directly proportional to the voltage and inversely proportional to the resistance so if we double the values of voltage and resistance the current should be same.

Series circuit is the circuit where all the components are connected in a single path for the current flow. In series circuit the total resistance is equal to the sum of all the resistance and total voltage drop is equal to the sum of all the voltage drops across the resistors. According to the Ohm’s law voltage across a conductor is directly proportional to the current flowing through it. I=V/R where I is current, V is voltage and R is resistance.

In the given question V = 10 v, I = 5 ma R=?

From Ohm’s law  I=V/R        5 =10/R

                             R= 10/5     = 2

If we double the value of voltage and resistance the current=?

V=20v, R= 4 then I=?

I=V/R           =20/4       = 5ma.

The current remains same.

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The $3,528 will be paid in full if it is collected on May 4. Credit sales are listed as accounts receivable, which is a component of short-term assets, on the balance sheet.

Credit sales are contracts that provide that the entire loan balance will be repaid at a later time. The customer does not pay the whole amount due in cash at the time of the sale, in which case the transaction is a credit sale. What is a credit sales entry? To record the sale of goods on credit, a journal entry known as a credit sales item is used in accounting. The entry is created by debiting the Accounts Receivable account and crediting the Sales account. Briefing: .02 x 3600 = 72 3600-72 = $3,528. Financial analysts can comprehend the relative size of one financial statement account to another using accounting ratios.

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A manometer attached to a pressurized nitrogen tank reads 28 inches of mercury. if the atmospheric pressure is 14.4 psia, the absolute pressure in the tank is 28.2 psia.

The atmospheric pressure is 14.4 psia, and the manometer reading is 28 inches of mercury. The difference in pressure between the atmosphere and the pressure in the tank is equal to the difference in height between the liquid levels in the manometer tubes.

1 inch of mercury is equal to approximately 0.491 psia, so 28 inches of mercury is equivalent to:

28 inches * 0.491 psia/inch = 13.788 psia

Therefore, the absolute pressure in the tank is:

14.4 psia + 13.788 psia = 28.188 psia

So, the correct answer is 28.2 psia.

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Given: [tex]\\$\sum_{i} \boldsymbol{p}_{i}=0$.[/tex] Angular momentum: [tex]\\$$\boldsymbol{J}=\sum_{i} \boldsymbol{r}_{i} \times \boldsymbol{p}_{i}$$[/tex]

A new system of axes: [tex]\\$\boldsymbol{r}_{i}^{\prime}=\boldsymbol{r}_{i}+\boldsymbol{R}$,[/tex] where [tex]$d \boldsymbol{R} / d t=0$[/tex] because we are effecting an instantaneous shift in the axes. Hence, [tex]\\$\boldsymbol{p}_{i}^{\prime}=\boldsymbol{p}_{i}$,[/tex] and

[tex]$$\begin{aligned}\boldsymbol{J}^{\prime} & =\sum_{i} \boldsymbol{r}_{i}^{\prime} \times \boldsymbol{p}_{i}, \\& =\sum_{i}\left(\boldsymbol{r}_{i}+\boldsymbol{R}\right) \times \boldsymbol{p}_{i}, \\& =\sum_{i}\left(\boldsymbol{r}_{i} \times \boldsymbol{p}_{i}+\boldsymbol{R} \times \boldsymbol{p}_{i}\right), \\& =\boldsymbol{J}+\left(\boldsymbol{R} \times \sum_{i} \boldsymbol{p}_{i}\right), \\& =\boldsymbol{J} .\end{aligned}$$[/tex]

A property known as angular momentum describes the rotational inertia of an object or system of objects when they are moving about an axis that may or may not pass through them. The Earth has spin angular momentum from its daily rotation around its axis and orbital angular momentum from its yearly revolution around the Sun.

An accurate explanation of angular momentum necessitates the identification of both a magnitude and a direction because it is a vector quantity. An orbiting object's angular momentum is proportional to its linear momentum, which is the sum of its mass m and linear velocity v, times the perpendicular distance r from the center of rotation to a line drawn parallel to its instantaneous motion and passing through the center of gravity of the object, or simply mvr.

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Q)  Angular momentum : Show that if the total linear momentum of a system of particles is zero, the angular momentum of the system is the same about all origins.

Answer:

thie is your answer come again

Explanation:

it is

The model rocket's velocity time connection graph demonstrates that its acceleration is constant between the time intervals of 0.0s 0.0 s and 2.5s 2.5 s.

The link between velocity time can be utilised to calculate an object's acceleration. The slope of the velocity-time graph will remain constant across the given time period if the graph displays a constant acceleration. The model rocket accelerates steadily from 0.0 seconds to 2.5 seconds in this instance.

By calculating the velocity difference across the time interval and dividing it by the time interval, the slope of the velocity-time graph may be used to determine the acceleration. The acceleration is the value that results. This may be accomplished by determining the slope and equation of the line that depicts the link between velocity and time.

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To convert 70 kilograms to pounds, you must multiply 70 by 2.2046. This is because there are 2.2046 pounds in 1 kilogram.

What is pound ?

Pound is the unit of measurement for weight and mass in the Imperial system of measurement. It is a unit of mass equal to 16 ounces or 0.45 kilograms. It is often used in the United States for measuring the weight of products. Pound is also used in other countries like the United Kingdom, Canada, and Australia. It is denoted by the symbol "lb". Pound is also used to measure force, where it is equal to a mass of one pound multiplied by the acceleration due to gravity, which is 9.8 m/s2.

Therefore, 70 kilograms is equal to 154.323 pounds.

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Gauss’s law is useful for calculating electric fields that are uniform.A closed surface (GS) can be easily find  along which the electric field is uniform.

In material science and electromagnetism, Gauss' regulation, otherwise called Gauss' transition hypothesis, (or once in a while essentially called Gauss' hypothesis) is a regulation relating the dissemination of electric charge to the subsequent electric field. In its basic structure, it expresses that the transition of the electric field out of an erratic shut surface is relative to the electric charge encased by the surface, regardless of how that charge is disseminated. Despite the fact that the law alone is lacking to decide the electric field across a surface encasing any charge dissemination, this might be conceivable in situations where evenness commands consistency of the field. Where no such evenness exists, Gauss' regulation can be utilized in its differential structure, which expresses that the dissimilarity of the electric field is corresponding to the neighborhood thickness of charge.

The law was first[1] figured out by Joseph-Louis Lagrange in 1773,[2] followed via Carl Friedrich Gauss in 1835,[3] both with regards to the fascination of ellipsoids. It is one of Maxwell's four conditions, which frames the premise of old style electrodynamics.[note 1] Gauss' regulation can be utilized to infer Coulomb's law,[4] as well as the other way around.

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Positive charges cause lines to radiate outward symmetrically from a point charge. The electric field lines should be getting closer to the charge because it is negative.

It is impossible to consider electric field lines as continuous curves. Electric field lines always point away from a positive charge and towards a negative point. In reality, electric fields start with positive charges and end with negative charges. Field lines never cross one another, too. Positive charge always causes electric lines of force to diverge; conversely, negative charge causes them to converge. If there is no charge present at a given spot, the electric field there is continuous. If there is charge there, the field is also discontinuous.

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(i) The wavelength of y = 4 sin (1000πt/λ + 0. 5x), where y and x are in cm and t is in second = 12.56 m

(ii) The speed of the wave = 6280 ./s

(iii) The frequency of the wave = 500 Hz

The wave function y(x,t) = A sin(ωt−Kx), the equation itself can be used to read the amplitude, which equals A. The angular frequency can be used to calculate the wave's period.

A = 4

ω = 1000π

k = 0.5

Hence,

(i) The wavelength:

λ = 2π / k

= 2π / 0.5

= 12.56 m

(i) The speed of the wave:

v = f λ

= (500 Hz x 12.56m)

= 6280 m/s

(iii) The frequency of the wave:

f = ω / 2π

= (1000π) / 2π

= 500 Hz

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The speed increase of the vehicle can be tracked down utilizing the equation: speed increase = (last speed - introductory speed)/time.

The formula is:

vf = vi + at

Where,

vf = 7v/3 (last speed)

vi = v (starting speed)

t = time taken to arrive at the last speed

Reworking the condition, we can track down speed increase (a) as:

a = (vf - vi)/t

We can then substitute the given qualities for vf, vi and t to track down the speed increase.

The speed increase of the vehicle can be tracked down utilizing the equation: speed increase = (last speed - introductory speed)/time. The speed increase can then be utilized to find the uprooting of the vehicle utilizing the equation: relocation = introductory speed * time + 0.5 * speed increase * time^2.

The speed increase of a vehicle can be determined by deciding the adjustment of speed over a specific timeframe, utilizing the condition speed increase = (last speed - introductory speed)/time. This speed increase can then be utilized to compute the vehicle's relocation during that time, utilizing the condition dislodging = introductory speed * time + 0.5 * speed increase * time^2. By knowing the underlying speed, last speed, and time, we can find both the speed increase and uprooting of the vehicle as it goes from v to 7v/3 on the on-ramp to a road.

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The complete question is:

A car travels on the entrance ramp to a freeway as it accelerates from v to the freeway speed of 7v3 in time t. Assume the car moves with constant acceleration. which of the following formula of velocity of kinematic should use?

a. v = vi + at.

b. v² = vi² + 2as.

c. s = vi*t + ½at²

The sled moves  160.97 meter up the incline before it comes to rest.

Energy cannot be created or destroyed, according to the law of conservation of energy.

According to conservation of energy:

initial kinetic energy = potential energy + work done against friction

1/2 × 20.0 × 4.0² = 20.0 × 9.8 ×h + 0.20 × 20.0 × 9.8 ×h

h = (1/2 × 20.0 × 4.0²) ÷ {(1 +0.20) × 20.0 × 9.8}

h = 68.03

Hence, l =  68.03/sin25° meter = 160.97 meter

Hence,  the sled moves  160.97 meter up the incline before it comes to rest.

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According to the question, given differential equation: y + y' = 0.

A differential equation is a mathematical equation that relates some function with its derivatives. It is a way to describe how a function changes over time in terms of its rate of change. Differential equations are used to solve a variety of real-world problems, from predicting weather patterns to describing the motion of planets in the solar system. They are also used to model physical systems such as electrical circuits and mechanical systems.

The order of the given differential equation is 1, and it is a linear equation. This is because the equation is linear in the highest derivative, which is y'. There are no other derivatives or nonlinear terms present in the equation.

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The acceleration of the particle is given as the derivative of velocity with respect to time.

The derivative of velocity is acceleration. Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning it has both magnitude and direction. Acceleration is typically measured in meters per second squared (m/s2). Acceleration can be positive, negative, or zero. Positive acceleration means that the velocity is increasing, negative acceleration means that the velocity is decreasing, and zero acceleration means that the velocity is constant. Acceleration can be caused by forces such as gravity, friction, and propulsion. For example, when an object is dropped, the force of gravity causes it to accelerate until it reaches a terminal velocity.

From the graph, it can be seen that the velocity of the particle increases with time when t is less than 1s, and it decreases with time when t is more than 1s. This implies that the acceleration of the particle is positive when t is less than 1s and is negative when t is more than 1s. Hence, the variation of acceleration of the particle with time is that it is positive when t is less than 1s and it is negative when t is more than 1s.

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