Path-goal theory predicts that subordinates who have a strong need for affiliation prefer directive leadership.
True
False

To derive the equation for the velocity vector as a function of time for the ball, we need to know the acceleration vector as a function of time. Once we have the acceleration, we can integrate it with respect to time to obtain the velocity.

Assuming that the ball is moving in a two-dimensional plane (i.e., the x-y plane), the acceleration vector can be expressed as:

a = ax(t) i + ay(t) j

where, i and j are unit vectors in the x and y directions, respectively. We can determine the expressions for ax(t) and ay(t) by applying Newton's second law of motion:

F = ma

Where, F is the net force acting on the ball, m is the mass of the ball, and a is its acceleration.

Let's assume that the ball experiences a net force of F = Fx i + Fy j, where Fx and Fy are the x and y components of the force, respectively. Then we can write:

F = Fx i + Fy j = ma

Equating the x and y components, we get:

Fx = m*ax

Fy = m*ay

Solving for ax and ay, we get:

ax = Fx/m

ay = Fy/m

Now we can integrate ax(t) and ay(t) with respect to time to obtain the expressions for the velocity components:

v_x(t) = v_{0x} + ∫ ax(t) dt

v_y(t) = v_{0y} + ∫ ay(t) dt

where v_{0x} and v_{0y} are the initial velocities in the x and y directions, respectively.

If we know the expressions for Fx and Fy as functions of time, we can substitute them into the above equations to obtain the velocity vector as a function of time for the ball.

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The two quantities that should be graphed to yield a straight line whose slope could be used to calculate a numerical value for the charge to mass ratio of an electron are electric field strength and velocity.

Velocity is a vector quantity that describes the rate of change of an object's position in a given amount of time. It is typically measured in meters per second (m/s), but can also be measured in other units such as feet per second (ft/s) or kilometers per hour (km/h). It is a measure of both the speed and direction of an object's motion, and is distinct from speed, which is simply the rate of motion in a given direction. Velocity can be calculated by taking the derivative of an object's position with respect to time. It is an important concept in physics and is used to describe the motion of objects in a variety of situations. For example, in a car, velocity is used to determine the car's acceleration, and in an airplane, velocity is used to describe the airspeed.

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Option (d) A is false, B is true. Statement A is false and statement B is true. The relationship between the packing fraction and the binding energy is more complex and depends on the details of the nuclear interactions.

Statement B is true. The packing fraction is defined as the difference between the mass of the nucleus and the mass number of the nucleus divided by the mass number. It is a measure of the binding energy per nucleon in the nucleus.

However, statement A is false. The packing fraction is related to the binding energy per nucleon, but a larger packing fraction does not necessarily imply a larger binding energy. In fact, a lower packing fraction (i.e., a less tightly bound nucleus) can sometimes have a larger binding energy per nucleon than a nucleus with a higher packing fraction. The relationship between the packing fraction and the binding energy is more complex and depends on the details of the nuclear interactions.

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p=2m is the formula for the relationship between linear momentum and kinetic energy (K. E.) Additional Details: The relationship between momentum and an object's mass and speed is straightforward.

(D) P=2mE. A body's kinetic energy is directly related to the squares of its total momentum. The mass and speed of a body immediately affect the linear momentum. Rightarrow E = dfrac12mv2, where E is gravitational acceleration, m is the body's mass, and v is the speed.

The object's overall energy is mgh. Its gravitational potential will turn into kinetic energy as it descends.The potential energy will fall while a kinetic energy could rise as the object continued to fall.

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Based on Energy a) ΔS = -3.77 J/K b)  ΔS = 10.08 J/K c) ΔS_cold  = 6.31 J/K d) change in entropy of the Universe has to be positive

Based on Energy :

(a) To calculate the change in entropy of the hot reservoir, we can use the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the amount of heat transferred, and T is the temperature in Kelvin. So, ΔS = -2.60 kJ / 690 K = -3.77 J/K.

(b) Using the same equation, we can calculate the change in entropy of the cold reservoir: ΔS = 2.60 kJ / 258 K = 10.08 J/K.

(c) To calculate the change in entropy of the Universe, we can add the changes in entropy of the hot and cold reservoirs: ΔS_univ = ΔS_hot + ΔS_cold = -3.77 J/K + 10.08 J/K = 6.31 J/K.

(d) The change in entropy of the Universe has to be positive in an irreversible process because the total entropy of the system and its surroundings always increases. The Second Law of Thermodynamics states that any process that occurs spontaneously (i.e. without external intervention) will always result in an overall increase in entropy. In this case, the heat transfer from the hot reservoir to the cold reservoir is an irreversible process, which means that the overall change in entropy of the Universe must be positive. If the change in entropy of the Universe were negative, it would imply that the process is reversible, which is not the case for an irreversible process. Therefore, the positive value for ΔS_univ in part (c) confirms that the process is irreversible.

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When the penguin is in the air, there is only one force acting on it.

The force (Fg) is the force due to gravity that acts downward.

The acceleration is also acting downward.

Acceleration and force act in the same direction. Consequently, the acceleration is in the downward direction.

Newton's second law states that the net force is equal to the penguin's mass (m) times its acceleration (a).

Fg= ma

a= -g

a= -9.8 m/s2

The acceleration of the Penguin is acting downwards since a= -9.8 m/s2

(Fg) s taken -ve because it is in the -y-direction (downward).

Hence, the correct solution this question is downwards.

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The time required for one revolution is π²/2 seconds.

The time required for one revolution of an object moving on a circular path can be found by dividing the circumference of the circle by the speed of the object. One revolution typically refers to the complete circular movement of an object around another object or axis. The circumference of a circle is given by the formula

C = 2πr,

where r is the radius of the circle.

In this case, the radius of the circle is π meters, so the circumference is

C = 2π(π) = 2π

The speed of the object is 4.0 m/s, so the time required for one revolution is:
t = C/v

t = 2π²/4.0

t = π²/2.

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The prediction of the combined (net) force on the cart is towards the left direction.

Net Force, which is essentially the total of all the forces operating on an item, is the combination or consequence of those forces.

Balanced forces are those acting on an item that add up to a net force of zero. The velocity of an object is unaffected by balanced forces, as seen in the illustration on the page opposite. Unbalanced forces are those acting on an item that add together to provide a net force that is not zero.

Motion is toward right but the cart is slowing down so the cart is accelerating towards left,

Now F = ma

Since, acceleration is to the left hence the net force is also to the left.

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The normal acceleration of a body travelling in a curved path is defined as the rate of change of its velocity vector. It is equal to the sum of the centripetal and tangential accelerations.

The magnitude of the normal acceleration is directly proportional to the radius of curvature, i.e a smaller radius of curvature implies a larger normal acceleration. Mathematically, the normal acceleration can be expressed as follows:

Normal acceleration = (v^2/r)

where v is the velocity of the body and r is the radius of the curvature. As the radius of the curvature decreases, the normal acceleration increases. Hence, the magnitude of the normal acceleration is directly proportional to the radius of curvature. On the other hand, it is inversely proportional to the diameter of curvature. The normal acceleration is also zero when the velocity of the body is constant. This happens when the body is travelling along a straight path. In such cases, the normal acceleration is zero since there is no change in the velocity vector in the direction perpendicular to the path.

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The correct solution to this question is that the magnitude of the normal acceleration is inversely proportional to the radius of curvature.

The curvature's reciprocal, R, is the radius of curvature in differential geometry. It is equal to the radius of the circular arc that, at that moment, most closely resembles the curve for a curve. The radius of curvature for surfaces is the diameter of a circle that fits a normal section or any combination of them the best.

The approximate radius of a circle at any given location or the curvature's vector length are both considered to be the radius of curvature of a curve. For any curve with the equation y = f(x), where x is a parameter, it exists.

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The early Greek epicycle model was preferred over the heliocentric model of the solar system because it provided a more precise account of observed planetary motions.

Although Copernicus' system does not require epicycles to produce retrograde motion, he was forced to use them nonetheless because of his insistence on uniform circular motion in order for his model to produce accurate predictions (i.e., to "preserve appearances"), particularly to replicate the planets' non-uniform speeds.

Because its proponents were unable to explain why, the heliocentric, or Sun-centered, model of the solar system never achieved widespread acceptance.

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The position -time relation from the graph is given x = - 4t + 2t². Then , at t = 2.8 s, x have the value of 4.48 m. Therefore, the velocity being 1.6 m/s.

Velocity of an object is the measure of distance travelled per unit time. It is a vector quantity having both magnitude and direction. The magnitude of velocity is called speed of the object.

The instantaneous velocity of an object is its velocity at a particular instant of time.

Given the position- time relation of an object.

x = - 4t + 2t²

then at t = 2.8 s

x = 4 × 2.8 s + 2 ×(2.8 s)² = 4.48 m.

Then,

velocity = distance travelled / time

v = 4.48 m/2.8 s = 1.6 m/s.

Therefore, the instantaneous velocity of the particle is 1.6 m/s at t = 2.8 s.

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The self-inductance per unit length of a long solenoid can be calculated using the formula: L = (μ_0 × n^2 × A) / l

where μ_0 is the permeability of free space, n is the number of turns per unit length, A is the cross-sectional area of the solenoid, and l is the length of the solenoid. A = π × R^2

L = (μ_0 × n^2 × π × R^2) / l

An apparatus that transforms electrical energy into mechanical energy is a solenoid. It is formed out of a wire coil that is tightly twisted around a cylindrical, ferromagnetic core. The core moves in a linear or circular motion when an electric current is run through the coil, creating a magnetic field that interacts with the core and causes it to move. Numerous devices, including door locks, valves, starting motors, and actuators for robotics and automation systems, require solenoids. Additionally, they are employed in research to generate magnetic fields for particle acceleration and control the motion of small objects. Electrical energy is transformed into mechanical work by a solenoid.

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Objective resolving power if used in air is 661 nm/cm , the resolving power of the objective if it is used in an oil-immersion microscope is    = 963 nm/cm

The ability of an optical instrument, such as a microscope or telescope, to differentiate and separate two objects that are close together is known as its resolution power.

Part A :

Resolving power = 1.22λ/D

              = 1.22(550 nm)/(1.0 cm)

                       = 661 nm/cm

Part B :

Resolving power = 1.22λn(oil)/D

                        = 1.22(550 nm)(1.45)/(1.0 cm)

                                    = 963 nm/cm

It is established by comparing the instrument's aperture diameter to the wavelength of light utilized. The instrument's ability to differentiate between two close objects improves with increasing resolving power. A telescope's lens or mirrors focus light on a single point as it travels through them. The telescope's resolving power is based on how close the two points can be to each other before they are impossible to tell apart. More distant stars, galaxies, and other celestial objects can be seen in the image with a higher resolving power. In order to comprehend the universe and conduct scientific research, resolve power is absolutely necessary.

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All three statements are correct based on the given information provided in the question.

All three statements are correct based on the given information. The first two statements relate to the amount of potential energy and kinetic energy the ball possesses, respectively, before impact with the board, which determines whether the board will break or not. The third statement relates to the conservation of energy, which dictates that the total energy of the system (the ball and the board) must remain constant, and some of the kinetic energy of the ball is transferred to the board as potential energy before the board breaks.

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Gravity affect the movement of the planets around the sun, stars grouped in galaxies, and galaxies grouped in clusters by applying force.

Gravitational force is indeed a non-contact, constantly attracting force. This implies it may act at a distance that does not require the interacting items to be in contact with each other. When we examine gravity operating on a system, we can assume that the gravitational force acts immediately on the system's center of mass.

Gravity keeps things together. It is a force that attracts matter towards it. Anything with mass creates gravity, but the amount of gravity is proportional to the amount of mass. Therefore, Jupiter has a stronger gravitational pull than Mercury. Distance also affects the strength of the gravitational force.

Therefore, gravity affect the movement of the planets around the sun by applying force.

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Two significant figures and include the appropriate units. I1 =2A.

The power of a positive attitude is often underestimated. People who come into life with a positive outlook have the ability to make the most out of any situation. They are more likely to take risks, have the courage to make difficult decisions, and work hard to achieve their goals. Positive attitudes also lead to better mental and physical health, as well as improved relationships with others. Having a positive attitude also leads to increased motivation, which can help people stay focused on their goals and stay motivated to achieve them.

The direction of the current through in the figure. to the right to the left.

Two significant figures and include the appropriate units. I2 = 4A.

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The correct statements for the focal point of a converging lens are:

A) A light ray entering parallel to the optical axis passes through the focal point on the other side of the lens.

C) A light ray passing through the focal point as it enters the lens goes through the focal point on the other side of the lens.

D) A light ray passing through the focal point as it enters the lens and exits the lens parallel to the optical axis.

A converging lens is a particular kind of lens that bends light in such a way that parallel light rays unite at a single focal point. Light bends towards the center of the lens because of its shape, which has a thicker center and a thinner edge. A distinct image is created at the focal point, which is where all of the refracted light converges. Common applications for this kind of lens include magnifying glasses, cameras, telescopes, and other optical equipment. Converging lenses—also known as convex lenses—may produce sharp, enlarged pictures because they can combine light. Converging lenses can be recognized by their form; they have a center that is rather thick.

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6.2 n force pushing two gliders along an air track. the 250 g spring between the gliders is compressed. the spring is firmly attached to the gliders, and it does not sag due to 3newton force applied on it.

Mass of right glider A, m=0.4kg

Mass of right spring, ms=0.2kg

External force f=6n

M+m+ms=fa

a=f/M+m+ms

a=6/0.6+0.4+0.2

a=5

f=0.6*5=3 newton

The push or pull on an object with has mass that result to change its velocity is known as force. Force is an external agent which is applied externally and is capacble of changing a stae of a body that means body's state of rest or motion. It has a magnitude and a direction.

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Photochemical smog is produced. Nitrogen oxides (NOx) and volatile organic compounds (VOCs) from vehicle exhaust combine with sunlight to create photochemical smog.

When sunlight interacts with nitrogen oxides and at least one volatile organic compound (VOC) in the atmosphere, photochemical smog is created. Automobile exhaust, coal-fired power plants, and industrial pollutants all produce nitrogen oxides.

When nitrogen oxides and volatile organic compounds (VOCs) combine with sunlight, a mixture of pollutants called photochemical smog is produced, which explains why there is a brown cloud above cities. Due to the fact that we receive the most sunshine in the summer, it tends to happen more frequently.

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The force with which the Earth is attracted towards the person is equal to the same force of 120 lbs.

This is due to the law of universal gravitation. This law states that any two objects in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Therefore, the Earth and the person both experience a force of 120 lbs due to their mutual attraction.

The law of universal gravitation states that any two objects in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the greater the mass of the objects and the closer they are to each other, the stronger the force of attraction will be. This law was first proposed by Isaac Newton in 1687 and is one of the most fundamental concepts in physics.

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The work done here is the change in kinetic energy. The kinetic energy to accelerate a 1.8 kg object from rest to 26 m/s is 608.4 J.

Work done is a physical quantity that measures the effectives of a force in moving an object. Like force it is a vector quantity having direction and magnitude.

The work done for moving an object from a lower speed to higher speed is equal to the change in its kinetic energy.

here, m = 1.8 kg

v = 26 m/s

initial speed u = 0

then initial kinetic energy = 0

Work done  = ΔKE

W = 1/2mv² - 0

W = 1/2 1.8 kg × 26 m/s ²

    = 608.4 J.

Therefore, the work done needed to accelerate the object is608.4 J.

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(a) Efficiency = (energy delivered to CD player) / (energy supplied by charger)

The energy delivered to the CD player is:

E_delivered = I_avg * V * t = (18.0 mA) * (1.60 V) * (2.40 h) = 0.062 mL

The energy supplied by the charger is:

E_supplied = I_charge * V_charge * t_charge = (13.5 mA) * (2.20 V) * (4.20 h) = 0.126 mL

where t_charge is the time the battery is charged.

Thus, the efficiency of the battery is:

Efficiency = E_delivered / E_supplied = 0.062 mL / 0.126 mL = 0.49 or 49%

(b) The internal energy produced in the battery during one charge-discharge cycle can be found by:

ΔU = E_supplied - E_delivered

ΔU = 0.126 mL - 0.062 mL = 0.064 mL

(c) The amount by which the temperature of the battery increases during the cycle can be found using the formula:

ΔT = ΔU / (m * c_eff)

where ΔT is the temperature increase, m is the mass of the battery, and c_eff is the effective specific heat of the battery.

ΔT = (0.064 mL) / (0.0150 kg * 975 J/kg·°C) = 4.26°C

Therefore, the temperature of the battery will increase by 4.26°C during one charge-discharge cycle if it is surrounded by ideal thermal insulation.

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The dependent variable in this experiment is the number of plants that can live in the water.

In an experiment, the dependent variable is the variable that is being measured or observed. It is the outcome variable that is affected by changes in the independent variable. In this case, the scientist is trying to determine how the amount of salt in the water affects the number of plants that can survive in the water.

Therefore, the number of plants is the variable that is being measured or observed, and it is the dependent variable in this experiment. The independent variable, in this case, would be the amount of salt in the water, which is being manipulated by the scientist.

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--The complete question is, A scientist conducted an experiment to determine how the amount of salt in a body of water affects the number of plants that can live in the water. In this experiment the dependent variable is--

The speed of the second block after the first collision is 2.5 m/s. The speed of the third 6 kg block after the second collision is 3.5 m/s.

Since the collision is elastic, momentum is conserved.

Initially, only the first block is moving with a velocity of 5 m/s. Therefore, the initial momentum is,

P = m1×v1 = 6 kg × 5 m/s = 30 kg m/s

After the first collision, both blocks have the same velocity, v since the collision is elastic.

[tex]P = m_1v_1 + m_2v_2\\30 = 6 \times v + 6 \times v_2\\30 = 12 \times v_2\\v_2 = \dfrac{30}{12}[/tex]

v₂ = 2.5 m/s

After the second collision, the two blocks stick together. The final momentum is,

[tex]P = m_1v_1 + m_2v_2 + m_3*v_3\\P = 6 \times 5 + 6 \times 2.5 + 6 \times v_3\\P = 42 kg m/s[/tex]

Since the blocks stick together, their mass becomes 12 kg.

[tex]P = m\times v\\42 = 12 \times v[/tex]

v = 3.5 m/s

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--The complete question is, A 6 kg block moves with a constant speed 5 m/s on a horizontal frictionless surface and collides elastically with an identical block initially at rest. The second block collides and sticks to the last 6 kg block which was initially at rest. What is the speed of the second 6 kg block after the first collision? What is the speed of the third 6 kg block after the second collision?--

The kinetic energy and the potential energy will be the same at point 1

At point 2 the kinetic energy is 0 while at point 3 the potential energy is 0.

The kinetic energy at 1 is zero while the potential energy at 2 is maximum

The momentum is 60 Kg m/s

The impulse is 900 Ns

Kinetic energy is the energy possessed by a moving object due to its motion. It is defined as the energy that an object possesses as a result of its motion, and is dependent on both the object's mass and velocity. The formula for calculating kinetic energy is:

Kinetic Energy = 1/2 x mass x velocity^2

where mass is the mass of the object in kilograms and velocity is its speed in meters per second.

Momentum = mv = 30 * 2 = 60 Kg m/s

Since Ft = mv

= 200 * 4.5 = 900 Ns

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The magnitude of the electric force on the raindrops (acquire an electric charge as they fall, suppose a 2.5-mm-diameter drop has a charge of +15 pC) droplet compare to the weight force = 204.134 x 10⁻⁶ N.

So, the weight of the droplet is more than the electric force.

To determine the electric force on the charge, use the equation:

The electric force on the charge = charge x electric field

= (15 x 10⁻¹² C) x 100

= 15 x 10⁻⁹ N

As force on positive charge operates in the direction of the electric field, it will go upward.

Determine the volume of the droplet:

V = 4/3 π R³

= 4/3 (2.5 x 10⁻³ m)³

= 20.83 x 10⁻⁹ m³

The mass of the droplet:

mass = density x volume

= (1000) x (20.83 x 10⁻⁹ kg)

= 20.83 x 10⁻⁶

Hence,

The weight = m x g

= (20.83 x 10⁻⁶) x (9.8)

= 204.134 x 10⁻⁶ N.

So, the weight of the droplet is more than the electric force.

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During an elastic collision, the force exerted by the car on the truck is equal in magnitude to the force exerted by the truck on the car. That is, the forces exerted by each object on the other are the same size.

In an elastic collision, the force exerted by the car on the truck is equal in magnitude to the force exerted by the truck on the car. This is because according to Newton's third law of motion, for every action, there is an equal and opposite reaction.

Therefore, the force that the car exerts on the truck is equal and opposite to the force that the truck exerts on the car.

In other words, the magnitude of the force exerted by the car on the truck is the same as the magnitude of the force exerted by the truck on the car.

So, to compare the force exerted by the car on the truck with that exerted by the truck on the car during the collision, we can say that they are equal in magnitude.

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A significant meteoroid collision caused the meteor crater to develop. The right response is option c.

A meteor is a streak of light in the sky that results from a meteoroid colliding with Earth's atmosphere. Meteoroids are rock or iron clusters that orbit the sun.

Meteor Crater, located close to Winslow, Arizona, is one of the most well-known craters on Earth. A 50-meter (164-foot), 150,000-ton meteorite fell into the desert roughly 50,000 years ago, instantaneously creating the crater. The diameter and depth of Meteor Crater are 1.2 km (0.75 miles) and 175 m (575 feet), respectively.

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--The complete question is, which of the following are possible explanations for the formation of the meteor crater?

a. volcanic explosion

b. a large pothole formed by swirling water action in an extremely large river

c. large meteoroid collision--

The control system is primarily based on a tachometer (sensor). It provides a linearly scaled voltage. To simplify the tasks, we simply assume is ks=1.

We often assume is - 30652102. The tachometer is an instrument whose objective is utilized in the measurement of the speed of the engine in revolutions per minute or rpm. This is generally used in road vehicles and vehicles. Tachometer is visible in the dashboard of your vehicle. A tachometer is an instrument which is used for measuring the rotation speed of a shaft or disk, examples will be in a motor or other machine. The device always displays and elicit the revolutions per minute (RPM) on a calibrated analogue dial, but digital displays are increasingly common.

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