Which one of the following instrument is most suitable for measuring thickness of

the physics book?

A. Meter rule ⃝ B. Vernier calipers ⃝

C. Measuring tape ⃝ D. Screw gauge ⃝

Answers

Answer 1

The most suitable instrument for measuring the thickness of a physics book is B. Vernier calipers, as they provide a higher degree of accuracy and precision compared to the other options.

One of the key advantages of Vernier calipers is their ability to provide measurements with a high level of precision. The Vernier scale allows for measurements to be read to a fraction of the smallest division on the main scale, significantly increasing the accuracy of the measurement.

This is especially useful when dealing with objects that have small dimensions or require precise measurements, such as the thickness of a book.

Furthermore, Vernier calipers often have a fine adjustment mechanism that enables the user to ensure a tight fit around the object being measured, minimizing any potential errors due to play or movement. This feature contributes to the overall accuracy of the measurements.

In comparison to other measuring instruments, such as a ruler or a tape measure, Vernier calipers provide a greater level of precision. Rulers, for example, typically have larger increments and are better suited for measuring longer distances rather than small thicknesses.

Tape measures, on the other hand, can be flexible and might not provide the same level of accuracy as Vernier calipers, especially when measuring thin objects.

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Related Questions

Suppose you create a Lorentz Force by passing a current through a conductor located in a magnetic field. What would happen to the Lorentz Force, if you reversed the direction of both the magnetic field and the direction of the flow of current at the same time

Answers

The reverse both the direction of the magnetic field and the flow of current in a conductor at the same time, the direction of the Lorentz Force would also reverse.



The current flows through a conductor in a magnetic field, the Lorentz Force acts in a direction perpendicular to both the current and the magnetic field. This causes the conductor to experience a force, which can be used to perform work or generate electricity. If the direction of the magnetic field or the current is reversed, the direction of the Lorentz Force will also reverse, causing the conductor to experience a force in the opposite direction. This phenomenon is used in many applications, including electric motors and generators. By reversing the direction of the magnetic field and the current, the direction of the Lorentz Force can be changed, allowing for the creation of torque or electrical energy. Understanding the interaction between magnetic fields and conductors is crucial for many technological advancements and has led to the development of many innovative devices and systems.

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1) A tourist accidentally drops a camera from a 50.0 m high bridge. What is the speed of the camera as it hits the water? *
2) Determine the total displacement of a car that is initially at 10 m/s but then accelerates at 2 m/s^2 for five seconds. *
3) A car travels down a long straight road at 20 km/h for 0.60 h. How far does the car travel during this interval? *
4) A skateboarder slides down a ramp starting from rest and moving to 10 m/s in 12 seconds. How far will the skater travel during this time interval?
5) A runner travels south along a straight path for 5.5 h with an average velocity of 1.75 km/h, then travels south for 7.5 h with an average velocity of 0.90 km/h. What is the hiker’s displacement for the total trip? *
6) A runner accelerates from rest for 3.2 seconds. If the runner travels 24.6m, what is the runner's acceleration? *
7) A car moving at 5 m/s accelerates at 0.2 m/s^2 for one minute. How fast is the car moving? *


Can someone please answer these questions for me :))

Answers

Question:

1) A tourist accidentally drops a camera from a 50.0 m high bridge. What is the speed of the camera as it hits the water? *

Answer:

28.0 m/s

Two resistors, one having half the resistance of the other, are connected to a battery as shown. What is the voltge across the bigger resistor?

Answers

The voltage across the bigger resistor, given the size, is 2/3 of the battery voltage.

How to find the voltage ?

Assuming the battery voltage is V. Also assuming the smaller resistor has the resistance, R, it means the bigger resistor would have the resistance of 2 R.

The current will be the same for both resistors and will be V / ( R + 2 R ) =  V / 3 R.

The voltage for the smaller resistor is therefore:

IR = V / 3 R x R

= V / 3

The voltage across the bigger resistor is V - V / 3 = 2 V / 3. This is 2 / 3 of the battery voltage.

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Two resistors, one having half the resistance of the other, are connected to a battery as shown. What

The voltage across the bigger resistor (R) is (2 V_B ) / 3.

What is the voltage across the bigger resistor?

The voltage across the bigger resistor is calculated by applying Ohm's law as shown below;

V = IR

where;

V is the of the batteryI is the current flowing in the circuitR is the resistance of the circuit

Since the two resistors are in series, the equivalent resistance is calculated as follows;

Re = R + R/2

Re = 3R/2

The current flowing in the circuit is calculated as follows;

I = V_B/Re

I = ( V_B ) x 2/3R

The voltage across the bigger resistor (R) is calculated as follows;

V' = IR

V' =  ( V_B) x 2/3R  x R

V' = (2V_B) / 3

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Two resistors, one having half the resistance of the other, are connected to a battery as shown. What

26. A weight of 20N stretches a spring by 0.5cm. Calculate the
extension when the applied weight is 60N.
A. 0.25cm
B.1.5cm C. 2.0cm D. 4.0cm

Answers

Answer:

26 a weight of 2on stretcges

how is electromagnets magnetic field is controlled by a switch​

Answers

Answer:

They affect by switch by the conductors

Explanation:

sana makatulong

If 80,000 Joules of heat is absorbed by 210 grams of ice at 0°C, what happens to the ice?
It partially melts and stays at 0°C
It completely melts but stays at 0°C
It completely melts and has a final temperature of 11.2°C
It completely melts and has a final temperature of 22.4°C
It completely melts and has a final temperature of 33.6°C

Answers

Answer:

It completely melts and has a final temperature of 22.4°C

Explanation:

(I am very bad at explaining, I am not a teacher, I am a student but I had exact same question on my test so I wanted to help.)

Okay, well to find the Heat required to melt Ice, we have to use the equation:

Q=(m·cΔT)+(m·hf)

Q= HeatM= MassC= Specific heatΔT= Change in temperature. hf= heat fusion

So we can just plug in the values into the equation and see which one adds up too 80,000. (there is probably a better way i just did it this way)

For this situation, we know that:

Mass=210 gramsSpecific heat = 2.10 (I got this number 2.10 from the internet. The universal number for specific heat of ice is 2.10 J/g°C ) Change in temperature= 0 °C or 11.2 °C or 22.4 °C or 33.6 °C (all the answers) Heat fusion=334 (universal number for heat fusion of melting ice is 334)

So we can just change the value of change and temperature and see which one equals 80,000.( I will bold the value of change in temperature.)

Q=(m·cΔT)+(m·hf)

(210g)*(2.10)*(0)+(210)*(334)=70140(210g)*(2.10)*(11.2)+(210)*(334)=75079.2(210g)*(2.10)*(22.4)+(210)*(334)=80018.4(210g)*(2.10)*(33.6)+(210)*(334)=84957.6

So which one equals 80,000? Equation #3 with the temperature at 22.4 °C

So the answer would be It completely melts and has a final temperature of 22.4°C.

Hope this makes sense, again I am not a teacher I am so bad at explaining, but I did my best. ;)

a 120 g granite cube slides down a 45 ∘ frictionless ramp. at the bottom, just as it exits onto a horizontal table, it collides with a 235 g steel cube at rest. assume an elastic collision. How high above the table should the granite cube be released to give the steel cube a speed of 200 cm/s ?

Answers

the granite cube should be released from a height of 0.338 m above the table to give the steel cube a speed of 200 cm/s after the collision.

To solve this problem, we need to use conservation of energy and momentum. First, we need to find the speed of the granite cube just before it collides with the steel cube. Since the ramp is frictionless, we can use conservation of energy to find the speed:

mgh = 1/2mv^2
v = √(2gh)

where m is the mass of the granite cube, h is the height of the ramp, and v is the speed of the granite cube. Substituting the values given in the problem, we get:

v = √(2 * 0.120 kg * 9.81 m/s^2 * sin(45°))
v = 1.47 m/s

Next, we can use conservation of momentum to find the speed of the steel cube after the collision. Since the collision is elastic, we know that:

m1v1 + m2v2 = m1v1' + m2v2'

where m1 and m2 are the masses of the granite and steel cubes, respectively, v1 and v2 are their speeds before the collision, and v1' and v2' are their speeds after the collision. Since the steel cube is at rest before the collision, we can simplify this equation to:

m1v1 = m1v1' + m2v2'

Substituting the values given in the problem, we get:

0.120 kg * 1.47 m/s = 0.120 kg * v1' + 0.235 kg * v2'

Solving for v2', we get:

v2' = (0.120 kg * 1.47 m/s - 0.120 kg * v1') / 0.235 kg

Now we can use conservation of energy again to find the height of the ramp. We want the steel cube to have a speed of 200 cm/s, which is 2 m/s. The kinetic energy of the steel cube after the collision is:

1/2 * 0.235 kg * (2 m/s)^2 = 0.470 J

This energy must come from the potential energy of the granite cube at the top of the ramp. So we have:

mgh = 0.470 J

Substituting the values we have found, we get:

0.120 kg * 9.81 m/s^2 * sin(θ) * h = 0.470 J

Solving for h, we get:

h = 0.470 J / (0.120 kg * 9.81 m/s^2 * sin(θ))
h = 0.338 m

Therefore, the granite cube should be released from a height of 0.338 m above the table to give the steel cube a speed of 200 cm/s after the collision.
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The granite cube should be released from a height of 0.78 m above the table to give the steel cube a speed of 200 cm/s after the collision.

Using conservation of energy and momentum, we can solve for the initial height of the granite cube:

Conservation of energy:

(1/2) * m_granite * v_granite^2 = m_granite * g * h

Conservation of momentum:

m_granite * v_granite = m_steel * v_steel_f

Using the given values, we can solve for h:

v_granite = (m_steel / m_granite) * v_steel_f

Substituting the given values:

v_granite = (235 g / 120 g) * 200 cm/s

v_granite = 392 cm/s

(1/2) * m_granite * v_granite^2 = m_granite * g * h

Substituting the given values and converting units to SI:

\((1/2) * 0.12 kg * (3.92 m/s)^2 = 0.12 kg * 9.81 m/s^2 * h \\h = 0.78 m\)

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In order to understand the concept of temperature it is necessaryto understand Question 1 answersthe zeroth law ofthermodynamics.the first law ofthermodynamics.the second law ofthermodynamics.all of theabove.only (b) and (c)above.

Answers

To understand the concept of temperature it is necessary to understand the zeroth law of thermodynamics.  This law is essential to the concept of temperature because it allows us to compare temperatures and to define a standard temperature scale.

What is temperature?Temperature is a measure of the amount of heat energy in a substance. The Zeroth law of thermodynamics states that if two systems are both in thermal equilibrium with a third system, then they must be in thermal equilibrium with one another. This law is essential to the concept of temperature because it allows us to compare temperatures and to define a standard temperature scale.Thermodynamics is the branch of science that deals with the relationships between heat and other forms of energy. The zeroth law is the most fundamental law of thermodynamics, and it defines the concept of temperature. Therefore, it is necessary to understand the zeroth law of thermodynamics to understand the concept of temperature.

So, option 1, zeroth law of thermodynamics is correct

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The temperature distribution T(x) at a distance x, measured from one end, along a bar of length L is given by
T(x)= Kx(L-x), for 0≤x≤L, K =constant.
(a) Express T(x) as a half-range sine series expansion.
(b) Express T(x) as a half-range cosine series expansion..
(c) Find the full-range Fourier series expansion of T(x).

Answers

(a) The half-range sine series expansion of T(x) is given by T(x) = Σ[Aₙsin(nπx/L)], where Aₙ = (4K/L) ∫[0,L] T(x)sin(nπx/L)dx.(b) The half-range cosine series expansion of T(x) is given by T(x) = A₀/2 + Σ[Aₙcos(nπx/L)], where Aₙ = (2K/L) ∫[0,L] T(x)cos(nπx/L)dx.(c) The full-range Fourier series expansion of T(x) is given by T(x) = A₀/2 + Σ[Aₙcos(nπx/L) + Bₙsin(nπx/L)], where A₀ = (1/L) ∫[0,L] T(x)dx, Aₙ = (2K/L) ∫[0,L] T(x)cos(nπx/L)dx, and Bₙ = (2K/L) ∫[0,L] T(x)sin(nπx/L)dx.

(a) In the half-range sine series expansion, we express T(x) as a sum of sine functions with different frequencies. The coefficients Aₙ are determined by integrating T(x) multiplied by the corresponding sine function over the interval [0,L]. Each coefficient represents the contribution of the corresponding sine function to the overall temperature distribution.

(b) In the half-range cosine series expansion, we express T(x) as a sum of cosine functions with different frequencies. The coefficients Aₙ are determined by integrating T(x) multiplied by the corresponding cosine function over the interval [0,L]. The first term A₀/2 represents the average value of T(x) over the interval.

(c) In the full-range Fourier series expansion, we consider both cosine and sine functions to represent T(x). The coefficients A₀, Aₙ, and Bₙ are determined by integrating T(x) multiplied by the corresponding functions over the interval [0,L]. A₀ represents the average value of T(x), Aₙ represents the contribution of cosine functions, and Bₙ represents the contribution of sine functions.

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when a ping pong ball rolling with a speed of 3.0 mls collides with a bowling balla t rest, the ping pong's speed after the collision will be close to

Answers

When a ping pong ball rolling with a speed of 3.0 m / s collides with a bowling ball at rest, the ping pong's speed after the collision will be close to 3 m / s

Let the ping pong ball be 1 and bowling ball be 2.

A ping pong ball weighs 2.7 g and a bowling ball weighs 2.85 kg

m1 = 2.7 g = 0.0027 kg

m2 = 2.85 kg

u1 = 3 m / s

u2 = 0

According to law of conservation of momentum,

m1 u1 + m2 u2 = m1 v1 + m2 v2

Ping pong ball's mass is so less compared to a bowling ball's mass. So the bowling ball will still remain at rest after collision.

v2 = 0

( 0.0027 * 3 ) + 0 = ( 0.0027 * v1 ) + 0

v1 = 3 m / s

Therefore, when a ping pong ball rolling with a speed of 3.0 m / s collides with a bowling ball at rest, the ping pong's speed after the collision will be close to 3 m / s

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Compare the wavelength of a 1.0-MeV gamma-ray photon with that of a neutron having the same kinetic energy. (For a neutron, mc^2 = 939 MeV)

Answers

The wavelength of the 1.0-MeV gamma-ray photon is much smaller than the wavelength of the neutron having the same kinetic energy at 1.99 x 10⁻¹⁹ m and 1.79 x 10⁻¹⁵ m respectively.

How to compare wavelengths?

The de Broglie wavelength λ of a particle can be given by the expression:

λ = h/p

where h = Planck's constant and p = momentum of the particle.

For a photon, the momentum can be given by:

p = E/c

where E = energy of the photon and c = speed of light.

For a gamma-ray photon with energy E = 1.0 MeV = 1.0 x 10^6 eV:

p = E/c = (1.0 x 10⁶ eV) / (3.0 x 10⁸ m/s) = 3.33 x 10⁻¹⁵ kg m/s

Substituting this momentum value in the expression for λ:

λ = h/p = (6.63 x 10⁻³⁴ J s) / (3.33 x 10⁻¹⁵ kg m/s) = 1.99 x 10⁻¹⁹ m

For a neutron, the momentum can be given by:

p = √(2mK)

where m = mass of the neutron, K = kinetic energy, and c = speed of light.

Substituting the given values:

p = √(2 x 939 MeV x (1.0 MeV / 938.3 MeV)) / c

p = 3.70 x 10⁻¹⁹ kg m/s

Substituting this momentum value in the expression for λ:

λ = h/p = (6.63 x 10⁻³⁴ J s) / (3.70 x 10⁻¹⁹ kg m/s) = 1.79 x 10⁻¹⁵ m

Therefore, the wavelength of the 1.0-MeV gamma-ray photon is much smaller than the wavelength of the neutron having the same kinetic energy. The gamma-ray photon has a wavelength of approximately 1.99 x 10⁻¹⁹ m, while the neutron has a wavelength of approximately 1.79 x 10⁻¹⁵ m.

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What happens to the force of gravity between two masses if they are moved closer?

It fluctuates.

It decreases.

It stays the same.

It increases.

Answers

The force of gravity between two masses increases as they are moved closer together.

option D.

What is Newton's law of universal gravitation?

Newton's law of universal gravitation states that the magnitude of the force between two masses is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.

F = GM²/R²

where;

M is massR is the distance between the masses

The force of gravity between two masses increases as they are moved closer together. This is because gravity is an attractive force that depends on the distance between the masses.

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Emily is pushing her little brother Tom on a sled. Tom has a mass of 40 kg and Emily
is pushing with a force of 10 N. However, the sled is sticking to the ice because of 2
N of friction. What is Tom's final acceleration?


PLZ HELP!!!

Answers

Answer:

The answer is 5 a

Explanation:

First subtract two from ten then because of the friction. Next divide 40 kg by 8 N. When you do that you will get 5 for acceleration. Always make sure that you put the symbol next to your answer.

If a dancer's breathing is deep and rapid after performing a folk dance,what is the intensity of his activity?

Answers

Answer:

Moderately Light

Explanation:

Dancer breathing deeply and rapid after performing a folk dance is moderately light kind of activity intensity.

Other examples of moderately intense exercise include brisk walking, hiking, playing tennis, pushing a lawn mover and water aerobics.

Moderately Intensity activities are those which allow you to move quickly or hard enough to consume three to six times more energy every minute than when you sit still.

The activity in which the performer of the folk music is involved is a moderately intense activity.

A folk dance is an activity in which the performer moves briskly and moves the body rapidly. It is a mildly vigorous activity hence the breathing rate  of the performer increases slightly.

Hence, we can say that the activity in which the performer of the folk music is involved is a moderately intense activity.

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A car goes into a skid and comes to a gradual stop, accelerating at a constant rate to do so. At the midpoint of the skid, how much of its kinetic energy has the car lost (as a percentage, give % as the units)?

Answers

The percentage of the lost kinetic energy of the car, at the midpoint of the skid, is 50%.

In physics, work is the measurement of the energy used to move objects. When you are walking, you're using energy to move your body so the work done would be greater than zero.

According to work-energy theorem, work is equal to force times displacement (W = F · x).

A type of energy is kinetic energy, which is the energy of a moving object. If an object is at rest, its kinetic energy is zero. Kinetic energy is equal to one half of a mass times velocity squared (KE = 0.5 · m · v²).

When a car goes into a skid and comes to a gradual stop, at the midpoint of the skid the car has spend 50% its kinetic energy. This is simply because the velocity of the car at the midpoint of the skid is half the velocity of the car when the car starts going into a skid, assuming constant acceleration.

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What two parts does a measurement have?

Answers

Answer:

Measurements and Units Accuracy, Precision, and Errors

Explanation:

this is A measurement is a quantitative observation that consists of two parts: a number and a unit.

The quantity (magnitude,numerical value) -units(in inch,meter,light year)

please help me, please i will mark brainliest

please help me, please i will mark brainliest

Answers

Answer:

conductor,neither,insulator

Explanation:

conductors allow electricity to flow through while insulators do not

HOPE IT HELPS

Conductor, neither, insulator

At 6: 00 am, a motorbike set off from town A to town B at a speed of 40km/h. At the same time, a car set off from town B to town A at a speed of 60km/h. What time did they meet

Answers

Answer:

One would need to know how far apart the towns are:

T = SA / 40      time it takes for first cyclist to travel S1

T = SB / 60       time it takes for cyclist B to travel distance S2

SA + SB = S     the distance between the towns

SB = 60 / 40 SA = 1.5 SA

SA + 1.5 SA = S

S = 2.5 SA where cyclist travels distance SA

The time will depend on the separation of the towns.

if rechargeable cell is being charged from a source of EMF the EMF of cell during charging is
A. always equal to its terminal potential difference
B. always greater than its terminal potential difference
C. always less than its terminal potential difference​
D. either equal or less than its terminal potential difference

Answers

Answer:

a

Explanation:

I think bec. I am in small school

what is the electric field at a distance r form an infinite sheet of charge with surface charge density sigma?

Answers

The electric field at distance r from a uniformly charged infinite sheet of charge density σ can be formulated as  σ/2ϵ

As per the Gauss's law, the total electric flux through a closed surface is 1/ϵo times the charge enclosed in the surface. It can be denoted as Ф= q/ϵo.

​The Electric flux expressed through a closed surface can be written as:

\(\int\limits^{} \, E.ds \\\int\limits^{} \, E.ds\) =  q/ϵo.

Here, E is the electric field, q is the charge enclosed in the surface and ϵo can be written as the permittivity of the free space.

The electric field computed at distance r from a uniformly charged infinite sheet of charge density σ can be formulated as σ/2ϵ.

In the expression, ϵo is the absolute permittivity of the free space, E is the electric field and σ is surface charge density.

The field is uniform and does not depend on the distance from the plane sheet of charge.

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Which types of electromagnetic waves have higher frequencies than the waves that make up ultraviolet light? Select two options. Radio waves infrared light microwaves gamma rays visible light X-rays.

Answers

Answer:

the answer is equal to the microwave gamma rays visible light x-rays.

what is the magnitude of the force exerted by the biceps fbiceps ? what is the magnitude of the force exerted by the elbow felbow ? express your answers in newtons separated by a comma.

Answers

The force exerted by the biceps and the elbow is 239.9 N and 215.89 N respectively.

When we use only your forearms to lift an object, assume that your biceps are the main muscle that lifts your arm. Suppose the weight of the forearm he is 1.50 kg. If the biceps is attached to the forearm 2.50cm from the elbow, with the forearm parallel to the floor, flex the biceps to hold a 950g ball on the end of the elbow at a distance of 36.0cm from the elbow.

Against this background,

forearm mass = 1.50 kg

forearm length = 2.50 cm

The weight of the ball is 950 g.

36.0 cm ball spacing

Forearm strength needs to be calculated. Balance Elbow Using

Torque,

Fb x Db = Wf x Df/2 + Wball x Dball

Putting Value,

Fb x .025 = 1.5 x 9.8 x .36/2 + 0

95 x 9.8 x 0.36

Fb = 239.9 N

Now elbow force,

Fb = Fl + Wf + Wb

Fl = Fb - Wf - Wb

Putting value,

Fl = 239 .9 - (1.5 x 9.8 ) - (0.95×9.8)

Fl = 215.89 N.

Therefore the force on the elbow is 215.89 N.

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In the reaction below, how would adding more of reactant A affect the equilibrium of the system? (2 points) A + B ⇄ C + D a Shift it to the right toward the products. b Shift it to the left toward the reactants. c Equally create more products and reactants. d It would have no effect.

Answers

Answer:

It wouldn't effect, sir/maam

For the more produce of product, it will

Depend upon

No of molesPressure Temperature

But,

I think question is not enough to provide answer

REVIEW
1 A train travelled along a
straight track from a particular
stop back to its depot.
This 5.0 km journey took
12 minutes. Calculate the
train's average speed. (Give
your answer in km/h.)

Answers

According to given data, the average speed of train is 25 km/h.

Equation :

Given data,

distance = 5 km

time = 12 minutes

average speed = ?

changing time from minute to hour

So,

hour = 12 / 60

hour = 0.2

Then to calculate speed use the formula,

s = d / t

s = 5km / 0.2hr

s = 25 km/h

What is speed?

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector value, whereas speed is a scalar value. It has a dimension of time-distance. As a result, the basic unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.

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Which of the following is an example of positive potential energy with reference to the floor? PLS HELP

Which of the following is an example of positive potential energy with reference to the floor? PLS HELP

Answers

Answer:

A

Explanation:

potential energy is usually at rest at the highest point in comparason to the ground

Miss
case of 16 calculators,
which she got for half
price. Shipping was $12.
which brought the total
to $100. What is the full
price for a case?

Answers

Miss case of 16 calculators, which she got for half price. Shipping was $12. Which brought the total to $100. The full price for a case is $176.

What is calculation?

A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or results.

Here the price of the calculator has to be calculated

The total price including the shipping is $100

She got 16 calculators

Shipping was $12

100 - 12 = 88

Since there was half price.

88 x 2  = $176

Therefore, the full price for a case is $176.

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A musical note has a frequency of 512 Hz. If the wavelength of the note is 0.685 m, what is the speed of the sound of that note?

Answers

Answer:

350.72 m/s

Explanation:

Formula for velocity of wave is;

v = fλ

Where;

v is speed

f is frequency

λ is wavelength

We are given;

f = 512 Hz

λ = 0.685 m

Thus;

v = 512 × 0.685

v = 350.72 m/s

Suppose a weight of 1 kg is attached to an oscillating spring with friction constant b=7 and stiffness constant k=6. Suppose the external forces on the weight are: F ext

(t)=−6te −3t
+e −3t
. y ′′
+7y ′
+6y=−6te −3t
+e −3t
a) Show y(t)=te −3t
is a possible position function for this weight. y ′1
+7y ′
+6y=−6tc −3t
+e −3t
r 2
+7r+6=0
(r+a)(r+1)
e −6t
e −t
y=1e −4t
+1e −t
y ′
=−61)e −4t
+Ae t
y ′
=−609e −4t
+e −+
(6,6e −4t
)+Me −t

b) Find a general equation for all possible position functions. y=Ae −6t
+AC 2
=−6+e 3t
+e −3t
(10 points) c) Find the exact motion equation for this weight if its initial position is y(0)=3, and its initial velocity is v(0)=y ′
(0)=

Answers

a) y(t) = te⁻³ᵗ is a possible position function.

b) General equation: y(t) = C₁e^(-2t) + C₂e^(-3t) + t(e^(-3t))(At + B).

c) Exact motion equation: y(t) = (23/5)e^(-2t) - (8/5)e^(-3t) + t(e^(-3t))(At + B), with initial conditions y(0) = 3 and v(0) = -7.

a) To show that y(t) = te⁻³ᵗ is a possible position function, we substitute it into the differential equation:

y(t) = te⁻³ᵗ

y'(t) = e⁻³ᵗ - 3te⁻³ᵗ

y''(t) = -6e⁻³ᵗ + 9te⁻³ᵗ

Substituting these expressions into the differential equation, we have:

-6e⁻³ᵗ + 9te⁻³ᵗ + 7(e⁻³ᵗ - 3te⁻³ᵗ) + 6(te⁻³ᵗ) = -6te⁻³ᵗ - e³ᵗ

Simplifying this equation, we find that both sides are equal, thus confirming that y(t) = te⁻³ᵗ is a possible position function.

b) The general equation for all possible position functions can be written as:

y(t) = C₁e^(-2t) + C₂e^(-3t) + t(e^(-3t))(At + B)

c) Given the initial conditions y(0) = 3 and y'(0) = v(0) = -7, we substitute these values into the general equation and solve for the constants:

3 = C₁ + C₂

-7 = -2C₁ - 3C₂

Solving these equations, we find C₁ = 23/5 and C₂ = -8/5.

The exact motion equation for the weight is:

y(t) = (23/5)e⁻²ᵗ - (8/5)e⁻³ᵗ + t(e⁻³ᵗ)(At + B)

Learn more about motion here:

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Suppose a weight of 1 kg is attached to an oscillating spring with friction constant b = 7 and stiffness constant k = 6. Suppose the external forces on the weight are: Fₑₓₜ(t) = - 6te⁻³ᵗ - e³ᵗ

y" + 7y' + 6y = - 6te⁻³ᵗ - e³ᵗ

a) Show y(t) = te⁻³ᵗ is a possible position function for this weight.

b) Find a general equation for all possible position functions.

c) Find the exact motion equation for this weight if its initial position is y(0) = 3, and its initial velocity is v(0) = y'(0) = -7.

I need help. It's 9th grade physical science

It takes a ball 2 minutes to roll back and forth on the ground from A to B to C. Using the diagram above, give the total distance traveled and the displacement of the ball.

What is the total distance traveled and the displacement of the ball?

I need help. It's 9th grade physical scienceIt takes a ball 2 minutes to roll back and forth on the ground

Answers

Answer:

i think its  c

Explanation:

It takes at least 4 people to push a refrigerator up a 10-meter ramp. How many people would be needed to push the same refrigerator to the same height using a 20-meter ramp? (Assume no friction for both ramps. )

Answers

Double the amount of people because the ramp went from 10-meter to 20-meter, so times by 2. 4 times 2 is 8.
The answer is 8 people.
Hope this helps!
Please give Brainliest!
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