A marble rolls along the track below with no friction. The sequence of positions on the track listed in order from the lowest kinetic energy to the highest kinetic energy is:

Answers

Answer 1

The marble's kinetic energy is lowest at the middle point and highest at the highest point.

Which positions on the track have the lowest to highest kinetic energy?

When a marble rolls along a track with no friction, its kinetic energy is determined by its height above the ground. The marble's kinetic energy is highest at the highest point on the track, where it possesses the most gravitational potential energy and converts it to kinetic energy as it descends. As the marble rolls down towards the lowest point, its kinetic energy decreases due to the loss of gravitational potential energy. Finally, at the middle point, the marble's kinetic energy is at its lowest since it is at the midpoint of its vertical motion and possesses minimal potential energy. Thus, the sequence from lowest to highest kinetic energy is: highest point, lowest point, middle point.

Kinetic energy: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass of the object and its velocity. Kinetic energy is a fundamental concept in physics and plays a crucial role in understanding the behavior of moving objects.

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Related Questions

Explain how you would apply any five pricing techniques to attract customers​

Answers

Answer:

Explanation:

1. DECOY PRICING

This occurs when customers make a purchase they must often choose between products with different prices and attributes.

This method of pricing is meant to influence the consumer's purchasing decision and maximise the sales of one particular product. The seller will offer at least three products; two of the products will have a similar or equal price. The two products with the similar prices should be the most expensive ones, and one of the two should be less attractive than the other.

2. LOSS LEADER

This is when a product is sold at a low price (often without profit) in order to stimulate other profitable sales or to attract new customers.

The main is that it will help the business to expand their market share as a whole. It's common practice when first entering a market as it introduces new customers to a service or product in the hope of building a customer base and securing future

3.ODD PRICING

This is a method of psychological pricing a product. Prices ending in 9, 95, 97, 99 are sometimes called “charm prices” and in this type of pricing, the seller fixes a price where the last digits are odd numbers. This is intended to give the buyer no room for manœuvering or for bargaining as the price appears to be less - a product priced at £9.99 will seems much cheaper than one priced at £10.00

4. PRICE DISCRIMINATION

The purpose of price discrimination is to capture the market's consumer surplus and generate the most revenue possible for a product. Identical goods or services are sold at different prices from the same provider to different segments of the market. Industries that commonly use price discrimination include the travel industry, pharmaceuticals and textbook publishers.

5. PRODUCT BUNDLE PRICING

Using this method, sellers will combine several products in the same package. It also serves to move old stock. Blu-ray and videogames are often sold using the bundle approach once they reach the end of their product life cycle. This technique is used at auctions where one attractive item may be included in a lot with a box of less interesting things. Buyers must bid for the entire lot. It’s a good way of moving slow selling products, and in a way is another form of promotional pricing.

A buffer system is set up with [ha] = 2[a-]. if pka = 5.5, what is the ph of the buffer?

Answers

A buffer system is set up with \([H_a]=2[-a]\). if \(p_{ka}=5.5\), the pH of the buffer is 5.2.

What is a buffer system?

A buffer system is a solution that prevents change in pH when acids or bases are added to the solution. They are made of either a weak acid and its salt or a weak base and its salt. The ratio of HX/X- does not change enough to affect pH significantly, when an acid or a base is added to a buffer.

What are the 3 buffer systems in the body?

The body's chemical buffer system contains of three different buffers:

The carbonate/carbonic acid bufferThe phosphate bufferThe buffering of plasma proteins.

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A group of students are conducting an investigation about charging through the process of friction. They then rub the two materials together. As they rub the materials together, there is a transfer of electrical charge from one material to the other material. The silk material has a greater electron affinity (attraction) than the glass. After this process the silk is __________ charged, the glass rod is ________ charged, and the overall net charge (combined charge on both objects) will be _________.

Answers

After the process of rubbing the materials together, the silk material is negatively charged, the glass rod is positively charged, and the overall net charge will be zero. This is because of transfer of electrons.

When two materials are rubbed together, such as silk and glass, there is a transfer of electrons between the materials. The transfer of electrons occurs because different materials have different electron affinities, which determines their ability to attract or release electrons.

In this case, the silk material has a greater electron affinity than the glass. This means that the silk material has a stronger attraction for electrons and tends to gain electrons from the glass.

As a result, electrons are transferred from the glass to the silk during the rubbing process. The silk gains electrons and becomes negatively charged, while the glass loses electrons and becomes positively charged.

Since the transfer of electrons between the silk and glass is equal in magnitude but opposite in sign, the overall net charge on both objects will be zero. This means that the positive charge on the glass cancels out the negative charge on the silk, resulting in a neutral overall net charge.

When silk and glass are rubbed together, the silk material becomes negatively charged, the glass rod becomes positively charged, and the overall net charge on both objects is zero. The transfer of electrons occurs due to the difference in electron affinity between the materials, resulting in opposite charges on the objects.

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If it is known that a motor battery has an input voltage of 12V and a capacity of 6 Ah, how much power and resistor value is required to turn on 8 lamps with a parallel circuit, with the specifications of each lamp having a maximum voltage of 3V and an electric current of 140 mA? How long did all the lights go on until they off?

Answers

Answer:

Part A

The power to turn on the lamp, ∑P = 3.36 W

Part B

The Resistor required is approximately 8.04 Ohms

Part C

The time for all the lights to go out is approximately 21.43 hours

Explanation:

The input voltage of the motor battery , V = 12 V

The capacity of the battery, Q = 6 Ah

The number of lamps in parallel = 8 lamps

The maximum voltage of each lamp,  = 3 V

The electric current in each lamp = 140 mA

The energy available in a battery, E = Q × V

For the battery, we have;

E = 6 Ah × 12 V = 72 Wh

The energy available in a battery, E = 72 Wh

Part A

The power used by the lamps, \(P_i\) = \(I_i\) × \(V_i\)

∴ The total power used by the lamp, ∑P = 8 × 0.14 A × 3 V = 3.36 W

The power to turn on the lamp, ∑P = 3.36 W

Part B

The resistance required, is given as follows;

Resistor required = (Battery voltage - Lamp voltage)/(The sum of bulb current)

∴ Resistor required = (12 V - 3 V)/(8 × 0.14 A)

The Resistor required = 8.03571429 Ohms

The Resistor required ≈ 8.04 Ohms

Part C

The time for all the lights to go out = The time for the lamps to use all the power available in the battery

The time for all the lights to go out, t = E/∑P

∴ t = 72 Wh/(3.36 W) = 21.4285714 h

∴ The time for all the lights to go out, t ≈ 21.43 h

The time for all the lights to go out = The time for the lamps to use all the power available in the battery = t ≈ 21.43 h

∴ The time for all the lights to go out ≈ 21.43 hours.

What is the correct chemical name for C7H8?

Answers

Answer:

Cycloheptatriene

Explanation:

Answer:

Cycloheptatriene or Toluene

Explanation:

I hope this helps!

the term that refers to the conflict that can occur when two or more organizations attempt to take control over a certain client group or territory is

Answers

The term that refers to the conflict that can occur when two or more organizations attempt to take control over a certain client group or territory is "turf war."

A turf war typically arises when multiple organizations or groups compete for dominance or control in a specific area or among a particular client base. This conflict often involves efforts to assert authority, gain influence, or secure resources within that territory or client group. Turf wars can occur in various contexts, such as business, politics, organized crime, or even within community or social service organizations. The term highlights the competitive nature of the conflict as organizations vie for power, market share, or control over a particular domain.

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A car runs at a constant speed of 15ms-1 for 30secs, and then accelerates uniformly to a speed of 25ms-1 over a time of 20secs. this speed is maintain for the next 300secs before the car is brought to rest with uniform deceleration in 30secs.
a. draw the velocity time graph of the motion. and calculate
b. the total distance traveled by the car
c. average speed of the car

Answers

Answer:

a. Please find the attached velocity time graph of the car's motion created with Microsoft Excel

b. The total distance traveled by the car is 8,725 meters

c. The average speed of the car is 22.9605263 m/s

Explanation:

The given parameters of the motion are;

The initial speed of the car, v₁ = 15 m/s

The time during which the car runs at the initial speed, t₁ = 30 seconds

The new speed the car then accelerates at 'a₁' to, v₂ = 25 m/s

The duration it takes for the car to accelerate to the new speed = 20 seconds

The time during which the car runs at the initial speed = 300 seconds

The time it takes the car to be brought to rest with a deceleration, 'a₂' from the new speed (20 m/s) = 30 seconds

The final speed of the car at rest, v₃ = 0 m/s

The acceleration, a₁ = (v₂ - v₁)/t₁ = (25 - 15)/20 = 1/2 m/s²

The deceleration , a₂ = (v₃ - v₂)/t₁ = (0 - 25)/30 = -5/6 m/s²

a. Please find attached the drawing of the velocity time graph of the motion created with Microsoft Excel

b. The total distance traveled by the car, 'Δx', is given b the area under the velocity time graph as follows;

Area of trapezoid, A₁ = (320 + 300)/2 × 10 = 3,100

Area of rectangle, A₂ = 15 × 350 = 5,250

Area of triangle, A₃ = 1/2×30×25 = 375

The total area under the velocity time graph = A₁ + A₂ + A₃ = 3,100 + 5,250 + 375 = 8,725

The total area under the velocity time graph = The total distance traveled by the car, Δx = 8,725 meters

c. The average speed of the car is given as follows;

\(The \ average \ speed \ of \ the \ car, \overline v =\dfrac{\Delta x}{\Delta t} = \dfrac{The \ total \ distance \ traveled by \ the \ car}{The \ total \ time \ the \ car \ travels}\)

Where;

Δt = The total time during which the car travels

∴ The average speed of the car = 8,725 m/(380 s) = 22.9605263 m/s

A car runs at a constant speed of 15ms-1 for 30secs, and then accelerates uniformly to a speed of 25ms-1

Which term is defined as the ratio of the speed of light in a vacuum to the speed of light in the material it is passing through?


index of reflection


index of refraction


angle of incidence


angle of reflection

Answers

Answer:

The index of refraction

What is the index of refraction?

The index of refraction tells us how much slower or faster light travels from one medium to another.

What is a medium? ⇒ the substance that light passes through

The formula to find the refractive index of a substance is the following:

\(n=\dfrac{c}{v}\)

\(c\) = the speed of light in a vacuum (\(3.00*10^8\) m/s)\(v\) = the speed of light in the medium

This makes the index of refraction defined as the ratio of:

the speed of light in a vacuum the speed of light in the material it passes through

Answer:

index of refraction

Explanation:

What should you do in case of radiation exposure?

Answers

Lock any windows and doors that are open. Head to the centre or basement of the structure. The recommended course of action is to stay as far away from the building's walls and top as you can since radioactive.

What is the highest source of radiation exposure?

If radon gas is allowed to build up in a residence, it not only poses a health concern to uranium miner but also to homeowners. It is typically the biggest source of exposure to natural radiation.

Why, in your opinion, is it crucial to be knowledgeable about radiation exposure?

We have been surrounded by radiation throughout our development. Therefore, the low amounts we are exposed each day are something our bodies are built to handle. However, excessive radiation can harm tissues by altering cell structure and DNA. Cancer is only one of the significant health issues this can lead to.

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A 1.5 kilogram rock is attached to a 2.5 m rope and is spun in a horizontal circle. The rope can withstand a maximum tension of 500 N. The rock is spun until the rope breaks. What speed was the rock traveling at when 500 N of tension broke the rope?

Answers

The speed at which the rock was travelling when the rope broke under a tension of 500 N is approximately **28.87 m/s.

With the concept of centripetal force in a circular motion, the centripetal force required to keep an object moving in a circle is given by the equation:

F_c = (mv^2) / r

Where F_c = centripetal force, m =mass of the object, v =velocity of the object, and r= radius of the circle.

In this case, the tension in the rope provides the centripetal force, so we have:

Tension = F_c

The maximum tension the rope can withstand is 500 N, set Tension = 500 N.

Rearrange the equation to solve for the velocity:

v^2 = (Tension * r) / m

v^2 = (500 N * 2.5 m) / 1.5 kg

v^2 = 833.33 m^2/s^2

Taking the square root of both sides:

v ≈ 28.87 m/s

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It takes 14 minutes, or 840s, to drive to the Rockaway Mall from MOHS. If the Rockaway Mall is
11.3 miles, or 181,856m away from the school, calculate the average speed for this trip.

Answers

If it takes 14 minutes, or 840 seconds, to drive from MOHS to the Rockaway Mall, the average speed for this route is 216 m/s.

What's the average speed response?

The total distance something has traveled is divided by the total amount of time it took to traverse that distance to arrive at its average speed. Speed is the current rate of movement of something. Average speed is the speed that a vehicle travels at on average over the course of a trip.

Give an example of the typical speed.

The average speed is calculated by dividing the total distance traveled throughout the entire time period. A person's average speed, for instance, is calculated as 40 miles divided by 40 minutes, or 1 mile per minute, if it takes them 40 minutes to drive 20 miles north, 20 miles south, and then 20 miles in between (60 mph).

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What is hybridization plsssss help,i will give brainliest to de person who explains well​

Answers

Answer: the process of an animal or plant breeding with an individual of another species or variety

Explanation:

there you go

Answer:

In chemistry, orbital hybridization (or hybridization) is the concept of mixing atomic orbitals into new hybrid orbitals (with different energies, shapes, etc., then the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory.

Explanation:

just copied it :|

Two magnets are aligned properly and it causes them to stick together tightly. Even thought the magnets force is stronger there is a also gravitational force pulling them together

Answers

The force of gravity between two magnets is really considerably smaller than the magnetic force, despite the fact that two magnets correctly aligned would attract and stay together firmly.

Any two mass-containing things in the cosmos are subject to the basic natural force of gravity. According to the formula F = G * m1 * m2 / r2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them, the gravitational force between two objects varies in strength depending on their masses and the distance between them. The magnetic fields of two magnets are what create the force between them. Two magnets are aligned properly and it causes them to stick together tightly.

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A ball is thrown vertically upward with an initial velocity of 99.4 meters per second. What is the maximum height reached by the ball

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The maximum height reached by the ball having initial velocity of 99.4 m/s is 494 meters.

According to the third law of motion , v² = u² + 2gH ,

where v is the final velocity of the ball, u is the initial velocity of the ball, g is the acceleration due to gravity and H is the height reached by the ball.

At maximum height, final velocity, v = 0.

Given that u = 99.4 m/s, g = -10 m/s (as the ball is moving upward). Hence,  0² = 99.4² + 2(-10)H ,20H = 99.4², H = 494.01 meters ~ 494 meters.

The maximum height reached by the ball with initial velocity of 99.4m)s is 494 meters.

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UVA and UVB rays can cause skin damage and skin cancer. True False

Answers

Answer:

true

Explanation:

they can cause skin damage

UVB rays have slightly more energy than UVA rays. They can damage the DNA in skin cells directly, and are the main rays that cause sunburns. They are also thought to cause most skin cancers.

A circular hoop of mass m, radius r, and infinitesimal thickness rolls without slipping down a ramp inclined at an angle θ with the horizontal. a. what is the acceleration αα of the center of the hoop? b. what is the minimum coefficient of (static) friction μminμmin needed for the hoop to roll without slipping?

Answers

The acceleration (α) of the center of the hoop: α = (mg * sin(θ)) / (2m) = (g * sin(θ)) / 2

The minimum coefficient of static friction (μmin) needed for the hoop to roll without slipping: μmin = α / (g * cos(θ)) = (g * sin(θ) / 2) / (g * cos(θ)) = tan(θ) / 2

The acceleration (α) of the center of the circular hoop can be determined by applying Newton's second law and the principle of conservation of angular momentum. Considering gravitational force (mg), normal force (N), and friction force (f) acting on the hoop, we can write:

mg * sin(θ) - f = m * α (1) (linear motion) and f * r = I * α/r (2) (angular motion)

For a hoop, the moment of inertia (I) is given by I = m * r^2. Substituting this into equation (2) and solving for f, we get:

f = m * α (3)

Now, substitute equation (3) into equation (1):

mg * sin(θ) - m * α = m * α

Rearranging the terms, we get the acceleration (α) of the center of the hoop:

α = (mg * sin(θ)) / (2m) = (g * sin(θ)) / 2

For the hoop to roll without slipping, the static friction (f) must be equal to the torque acting on the hoop. The minimum coefficient of static friction (μmin) can be determined using the frictional force equation:

f = μmin * N

Since the normal force (N) equals mg * cos(θ), the frictional force can be written as:

f = μmin * mg * cos(θ)

Now, substituting f = m * α from equation (3) into this equation, we get:

m * α = μmin * mg * cos(θ)

Rearranging the terms, we find the minimum coefficient of static friction (μmin) needed for the hoop to roll without slipping:

μmin = α / (g * cos(θ)) = (g * sin(θ) / 2) / (g * cos(θ)) = tan(θ) / 2

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Can the sun explain global warming? ( 2 points) Suppose that the Earth has warmed up by 1 K in the last hundred years. i) How much would the solar constant have to increase to explain this? ii) Compare this to the observed fluctuation of the solar constant over the past 400 years (shown in class) For part (i), begin with the standard 'blackbody' calculation from class, that is: set α=0.30, and assume that the Earth acts as a blackbody in the infrared.

Answers

No, the sun cannot explain global warming. Global warming is a phenomenon in which the temperature of the Earth's surface and atmosphere is rising continuously due to human activities such as deforestation, burning of fossil fuels, and industrialization.

This increase in temperature cannot be explained only by an increase in solar radiation.There are several factors which contribute to global warming, including greenhouse gases such as carbon dioxide, methane, and water vapor. These gases trap heat in the Earth's atmosphere, which causes the planet's temperature to rise. The sun's radiation does contribute to global warming, but it is not the main cause.

i) To calculate the increase in solar radiation that would cause the Earth to warm up by 1 K, we can use the following formula:ΔS = ΔT / αWhere ΔS is the increase in solar constant, ΔT is the increase in temperature, and α is the Earth's albedo (reflectivity).α = 0.30 is the standard value used for the Earth's albedo.ΔS = ΔT / αΔS = 1 K / 0.30ΔS = 3.33 W/m2So, to explain the increase in temperature of 1 K over the last hundred years, the solar constant would need to increase by 3.33 W/m2.

ii) The observed fluctuation of the solar constant over the past 400 years has been around 0.1% to 0.2%. This is much smaller than the 3.33 W/m2 required to explain the increase in temperature of 1 K over the last hundred years. Therefore, it is unlikely that the sun is the main cause of global warming.

The sun cannot explain global warming. While the sun's radiation does contribute to global warming, it is not the main cause. The main cause of global warming is human activities, particularly the burning of fossil fuels, which release large amounts of greenhouse gases into the atmosphere.

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mechanism of flow of current in a conductor

Answers

Your mom is the answer because I said that your mom is the answer. Now give me my points

Answer:

The mass of earth 6*10^24kg and radius is 400kg Now find the value of acceleration due to gravity when a object is 3600km from the earth surface

which of the following statements about gravitational waves are true? select all that apply. which of the following statements about gravitational waves are true?select all that apply. the emission of gravitational waves from merging black holes is predicted by newton's universal law of gravitation. two orbiting neutron stars or black holes will gradually spiral toward each other as a result of energy being carried away by gravitational waves. the emission of gravitational waves from merging black holes is predicted by einstein's general theory of relativity. scientists seek to detect gravitational waves by using powerful gamma-ray telescopes. although gravitational waves are an important theoretical prediction, we do not yet have any observational evidence that they exist. the first direct detection of gravitational waves, announced in 2016, came from the ligo observatory. submit

Answers

The correct statements regarding gravitational waves are: The emission of gravitational waves from merging black holes is predicted by Einstein's General Theory of Relativity, Two orbiting neutron stars or black holes will gradually spiral toward each other as a result of energy being carried away by gravitational waves, The first direct detection of gravitational waves, announced in 2016, came from the LIGO observatory.

The correct options are (B), (C) and (F).

Einstein's General Theory of Relativity predicts the production of gravitational waves from merging black holes. According to the theory, any two heavy objects that circle one other will cause ripples in spacetime that propagate away as gravitational waves.

As a result of gravitational waves carrying away energy, two circling neutron stars or black holes will progressively spiral towards one other. The gravitational waves increase stronger as they go closer, driving the objects to spiral faster and faster until they ultimately join.

The Laser Interferometer Gravitational-Wave Observatory (LIGO) claimed the first direct detection of gravitational waves in 2016. The discovery validated Einstein's theory and opened the door to a new technique of investigating the cosmos.

Therefore, options B, C and F are correct.

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What is the change in momentum of 10 kg object if a 60 Newton impulse is given to it?

Answers

If a 60 Newton-second impulse is given to an object, the change in momentum  is 60 kg-m/s.

What is impulse?

In physics, the term "impulse" is used to characterize or measure the impact of force operating gradually to alter an object's motion. It is often stated in Newton-seconds or kilograms per second and is denoted by the symbol J.

Impulse of force is = force applied × time interval = change in momentum.

Mass of the object is =  10 kg

Applied impulse is = 60 Newton-second.

Hence,  change in momentum is = 60 kg-m/s, if a 60 Newton-second impulse is given to an object,

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the magnet is dropped frown the tube. what is the direction of the induced current below the magnet as viewed from above

Answers

Answer:

When a magnet is dropped through a tube, the direction of the induced current below the magnet, as viewed from above, follows Lenz's Law. Lenz's Law states that the induced current will flow in a direction that creates a magnetic field opposing the change in the magnetic field that induced it.

As the magnet falls through the tube, its motion creates a changing magnetic field. According to Lenz's Law, the induced current will produce a magnetic field that opposes the motion of the magnet. This means that the induced current will create a magnetic field that points upward, opposite to the downward motion of the magnet.

Therefore, the direction of the induced current below the magnet, as viewed from above, would be in a clockwise direction.

a 43 g particle is moving to the left at 29 m/s . how much net work must be done on the particle to cause it to move to the right at 33 m/s ?

Answers

The net work required to change the motion of the 43g particle is approximately 5.332 J.

To calculate the net work required to change the motion of a 43g particle moving to the left at 29 m/s to move to the right at 33 m/s, we need to follow these steps:

1. Convert the mass of the particle from grams to kilograms:

43 g = 0.043 kg


2. Calculate the initial kinetic energy (KE_initial) of the particle using the formula

KE_initial = 0.5 * m * v_initial², where m is the mass and v_initial is the initial velocity (-29 m/s, negative because it's moving to the left).


3. Calculate the final kinetic energy (KE_final) of the particle using the formula

KE_final = 0.5 * m * v_final², where v_final is the final velocity (33 m/s, positive because it's moving to the right).


4. Calculate the net work (W_net) required using the formula W_net = KE_final - KE_initial.

Following these steps:

1. Mass = 0.043 kg
2. KE_initial = 0.5 * 0.043 kg * (-29 m/s)² = 18.0815 J
3. KE_final = 0.5 * 0.043 kg * (33 m/s)² = 23.4135 J
4. W_net = 23.4135 J - 18.0815 J = 5.332 J

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Find the magnitude of ax, the acceleration of the car after the brakes are applied.

Answers

The magnitude of ax is given by |ax|= | v₀²/2(d −v₀t) |

acceleration: change in velocity with respect to time.

It is a vector quantity. That means it has both magnitude. As well as direction.

a = dv/dt

where

dv = change in velocity

dt = Time

the unit of acceleration is m/s²

magnitude of  acceleration is represented by its unit and the direction is represented by a unit vector.

according to the Newton's Second Law acceleration is proportional to the total force and inversely proportional to the objects mass.

magnitude of acceleration is proportional to magnitude of this force.

The magnitude of ax is given by |ax|= | v₀²/2(d −v₀t) |

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A speedboat increases in speed from 17.3 m/s to 27.1 m/s in a distance 172 m. Find the magnitude of its acceleration. Answer in units of m/s2.
Show work please:)​

Answers

Answer:

1.26 m/s²

Explanation:

Given:

Δx = 172 m

v₀ = 17.3 m/s

v = 27.1 m/s

Find: a

v² = v₀² + 2aΔx

(27.1 m/s)² = (17.3 m/s)² + 2a (172 m)

a = 1.26 m/s²

Consider the polynomial

() = −0. 14 − 0. 153 − 0. 52 − 0. 25 + 1. 2

The true value of its derivative at x=0. 5 is ′

(0. 5) = −0. 9125. Use backward, forward, and centered

first finite differences to estimate the derivative numerically if the step size ∆ = 0. 25, and determine

the percent error between the true value and each of the estimated values (percent error is given by

= −


converted to a percentage. ) What value of ∆ would you have to use for the backward and forward

finite differences to get the same percent error as the centered finite difference (hint: it should be less

than 0. 25. )

Answers

The backward finite difference method for estimating the derivative at x=0.5 is:

(f(0.5) - f(0.25)) / (0.5 - 0.25) = (-0.14 - (-0.4025)) / (0.5 - 0.25) = 0.2625 / 0.25 = 10.5

The percent error between this estimate and the true value is:

|(10.5 - (-0.9125)) / (-0.9125)| * 100% = |11.4125 / (-0.9125)| * 100% = 12.48%

The forward finite difference method for estimating the derivative at x=0.5 is:

(f(0.75) - f(0.5)) / (0.75 - 0.5) = (-0.6275 - (-0.14)) / (0.75 - 0.5) = -0.4875 / 0.25 = -1.95

The percent error between this estimate and the true value is:

|(-1.95 - (-0.9125)) / (-0.9125)| * 100% = |-1.0375 / (-0.9125)| * 100% = 1.14%

The centred finite difference method for estimating the derivative at x=0.5 is:

(f(0.75) - f(0.25)) / (0.75 - 0.25) = (-0.6275 - (-0.4025)) / (0.75 - 0.25) = -0.225 / 0.5 = -0.45

The percent error between this estimate and the true value is:

|(-0.45 - (-0.9125)) / (-0.9125)| * 100% = |0.4625 / (-0.9125)| * 100% = 0.51%

To get the same percent error as the centred finite difference, we would have to use a step size of ∆ = 0.125.

This is because a smaller step size means a smaller difference between the estimates and the true value, and therefore a smaller percent error.

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If a bicyclist travels 25 km/h, how long will it take her to travel 40 km?

Answers

Answer: 1.6 hours

Explanation: 40/1.6 = 25

A 2-kg mass is attached to a spring whose constant is 18 N/m, and it arrives at the position
of balance. From
t = 0, an external force equal to
f(t)=2sin2t.
Find the resulting equation of motion.

Answers

The resulting equation of motion for the system is given by m × x''(t) + k × x(t) = f(t), which is 2 × x''(t) + 18 * x(t) = 2 * sin(2t).

What is  equation of motion?

The equations of motion are a set of mathematical relationships that describe the motion of objects under the influence of forces. There are different sets of equations of motion, depending on the specific scenario and the type of motion being considered (linear motion, projectile motion, circular motion, etc.). The equations of motion for linear motion, also known as the equations of uniformly accelerated motion.

To find the equation of motion for the system, we start with Newton's second law of motion, which states that the sum of forces acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the 2-kg mass attached to the spring.

The force exerted by the spring is proportional to the displacement of the mass from its equilibrium position, and it can be expressed as F_spring = -k× x(t), where k is the spring constant and x(t) is the displacement of the mass at time t.

In addition to the force exerted by the spring, there is an external force f(t) = 2 ×sin(2t) acting on the mass.

Applying Newton's second law, we have the equation of motion: m ×x''(t) + k ×x(t) = f(t).

Substituting the given values, m = 2 kg and k = 18 N/m, we obtain 2 ×x''(t) + 18 × x(t) = 2 ×sin(2t).

Therefore, the resulting equation of motion for the system is 2 × x''(t) + 18 × x(t) = 2 × sin(2t).

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Increased global temperature may lead to more forest fires, longer droughts, and loss of habitat. How will this effect many species? *

Answers

Answer:

Many species will be affected by increased global temperatures due to following reasons as mentioned.

As snow at poles will continue to melt and habitat for many species will be lost. This is create imbalance in the food chain of oceans which are prime source of food for many species. Some species will thrive as their hunters will be eradicated due to loss of habitat and overall food chain balance will be disturbed. This will cause species to go extinct.

The cycle of rain will be disturbed causing an imbalance in water cycle which will cause droughts and species will suffer and die eventually will go extinct.

Help please

What are the advantages and disadvantages of building a tricycle
versus a bicycle?

Answers

Answer: The advantage is it doesn't tip over as quickly therefore the rider is less likely to get hurt. The disadvantage is the rider won't be able to learn how to balance because they didn't use the bicycle and the tricycle already balanced for you.

Explanation:

Hope this helps comment if you need more help!

a)What is the current I 1 through the resistor R 2?

b) What is the the potential difference across each of the two resistors R2,R3?

a)What is the current I 1 through the resistor R 2?b) What is the the potential difference across each

Answers

In this given circuit, there are two resistors, R2 and R3 connected in series with a battery of 12 V as shown below;\(\Delta V = V = 12 V\)Let us first find the total resistance of the circuit.

Using the formula, resistances in series add up to give the total resistance of the circuit\(R_T = R_2 + R_3 = 8\ \Omega + 12\ \Omega = 20\ \Omega\)

Using Ohm's Law; the current through the circuit can be calculated as follows;

\(I_T = \frac{V}{R_T} = \frac{12\ V}{20\ \Omega} = 0.6\ A\)

Thus, the current through each of the resistors, R2 and R3 is the same and it is equal to the total current of the circuit;\(I_1 = I_2 = 0.6\ A\)

The potential difference across each of the two resistors, R2 and R3 is different because of the difference in resistance. Using Ohm's Law, the potential difference across each resistor can be calculated as follows;

\(\Delta V_2 = V_{R_2} = I_2 \cdot R_2 = 0.6\ A \cdot 8\ \Omega = 4.8\ V\)

\(\Delta V_3 = V_{R_3} = I_2 \cdot R_3 = 0.6\ A \cdot 12\ \Omega = 7.2\ V\)

Thus, the potential difference across resistor R2 is 4.8 V and across resistor R3 is 7.2 V.

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