A cars engine supplies 6445 N A force to get a car going. If the car is mass is 1040 kg what is the cars acceleration round to the nearest tenth

(a) The amplitude of the wave is 0.2 m.

(b) The period of the wave is  4 s.

(c) The wavelength of the wave is 100 m.

(a) The amplitude of the wave is the maximum displacement of the wave.

amplitude of the wave = 0.2 m

(b) The period of the wave is the time taken for the wave to make one complete cycle.

period of the wave = 5.5 s - 1.5 s = 4 s

(c) The wavelength of the wave is calculated as follows;

λ = v / f

where;

f = 1/t = 1 / 4s = 0.25 Hz

λ = ( 25 m/s ) / 0.25 Hz

λ = 100 m

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The velocity of the car moving in the circular path is determined as 1.67 m/s.

Linear velocity is the measure of the rate of change of displacement with respect to time when the object moves along a straight path.

v = d/t

where;

v = (6 x 1000 m) / (1 x 3600 s)

v = 1.67 m/s

Thus, the velocity of the car moving in the circular path is determined as 1.67 m/s.

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Answer:

the proton speed of the proton was 1.6 × 10⁶ m/s

Explanation:

Given the data in the question;

Radius r = 6.42 cm = 0.0642 m

magnetic field B = 0.260 T

we know that; charge of proton q = 1.602 × 10⁻¹⁹ C

And mass of proton m = 1.672 × 10⁻²⁷ kg

we know that; Magnetic Force F = qvBsinθ

where q is the charge of proton, v is velocity, B is the magnetic field and θ is  angle ( 90° )

Also the Centripetal force experienced by the particle is;

F = mv² / r

where r is radius, m is mass of proton and v is velocity

hence;

qvBsinθ = mv² / r

we solve for v

rqvBsinθ = mv²

divide both sides by mv

rqvBsinθ / mv = mv² / mv

rqBsinθ / m = v

so we substitute

v = [ 0.0642 m × (1.602 × 10⁻¹⁹ C) × 0.260 T × sin(90°) ] /  1.67 × 10⁻²⁷ kg

v = 2.6740584 × 10⁻²¹ / 1.672 × 10⁻²⁷

v = 1.6 × 10⁶ m/s

Therefore, the proton speed of the proton was 1.6 × 10⁶ m/s

Answer: Participating in all of the above can improve flexibility.

Explanation:

A practice that helps in improving or developing inherent power in order to bring peace and harmony to the body of a person is called yoga.

Yoga includes different postures that also help in providing flexibility to the body.

Pilates is another method of providing muscular strength and low impact flexibility to a human body.

Swimming also a good exercise that provides flexibility.

Thus, we can conclude that participating in all of the above can improve flexibility.

If a frictionless plane is 10.0 m long and inclined at 36.0°.

We can use conservation of energy to find the distance that the first sled travels up the incline. The potential energy of the sled at the bottom of the incline is zero, and its kinetic energy is:

KE = (1/2)mv^2

where m is the mass of the sled and v is its speed. At the point where the sled stops, all of its kinetic energy has been converted into potential energy, so we can write:

mgh = (1/2)mv^2

where h is the height that the sled has traveled up the incline. Solving for h, we get:

h = (v^2)/(2g)

where g is the acceleration due to gravity. Using the given values, we have:

h = (6.00 m/s)^2 / (2 * 9.81 m/s^2) = 1.83 m

So the first sled travels a distance of 10.0 m - 1.83 m = 8.17 m up the incline.

b. To find the initial speed of the second sled, we can use conservation of energy again. At the top of the incline, the sled has potential energy:

PE = mgh

where h is the height of the incline. As the sled slides down the incline, its potential energy is converted into kinetic energy:

KE = (1/2)mv^2

where v is the speed of the sled at the bottom of the incline. We can equate these two expressions and solve for v:

mgh = (1/2)mv^2

v = sqrt(2gh)

Using the given values, we have:

v = sqrt(2 * 9.81 m/s^2 * 10.0 m * sin(36.0°)) = 12.2 m/s

So the second sled must be released from the top of the incline with an initial speed of 12.2 m/s.

The position of the sled as a function of time is given by:

y = -0.5gt^2 + Vi*t + h

where y is the vertical position of the sled, t is the time, Vi is the initial speed of the sled, and h is the height of the incline. At the bottom of the incline, y = 0, so we can solve for the time it takes for the second sled to reach the bottom:

0 = -0.5gt^2 + Vi*t + h

t = (Vi ± sqrt(Vi^2 - 2gh)) / g

Since we want both sleds to reach the bottom at the same time, we set the time for the first sled to slide down the incline equal to this expression for t and solve for Vi:

t = sqrt(2h/g) = sqrt(2 * 1.83 m / 9.81 m/s^2) = 0.619 s

0 = -0.5gt^2 + Vi*t + h

Vi = (h - 0.5gt^2) / t

Vi = (1.83 m - 0.5 * 9.81 m/s^2 * (0.619 s)^2) / 0.619 s

Vi = 5.68 m/s

So the initial speed of the second sled is about  5.68 m/s

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Answer:

Motivation is the process that initiates, guides, and maintains goal-oriented behaviors.

Explanation:

This is a sinusoidal wave with parts defined as follows:

  a = crest       b = trough      c = amplitude       d = wavelength

A crow flies forward and backward. Its motion is shown on the following graph of horizontal position x vs. time t.

What is the instantaneous velocity of the crow at t = 9 s?

Answer: -0.50 m/s

A crow flies forward and backward. Its motion is shown in the following graph and the instantaneous velocity of the crow at t = 9 s is -0.5 m/s.

From the figure, it shows that from t = 8sec to t = 12 sec the displacement is decreasing, so velocity will be the slope of the straight line.

The velocity is given by:

velocity = -Δx ÷ Δt

velocity = (-2) ÷ (12-8)

velocity = -2 ÷ 4

velocity = -0.5 m/s

Therefore, A crow flies forward and backward. Its motion is shown in the following graph and the instantaneous velocity of the crow at t = 9 s is -0.5 m/s.

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(a) The magnitude of the angular momentum of the system is 5,252 kg m²/s.

(b) The rotational energy of the system is 2,826 J.

(c) The new moment of inertia is 31.25 Kgm².

(d) The new speed of each astronaut is 420.15 m/s.

(e) The new rotational energy of the system is 65.82 kJ.

(f) The work is done by the astronauts in shortening the rope -45,317,098 KJ.

(a) To calculate the magnitude of the angular momentum of the system, we can use the following equation:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since we are treating the astronauts as particles, we can assume they are point masses and use the formula for the moment of inertia of a point mass:

I = mr²

where m is the mass of each astronaut and r is the distance between them. The angular velocity can be found from the linear velocity and the distance between the astronauts:

ω = v/r

Putting in the given values, we get:

r = 5.00 m

m = 90.5 kg

v = 5.80 m/s

I = 2(mr²) = 2(90.5 kg)(5.00 m)²

              = 4,525 kg m²

ω = v/r = 5.80 m/s / 5.00 m

           = 1.16 rad/s

L = Iω = (4,525 kg m²)(1.16 rad/s)

          = 5,252 kg m²/s

Therefore, the magnitude of the angular momentum of the system is 5,252 kg m²/s.

(b) To calculate the rotational energy of the system, we can use the following equation:

E = (1/2)Iω²

Putting in the values for I and ω that we found in part (a), we get:

E = (1/2)(4,525 kg m²)(1.16 rad/s)²

  = 2,826 J

Therefore, the rotational energy of the system is 2,826 J.

(c) When the distance between the astronauts is shortened to 5.00 m, the moment of inertia of the system changes. We can calculate the new moment of inertia using the parallel axis theorem:

I = Icm + md²

where Icm is the moment of inertia about the center of mass (which remains the same), m is the mass of each astronaut, and d is the distance between each astronaut and the center of mass (which is half the original distance, or 2.50 m).

The new moment of inertia is:

I = Icm + 2md²

 = 2(m(2.50 m)²)

 = 31.25 kg m²

Therefore the new moment of inertia is 31.25 Kgm².

(d) To find the new speeds of the astronauts, we can use the conservation of angular momentum:

L = Iω = L'

where L is the initial angular momentum (which we found in part (a)) and L' is the new angular momentum (which we can find using the new moment of inertia and the new distance between the astronauts, which is 5.00 m).

Solving for ω', we get:

ω' = L' / I = L / I'

Putting in the values, we get:

L' = L = 5,252 kg m²/s

I' = 31.25 kg m²

ω' = 5,252 kg m²/s / 31.25 kg m² = 168.06 rad/s

The new speed of each astronaut is the tangential velocity at a distance of 2.50 m from the center of mass, which can be found using the formula:

v = ω'r

where r is the distance from the center of mass. Putting in the values, we get:

v = 168.06 rad/s * 2.50 m = 420.15 m/s

Therefore, the new speed of each astronaut is 420.15 m/s.

(e) To find the new rotational energy of the system after the astronauts have shortened the rope to 5.00 m, we can use the conservation of angular momentum:

L = Iω

where L is the angular momentum of the system, I is the moment of inertia of the system, and ω is the angular speed of the system. Since the rope is assumed to have negligible mass, we can treat the system as two point masses moving in a circle around their center of mass. The moment of inertia of this system can be calculated as:

I = 2mr²/5

where m is the mass of each astronaut and r is the distance between them. Initially, the moment of inertia of the system is:

I = 2 * 90.5 kg * (10.0 m / 2)² / 5

= 3638 kg m²

The initial angular momentum of the system is:

L = Iω = 3638 kg m² * (5.80 m/s) / (10.0 m / 2)

          = 4213.6 kg m²/s

After the astronauts have shortened the rope to 5.00 m, the moment of inertia of the system is:

I' = 2 * 90.5 kg * (5.00 m / 2)² / 5

  = 1352.5 kg m²

Since the angular momentum of the system is conserved, the new angular speed of the system is:

ω' = L/I' = 4213.6 kg m²/s / 1352.5 kg m² = 3.115 rad/s

E' = (1/2)I'ω'² = (1/2) * 1352.5 kg m² * (3.115 rad/s)²

                    = 65,817.6 J

                    = 65.82 kJ

Therefore, the new rotational energy of the system is 65.82 kJ.

(f) The work done by the astronauts in shortening the rope is:

W = ∫F dl = (F' - F) ∫dl

   = (6,043,064.25 N - 630.56 N) * (-7.50 m)

   = -45,317,098 KJ

Therefore, the work is done by the astronauts in shortening the rope -45,317,098 KJ.

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Answer:

Answer is C. Speed

90.1 g of ice are still present in the container. Calculating the heat received by the ice to melt and the heat lost by the tea is necessary until it reaches an equilibrium temperature of 33.1 ◦C .

Consider how much energy is required to melt one kilogramme of ice at zero degrees to produce one kilogramme of water at zero degrees. The energy required to melt one kilogramme of ice is determined by Q = mLf = (1.0 kg)(334 kJ/kg) = 334 kJ using the equation for a change in temperature.

In order to calculate how much heat is gained by the ice melting, we must first calculate how much heat is lost by the tea as it cools from 33.1 °C to 0.0 °C.

Tea loses the following amount of heat: q1 = m1CT1 = 0.185 kg) (4186 J/kg C) (33.1 C - 0.0 C) = 26298.93 J.

Heat required for ice to melt is given by the formula: q2 = m2Hf = (0.0903 kg)(333.55 kJ/kg) = 30062.56 J

We may set q1 = q2 to get the mass of ice still present because the system is in thermal equilibrium:

m2 = q2/Hf = 333.55 kJ/kg / 30062.56 J = 0.0901 kg

Finally, we round the mass to two significant digits and convert it to grammes:

m2 = 90.1 g

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The psychologist who emphasizes the social learning perspective explain this behavior would say that Ibrahim has observed others who model aggressive behavior. Option B

According to social psychology, aggression refers to any conduct or action intended to hurt a person, an animal, or cause physical injury to property. Here are a few instances of aggressive behavior: physical harm. screaming, cursing, and foul language.

Aggression is an overt or covert social engagement that is frequently harmful and intended to cause harm to another person.

Aggressive behavior is forceful, reactive, and impulsive behavior that frequently leads to breaching social norms or the law.

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In the study of personality, the Five-factor model includes different traits that underlie one’s basic tendencies.

The Five-factor model is a scientific theory that states traits of the personality of an individual are due to its biology and therefore they respond to adaptations, which are central in the biology field.

In conclusion, in the study of personality, the Five-factor model includes different traits that underlie one’s basic tendencies.

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Answer:

C

Explanation:

Sublimation is when a solid turns into a gas.

A is not sublimation, it is condensation (gas to liquid = water vapor to dew)

B is evaporation (liquid to gas = liquid deodorant to gas)

D is melting (solid to liquid = ice cream to liquid ice cream)

E is condensation (gas to liquid = water vapor to water droplets)

C is the correct answer, because dry ice is a solid and carbon dioxide is a gas, so it is changing from solid to gas.

Answer: The speed is 15.5 m/s

Explanation:

The kinetic energy can be written as:

K = (1/2)*m*v^2

where m is the mass and v is the speed.

Then we have that:

18 j = (1/2)*0.15kg*v^2

Now we solve this for v.

√(18*2/0.15) = v

15.5 m/s = v

Answer:

a. i) The pressure drop per unit length is 52,151.89 Pa

ii) The atmospheric pressure ≈ 19.175 × The pressure drop along 10 cm length of aorta

b i) The power required for the heart to push blood along a 10 cm length of aorta, is 2.6075945 Watts

ii) The basal metabolic rate ≈ 38.35 × The power to push the blood along a 10 cm length of aorta

c. i) Please find attached the drawing for the velocity profile created with Microsoft Excel

ii) The velocity at the center is approximately 2.04 m/s

Explanation:

The given diameter of the aorta, D = 2.5 cm = 0.025 m

The maximum flow rate, Q = 500 cm³/s = 0.0005 m³/s

Assumptions;

The blood flow is laminar

The blood is a Newtonian fluid

The viscosity of water ≈ 0.01 poise = 1 cp

a. i) The pressure drop per unit length of pipe ΔP/L is given by the Hagen Poiseuille equation as follows;

\(Q = \dfrac{\pi \cdot R^4}{8 \cdot \mu} \cdot \left(\dfrac{\Delta p}{L} \right)\)

Where;

Q = The flow rate = A·v

A = The cross sectional area

R = The radius = D/2

Δp/L = The pressure drop per unit length of the pipe

Therefore, we have;

\(\dfrac{\Delta p}{L} = \dfrac{Q\cdot 8 \cdot \mu }{\pi \cdot R^4} = \dfrac{0.0005 \times 8 \times 1}{\pi \times 0.0125^4 } = 52151.89\)

The pressure drop per unit length ΔP/L = 52,151.89 Pa

ii) The pressure, ΔP, drop along 10 cm (0.1 m) length of aorta = ΔP/L × x;

∴ ΔP = 52,151.89 Pa × 0.1 m = 5,215.189 Pa

Given that the atmospheric pressure, \(P_{atm}\) = 10⁵ Pa, we have;

\(P_{atm}\)/ΔP = 10⁵/5,215.189 ≈ 19.175

Therefore, the atmospheric pressure is approximately 19.175 times the pressure drop along 10 cm length of aorta

b. i) The power, P = Q × ΔP

Therefore, the power required for the heart to push blood along a 10 cm length of aorta, is P₁₀ = 0.0005 m³/s × 5,215.189 Pa = 2.6075945 Watts

ii) Therefore compared to the basal metabolic rate of, 'P', 100 W, we have;

P/P₁₀ = 100 W/2.6075945 Watts = 38.349521 ≈ 38.35

The basal metabolic rate is approximately 38.35 times more powerful than the power to push the blood along a 10 cm length

c. i) The velocity profile across the aorta is given as follows;

\(v_m = \dfrac{1}{4 \cdot \mu} \cdot \dfrac{\Delta P}{L} \cdot R^2\)

Where;

\(v_m\) = The velocity at the center

We get;

\(v_m = \dfrac{1}{4 \times 1} \times 52,151.89 \times 0.0125^2 \approx 2 .04\)

The velocity at the center, \(v_m\) ≈ 2.04 m/s

ii) The velocity profile, v(r), is given by the following formula;

\(v(r) = v_m \cdot \left[1 - \dfrac{r^2}{R^2} \right]\)

Therefore, we have;

\(v(r) = 2.04 - \dfrac{2.04 \cdot r^2}{0.0125^2} \right] = 2.04 - 163\cdot r^2\)

The velocity profile of the pipe is created with Microsoft Excel

Answer:

t = 7.5 s

Explanation:

The distance traveled by the car at the time of meeting of the two cars must be the same. First, we calculate the distance traveled by the police car. For that we use 2nd equation of motion. Here, we take the time when police car starts to be reference. So,

s₁ = Vi t + (0.5)gt²

where,

s₁ = distance traveled by police car

Vi = Initial Velocity = 0 m/s

t = time taken

Therefore,

s₁ = (0 m/s)(t) + (0.5)(9.8 m/s²)t²

s₁ = 4.9 t²

Now, we calculate the distance traveled by the car. For constant speed and time to be 1 second more than the police car time, due to car starting time, we get:

s₂ = Vt = V(t + 1)

where,

s₂ = distance traveled by car

V = Velocity of car = (100 km/h)(1000 m/1 km)(1 h/ 3600 s) = 27.78 m/s

Therefore,

s₂ = 27.78 t + 27.78

Now, we know that at the time of meeting:

s₁ = s₂

4.9 t² = 27.78 t + 27.78

4.9 t² - 270.78 t - 27.78 = 0

solving the equation and choosing the positive root:

t = 6.5 s

since, we want to know the time from the moment car crossed police car. Therefore, we add 1 second of starting time in this.

t = 6.5 s + 1 s

t = 7.5 s

Answer:

Find the explanation below.

Explanation:

Earth is properly designed to support life. This is seen in the favorable temperature that supports life, the water cycle that recycles water for plant and animal life, the atmosphere, energy, and nutrients.

1. Temperature: The temperature which is regulated by the different weather conditions such as the rains, snows, dry seasons all help to maintain a stable condition for life.

2. Water: The water cycle through processes like evaporation, condensation, precipitation, helps to ensure that there is never a lack of water in the earth. The numerous water bodies like the seas, oceans, rivers, lakes, also provide a habitat for some living things. Water makes up 70% of the earth.

3. Atmosphere: The atmosphere is a mixture of gases in the right proportions that are necessary for life. Oxygen, Nitrogen, Carbon, etc are released and inhaled by man and other living things. They are also involved in so many biochemical reactions that help in metabolism and catabolism.

4. Energy: Energy generated from the sun and within the earth is stored in various forms and is always conserved. This energy is converted to different states such as the potential, chemical, kinetic, mechanical forms to get work done and to release heat.

5. Nutrients​: Though cycles such as the carbon, nitrogen, oxygen, and phosphorous cycles, the earth maintains its stock of essential nutrients that help to sustain life.

An interdisciplinary approach encompassing climatology, oceanography, environmental science, and other fields of study is necessary to evaluate the Earth's capacity to support life.

Temperature: Monitoring and analyzing climate data from numerous sources, including weather stations, satellites, and ocean buoys, is necessary to determine the Earth's temperature. To understand how temperature patterns vary over time, scientists look at long-term trends, seasonal variations, and severe events. They forecast future temperature increases and their possible effects on life and ecosystems using global climate models.

Water: Monitoring freshwater availability, water quality, and water distribution throughout various regions are all part of the assessment of Earth's water resources. Studies of precipitation patterns, data on ice melting from polar regions, and measurements of water levels in lakes, rivers, and aquifers are all conducted by researchers. Testing for toxins, pollutants, and chemical compositions is part of evaluating water quality to make sure it adheres to acceptable standards for both ecological and human health.

Atmosphere: scientists measure and research a number of factors, such as greenhouse gases, air quality, and atmospheric pressure, in order to evaluate the Earth's atmosphere. Carbon dioxide (CO2), methane (CH4), and other greenhouse gases are measured at monitoring sites throughout the globe to better understand how they contribute to climate change. Pollutants like particle matter and ozone, which have an influence on both human health and ecosystems, are measured by air quality monitoring stations.

Energy: studying diverse energy sources and their effects on the environment and ecosystems is necessary to evaluate the amount of energy present on Earth. Scientists assess the usage of non-renewable energy sources like fossil fuels as well as renewable energy sources like solar, wind, hydro, and geothermal energy. To create sustainable energy plans that support life on Earth, they examine energy consumption trends, carbon emissions, and energy efficiency.

Nutrients: studying nutrient cycles and availability in soils, oceans, and terrestrial ecosystems is necessary for evaluating the availability of nutrients in the Earth's ecosystems. To determine the nutrient levels for agriculture and plant growth, researchers examine soil samples. In order to gauge the productivity and availability of nutrients for marine life, they also research marine ecosystems.

Hence, an interdisciplinary approach encompassing climatology, oceanography, environmental science, and other fields of study is necessary to evaluate the Earth's capacity to support life.

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Answer:

I’m pretty sure it’s B. It is harmful to the person and beneficial to the bacteria.

Explanation:

I’m taking the test right now. But if you think about it the bacteria is fighting off the medicine to which means the bacteria will just keep growing. So I’m 97% sure it’s B. Good luck you can do it don’t stop believing in yourself!!!!!! Hope I helped. And remember at the end of the day all that matters is love and happiness not grades!!!!!!!

Answer:

Answer is B!

Explanation:

I took the cumulative exam and got 100%

The weight of the fourth casting is 48 kg.

Given - The weight of three castings -

45.302kg

44.982kg

45.716kg

To find - The average weight if the 4th casting is taken the average weight becomes 46kg what is the weight of the 4th casting​

Solution -

Let's calculate the average weight of the first three castings using the given weights:

Average weight = (Weight of first casting + Weight of second casting + Weight of third casting) / 3

Average weight = (45.302 kg + 44.982 kg + 45.716 kg) / 3

Average weight = 136.000 kg / 3

Average weight = 45.3333... kg (rounded to four decimal places)

Now, let's calculate the weight of the fourth casting by using the average weight and the desired overall average weight:

Total weight of all four castings = Average weight * 4

Total weight of all four castings = 46 kg * 4

Total weight of all four castings = 184 kg

To find the weight of the fourth casting, we subtract the total weight of the first three castings from the total weight of all four castings:

Weight of the fourth casting = Total weight of all four castings - Total weight of first three castings

Weight of the fourth casting = 184 kg - 136 kg

Weight of the fourth casting = 48 kg

Therefore, the weight of the fourth casting is 48 kg

To increase the potential energy of a magnet in a gravitational field, you can move it higher in the gravitational field. This will increase the force of gravity acting on the magnet, which increases its potential energy.

Potential energy is the stored energy of an object due to its position or configuration. It is the energy that an object possesses due to its place in a force field or its configuration relative to other objects. Potential energy can be either kinetic or gravitational. Kinetic potential energy is energy stored due to the motion of an object, whereas gravitational potential energy is the energy stored due to the gravitational force acting upon it.

a. To increase the potential energy of a magnet in a gravitational field, you can move it higher in the gravitational field. This will increase the force of gravity acting on the magnet, which increases its potential energy.

b. To increase the potential energy of a magnet in a magnetic field, you can increase the strength of the magnetic field. When the magnetic field is stronger, it exerts a greater force on the magnet, which increases its potential energy.

c. The cause of both phenomena is the force of the gravitational or magnetic field acting on the magnet. The effect is an increase in the potential energy of the magnet.

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When an object falls the gravitational field of the earth exerts a force called the "gravitational force". This force is exerted on the body due to gravity, it is not the body that exerts a force on itself.

The 99% confidence interval for the average maximum HP for the experimental engine is (610.12, 689.88).

To calculate the confidence interval for the experimental engines' average maximum HP, we can use the following formula:

To find the z-score for α=0.01, we can refer to a standard normal distribution table or use a calculator. The z-score is approximately 2.58.

Substituting the given values into the formula, we get:

CI = 650 ± 2.58*(60/√25) CI = 650 ± 30.96

Rounding to two decimal places, the confidence interval for the experimental engines' average maximum HP is:

CI = [619.04 HP, 680.96 HP]

Therefore, we can say with 99% confidence that the true average maximum HP for the experimental engines falls between 619.04 HP and 680.96 HP. Thus, we can conclude that the experimental engines' average maximum HP is likely to be within this range. However, note that this range does not include the manufacturer's claimed maximum HP of 630 HP, which may indicate that the engines are performing below expectations.

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Answer:

The acceleration of the mass is 2 meters per square second.

Explanation:

By Newton's second law, we know that force (\(F\)), measured in newtons, is the product of mass (\(m\)), measured in kilograms, and net acceleration (\(a\)), measured in meters per square second. That is:

\(F = m\cdot a\) (1)

The initial force applied in the mass is:

\(F = (10\,kg)\cdot \left(2.5\,\frac{m}{s^{2}} \right)\)

\(F = 25\,N\)

In addition, we know that force is directly proportional to acceleration. If the smaller force is removed, then the initial force is reduced to \(\frac{4}{5}\) of the initial force. The acceleration of the mass is:

\(\frac{25\,N}{20\,N} = \frac{2.5\,\frac{m}{s^{2}} }{a}\)

\(a = 2\,\frac{m}{s^{2}}\)

The acceleration of the mass is 2 meters per square second.

Answer:

22.4 s

Explanation:

The following data were obtained from the question:

Mass (m) = 75 Kg

Height (h) = 50 ft

Power (P) = 500 W

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) =?

Next, we shall convert 50 ft to metres (m). This can be obtained as follow:

1 ft = 0.3048 m

Therefore,

50 ft = 50 ft × 0.3048 m / 1 ft

50 ft = 15.24 m

Thus, 50 ft is equivalent 15.24 m.

Next, we shall determine the energy used by the student to walk up three flights of stairs. This can be obtained as follow:

Mass (m) = 75 Kg

Height (h) = 15.24 m

Acceleration due to gravity (g) = 9.8 m/s²

Energy (E) =?

E = mgh

E = 75 × 9.8 × 15.24

E = 11201.4 J

Finally, we shall determine the time taken for the student to travel up the three flights of stairs. This can be obtained as follow:

Power (P) = 500 W

Energy (E) = 11201.4 J

Time (t)

Power (P) = Energy (E) / Time (t)

500 = 11201.4 /t

Cross multiply

500 × t = 11201.4

Divide both side by 500

t = 11201.4 /500

t = 22.4 s

Therefore, it will take the student 22.4 s to travel up the three flights of stairs.

The time taken for the student to travel up the three stairs is 22.4 s.

The given parameters;

The gravitational potential energy of the student due to vertical position of the three stairs is calculated as;

\(P.E = mgh\\\\P.E = 75 \times 9.8 \times 15.24 \\\\P.E =11,201.4 \ J\)

The time taken for the student to travel up the three stairs is calculated as follows;

\(E = Pt\\\\t = \frac{E}{P} \\\\t = \frac{11,201.4}{500} \\\\t = 22.4 \ s\)

Thus, the time taken for the student to travel up the three stairs is 22.4 s.

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Answer:

19.5

Explanation:

momentum = mass * velocity

momentum = 6.5 * 3

momentum = 19.5

Answer: Gravity

Explanation:A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.

Answer:

356°C.

Explanation:

(1). The first step to the solution to this particular Question/problem is to determine the Biot number, and after that to check the equivalent value of the Biot number with plate constants.

That is, Biot number = (length × ∞)÷ thermal conductivity. Which gives us the answer as ∞. Therefore, the equivalent value of the ∞ on the plates constant = 1.2732 for A and 1.5708 for λ.

(2). The next thing to do is to determine the fourier number.

fourier number = [α = 97.1 × 10−6 m2/s × 15 s] ÷ (.05m)^2 = 0.5826.

(3). The next thing is to determine the temperature at the center plane after 15 s of heating.

The temperature at the center plane after 15 s of heating = 500°C [ 25°C - 500°C ] [1.2732] × e^(-1.5708)^2 ( 0.5826).

The temperature at the center plane after 15 s of heating = 356°C.

The net work done (in J) required to accelerate a 1500 kg car from 55 m/s to 65 m/s is 3127500 J

First, we shall obtain the initial kinetic energy. Details below:

KE₁ = ½mu²

= ½ × 1500 × 55²

= 41250 J

Next, we shall final kinetic energy. Details below:

KE₂ = ½mv²

= ½ × 1500 × 65²

= 3168750 J

Finally, we shall determine the net work done. Details below:

W = KE₂ - KE₁

= 3168750 - 41250

= 3127500 J

Thus, the net work done is 3127500 J

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The radius of the wire that would exhibit some strain the same strain as a spider is 0.06m.

The strain in a wire is given by the change in length divided by the original length, and is equal to the force applied divided by the cross-sectional area times the Young's modulus.

The force applied to the spider's thread is the weight of the spider, which is 1.0 x 10⁻³ kg x 9.8 m/s² = 9.8 x 10⁻³N.

The original length of the spider's thread is L = h, where h is the height of the spider.

The change in length is given by ΔL = FL/AY, where F is the force applied, L is the original length, A is the cross-sectional area, and Y is the Young's modulus.

Solving for the cross-sectional area, A = FL/ΔL = FL/ (FY/Y) = FLY/F = LY/F = πr²

We can now substitute the known values into the equation and solve for the radius, r:

πr² = LY/F = hY/F = 4.5 x 10 N/m² x (13 x 10⁻⁶ m) / (9.8 x 10⁻³ N)

r = sqrt(hY/Fπ) = sqrt(4.5 x 10 N/m² x (13 x 10⁻⁶ m) / (9.8 x 10⁻³ Nπ))

The radius of the aluminum wire that would exhibit the same strain as the spider's thread is the same as the calculated radius, 0.06m.

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