That indicates a downward-pointing velocity of 19.2 m/s at that precise moment.
What is a acceleration explain?Acceleration is the rate where the speed and the direction of velocity vary over time. A point or object going straight forward is accelerated when it accelerates or decelerates. Even though the velocity is constant, motion on a circle accelerates since the direction is always shifting.
Briefing:On Earth, gravity accelerates at a rate of 9.8 m/s². That means that any object that is just subject to the force of gravity experiences a downward acceleration of 9.8 m/s per second.
The ball accelerates by -(down)9.8 m/s per second after the throw.
Three seconds later, the ball's speed is
Three seconds later, the ball's speed is
20 + 4(-9.8) = 20 - 39.2
20 - 39.2 = - 19.2 m/s .
That indicates a downward-pointing velocity of 19.2 m/s at that precise moment.
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An Eider duck is flying Northeast at 25 m/s at an angle of 36.9 degrees to the ground (from the positive
X-axis). What are the horizontal and vertical velocities, respectively, of the duck's flight?
Answer:
Horizontal = 19.99212 m/s Vertical = 15.0151 m/s
Explanation:
Horizontal = Cos(36.9) x 25
Vertical = Sin(36.9) x 25
a car passes by a flag at 160m and 8 seconds later it passes by a flag at 240m. What is the average Speed of the car
24 is the average Speed of the car.
What is an average speed and an illustration?
Calculating average speed involves dividing the total distance traveled by the time interval. For instance, if it takes a person 40 minutes to travel 20 miles north, 20 miles south, and finally 20 miles in between, their average speed is 40 miles divided by 40 minutes, or 1 mile per minute (60 mph).
a flag at 160m
t = 8
d = 160/8
= 20
d2 = 240/8
= 30
the average Speed = 2d1 d2/d1+d2
= 2 * 20 * 30/50
= 24
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Please someone answer this quickly!! I'll give 20 points for it, I just need the answers :)
The potential energy of the person mass 95 Kg sitting on top of a slid 3 m high is 2795.85 J
How do i determine the potential energy of the person?The following data were obtained from the question:
Mass of person (m) = 95 KgHeight of slid (h) = 3 mAcceleration due to gravity (g) = 9.81 m/s² Potential energy of person (PE) = ?The potential energy of the person can be obtained as follow:
PE = mgh
Inputting the given parameters, we have:
= 95 × 9.81 × 3
= 2795.85 J
Thus, the potential energy of the person is 2795.85 J
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Which of the following describes air temperature and air pressure at higher altitudes?
Group of answer choices:
Air temperature increase while air pressure decreases
Air temperature and air pressure both decrease
Air temperature and air pressure both increase
Air temperature decreases while air pressure increases
Answer:
Air temperature and air pressure both decreases
Answer: A
Explanation:
A small metal sphere has a mass of 0.19 gg and a charge of -23.0 nCnC. It is 10.0 cmcm directly above an identical sphere that has the same charge. This lower sphere is fixed and cannot move. If the upper sphere is released, it will begin to fall.What is the magnitude of its initial acceleration?
Answer:
a = -7.29 m / s²
Explanation:
For this exercise we must use Newton's second law,
F -W = m a
Force is electrical force
F = k q₁ q₂ / r²
k q₁ q₂ / r² -mg = m a
indicate that the charge of the two spheres is equal
q₁ = q₂ = q
a = (k q² / r² - m g) / m
a = k q² / m r² - g
Let's reduce the magnitudes to the SI system
m = 0.19 g (1kg / 1000 g) = 1.9 10⁻⁴ kg
q1 = q2 = q = -23.0 nC (1C / 10⁹ nC) = -23.0 10⁻⁹ C
r = 10.0 cm (1m / 100cm) = 0.1000 m
let's calculate
a = 9 10⁹ (23.0 10⁻⁹)² / (0.1000² 1.9 10⁻⁴) - 9.8
a = -7.29 m / s²
The negative sign indicates that the direction of this acceleration is downward
why do think chopping of wood is a physical change but burning of wood is a chemical change
Answer: Burning of wood is a chemical change while cutting of wood is a physical change because during burning, new substances are formed. After burning, we cannot get original substance, (i.e. wood) back. Cutting of wood into small pieces is a physical change because no new substance is formed.
A charge of 3 micro-c (left) and a charge of 7 micro-c (right) are separated by 50 cm on the x-axis. What is the electric potential at 70 cm to the right of the left charge?
The electric potential at 70 cm to the right of the left charge is 7.125 x \(10^3 V.\)
To calculate the electric potential at a point due to two point charges, we need to use the following formula:
V = kq1 / r1 + kq2 / r2
where V is the electric potential, k is Coulomb's constant (\(9 x 10^9 N m^2 / C^2\)), q1 and q2 are the magnitudes of the charges, r1 and r2 are the distances between the point and the charges.
In this case, the left charge has a magnitude of 3 micro-c and the right charge has a magnitude of 7 micro-c. The distance between the left charge and the point of interest (70 cm to the right of the left charge) is 120 cm, and the distance between the right charge and the point of interest is 50 cm.
So, plugging in the values, we get:
V = (9 x \(10^9\)N \(m^2\) / \(C^2\)) x (3 x \(10^-6\) C) / 1.2 + (9 x \(10^9\) N \(m^2\) / \(C^2\)) x (7 x \(10^-6\) C) / 0.5
Simplifying this expression gives:
V = 7.125 x\(10^3\) V
Therefore, the electric potential at 70 cm to the right of the left charge is 7.125 x \(10^3 V.\)
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A Newtonian fluid (μ=5x10-3 Ns/m2, rho=1.1g/cm3) flows between 2
parallel plates that are separated by 10mm. A pitot was used to
measure the velocity of the flow at various points between the
plates; Determine the shear stress distribution in the fluid using 2 approaches: a) Using the tabulated data, use numerical differentiation to determine the shear stress distribution Forward Difference: \( \f
Using the tabulated data and forward difference numerical differentiation, the shear stress distribution in the fluid can be determined.
To calculate the shear stress distribution using forward difference numerical differentiation, we need the velocity data at various points between the plates. However, the given information does not provide any velocity measurements. Without velocity data, it is not possible to determine the shear stress distribution.
If you have the velocity data, please provide it so that I can assist you further in calculating the shear stress distribution using the forward difference numerical differentiation method.
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Would a glowing rod be hotter if it was white or red? Why?
Answer:
White
Explanation:
Red comes from the lowest energy range of and blue from the highest.
suppose you start another weakly damped oscillator with the same initial conditions as in the figure and with all parameters unchanged except for increased damping. how does the trajectory in the phase space change?
If the damping within a weakly damped oscillator is increased, its trajectory within phase space shall exhibit a faster decay towards equilibrium.
What happens to the oscillations?As such, oscillations will occur with less frequency and amplitude will subsequently reduce more rapidly than what was observed in the original system.
It can also be seen that the phase space trajectory will spiral inward. This resembles a more direct route to stable equilibrium while reflecting the higher energy dissipation attributed to enhanced damping.
Overall, the system will achieve its endpoint at an expedited rate and evoke lesser amounts of oscillatory behavior.
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There is a tender for building a new mall in Alexandra, what are the three main stakeholders and their functions required to ensure the completion of the project. 1.2 During the construction of a road in a particular community. who represent the community and what is their duties. 1.3 Before any type of Civil Engineering project is carried out, what needs to be done ensure the viability of the project. 1.4 The contractor has won a tender for construction of a Bridge, show its hierarchy of working when carrying out the work. 1.5 A 50 km road construction is to take place, the duration of the project is 10 days, draw the bar chart of the project. Question 2 (10) 2.1 Why is Risk Management necessary in a project?
For a successful final touch of a construction venture, key stakeholders consisting of the consumer/proprietor, architect/layout group, and creation contractor are crucial. Risk management is necessary to perceive and mitigate capacity risks, ensuring project success and minimizing disruption
The 3 important stakeholders for the development of a new mall in Alexandra are:
Client/Owner: The patron/proprietor is the entity or agency initiating the mission. Their feature is to define the task necessities, provide the important funding, and oversee the entire task. Architect/Design Team: The architect and layout crew are answerable for developing the architectural and structural plans for the mall.Construction Contractor/Builder: The production contractor is chargeable for executing the construction sports and bringing the mall to reality.During the construction of an avenue in a particular network, the network is represented by:
Local Authorities: The local authorities, which include the municipal or city council, represent the community's pastimes. Their duties consist of engaging with the network to apprehend their needs and issues associated with the road construction project.
Before any sort of Civil Engineering mission is executed, the subsequent steps want to be taken to ensure the viability of the challenge:
Feasibility Study: A feasibility observation is performed to assess the technical, financial, criminal, and environmental components of the venture. Environmental Impact Assessment: An environmental impact evaluation is performed to evaluate the capacity environmental consequences of the undertaking.Design and Engineering: Detailed layouts and engineering paintings are conducted to develop the challenge plans and specifications.Cost Estimation and Budgeting: Cost estimation is carried out to decide the overall undertaking price, together with substances, hard work, devices, and other expenses.The hierarchy of running for a contractor sporting out the development of a bridge typically consists of the subsequent degrees:
Project Manager: The undertaking supervisor oversees the complete creation mission, which includes making plans, scheduling, budgeting, and coordinating resources.Site Manager: The website online supervisor is accountable for on-site operations and coordination. They control the daily sports, supervise the development group, screen development, and ensure adherence to safety and high-quality requirements.Foremen and Supervisors: Foremen and supervisors are chargeable for particular areas or trades inside the production process. They supervise the people, coordinate duties, and make sure that work is done in step with the mission plans and specs.Skilled Workers: Skilled employees consist of carpenters, masons, electricians, welders, and other specialized tradespeople who perform the actual construction obligations.Laborers: Laborers are liable for assisting skilled people, wearing materials, and appearing fashionable hard work obligations required for the construction work.To draw the bar chart (also referred to as a Gantt chart) for a 50 km street creation undertaking with a duration of 10 days, the chart could represent the obligations and their respective intervals. However, a standard bar chart for an avenue creation undertaking may also include duties including surveying, excavation, laying subbase, paving, and street markings, amongst others.
The horizontal axis represents the timeline (in days), and the vertical axis represents the responsibilities. Each undertaking is represented with the aid of a horizontal bar that suggests its length.
Question 2 (10):
2.1 Risk control is vital in a venture for the following motives:
Identify and Assess Risks: Risk control allows perceive capability risks and investigate of their potential impact on the assignment.Mitigate and Control Risks: Through chance management, proactive measures can be taken to mitigate and control dangers. Enhance Decision-Making: By considering risks and their capacity outcomes, danger control gives treasured information for choice-making. Improve Project Performance: Effective risk control contributes to better mission performance by minimizing disruptions, delays, and price overruns. Stakeholder Communication: Risk management helps communication with project stakeholders by supplying transparency about capacity risks and the way they'll be controlled.Overall, change management is important for figuring out, analyzing, and responding to risks in a systematic and proactive manner. It enables ensuring task success by using lowering uncertainties and maximizing opportunities for task delivery within the preferred parameters.
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A beverage can is dropped from rest and from a bridge at height 100 m. how much time does the can take to fall through the bottom 20.0 m?
The can will take approximately 2.02 seconds to fall through the bottom 20.0 m
To find the time it takes for the can to fall through the bottom 20.0 m, we can use the equation for the time taken by an object in free fall:
t = √(2h/g)
where t is the time, h is the height, and g is the acceleration due to gravity.
In this case, the height (h) is 20.0 m. The acceleration due to gravity (g) is approximately 9.8 m/s².
Plugging these values into the equation:
t = √(2 * 20.0 / 9.8)
Simplifying:
t = √(40.0 / 9.8)
t ≈ √4.08
t ≈ 2.02 seconds
Therefore, the can will take approximately 2.02 seconds to fall through the bottom 20.0 m.
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The use of fire-resistive materials when constructing a building is an example of: risk transfer risk control risk avoidance risk retention QUESTION 4 Which of the following statements is correct. 1. One of the pre-loss objectives of risk managers is to meet any legal requirements the company may face. II. One of the post-loss objectives of risk managers is to maximize his own wealth. I only II only Both I and II Neither I nor II
The correct statement is "I only." One of the pre-loss objectives of risk managers is to meet any legal requirements the company may face.
The use of fire-resistive materials when constructing a building is an example of risk control. This is because risk control involves taking proactive steps to reduce the likelihood or severity of loss when an incident occurs. Fire-resistive materials are designed to withstand fire, and they are meant to slow down or contain the spread of fire in a building, thus reducing the risk of loss or damage.
In risk management, risk control is one of the four basic methods used to handle or mitigate risks. The other methods include risk transfer, risk avoidance, and risk retention. Risk transfer involves shifting the risk of loss to another party, such as through insurance or contract agreements. Risk avoidance involves eliminating the activity that could lead to loss or harm, while risk retention involves accepting the risk and dealing with any losses that may occur. As for the second question, the correct statement is "I only."
One of the pre-loss objectives of risk managers is to identify, assess, and evaluate potential risks that could negatively affect an organization. They also work to develop strategies to manage these risks and to ensure that the company is meeting any legal or regulatory requirements. On the other hand, one of the post-loss objectives of risk managers is to minimize the impact of losses that occur. They work to evaluate the effectiveness of the company's risk management strategies and to ensure that the company recovers from the loss as quickly as possible. Maximizing the risk manager's wealth is not a post-loss objective of risk managers.
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If a flexible air-filled container has a volume of 40 cu ft on the surface, what would the volume be at 99 feet in sea water? (rounded off)
The volume of a flexible air-filled container would decrease as it descends deeper into the sea due to increased water pressure. The exact volume at 99 feet in seawater can be determined using the principles of Boyle's Law.
Boyle's Law states that the volume of a gas is inversely proportional to the pressure exerted on it, provided the temperature remains constant. As the container descends into the sea, the water pressure increases, resulting in a decrease in volume.
To calculate the volume at 99 feet in seawater, we need to consider the pressure difference between the surface and the given depth. The pressure at 99 feet in seawater is approximately 4 times the atmospheric pressure at the surface. Since the volume is inversely proportional to the pressure, the volume at 99 feet would be 1/4th of the initial volume at the surface.
Therefore, the volume at 99 feet in seawater would be approximately 40 cu ft / 4 = 10 cu ft (rounded off). As the container descends deeper into the sea, the increasing pressure compresses the air inside, leading to a reduction in volume.
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Why do you think the area of environmental science has been in existence for the last fifty to sixty years?
Answer:
Because environmental history deals with some of the most important issues regarding the future of our planet. The hi/story of nature parks around the globe. understand the impact of humans on pollution and health. It opens our eyes for the scarcity of resources and for their conservation into the future.
Explanation:
:-)
B.
An object thrown or shot vertically into the air reaches a maximum height after t secondsâ (when time is measured inâ seconds), where t is theâ k-coordinate of the vertex of the parabola.
The maximum height of an object thrown or shot vertically into the air is reached after t seconds, where t is the k-coordinate of the vertex of the parabola.
When an object is thrown or shot vertically, its motion can be modeled by a parabolic function.
The vertex of this parabola represents the highest point the object will reach, and the k-coordinate of the vertex represents the time it takes for the object to reach that height.
Hence, The maximum height of a vertically thrown or shot object is attained at the k-coordinate of the vertex of the parabola, which corresponds to the time t in seconds.
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how many wavelengths thick is a 1/2 mm thumbnail
how many wavelengths thick is 100 micrometer thick hair
The amount of wavelength of light thick is the thumbnail x/y.
Given:
Wavelength of light= x
Thickness of thumbnail= y
The amount of wavelength thick the thumbnail is x/y
What is wavelength?
Wavelength is the distance between identical points (adjacent peaks) in adjacent cycles of a waveform signal propagated in space or along a wire. In wireless systems, this length is usually given in meters (m), centimeters (cm), or millimeters (mm).To know more about wavelength, click the link given below:
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Fill in the blank to balance the equation: ___ AgI + Na₂S → Ag₂ + 2NaI
Answer:2AgI + Na2S → Ag2S + 2NaI I am pretty sure this is the answer
Explanation:
Which characteristic is the same for every color of light in a vacuum?.
In a vacuum all colors of light travel with same speed and this is the reason a white ray travels through the vacuum without going through any dispersion..
What is speed?Speed of light is the distance per time light waves propagate through different materials. The value for the speed of light in a vacuum is now defined as exactly 299,792,458 metres per second.
Therefore, In a vacuum all colors of light travel with same speed and this is the reason a white ray travels through the vacuum without going through any dispersion
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two small insulating spheres with radius 7.00×10−2 m are separated by a large center-to-center distance of 0.545 m . one sphere is negatively charged, with net charge -1.50 μc , and the other sphere is positively charged, with net charge 4.15 μc . the charge is uniformly distributed within the volume of each sphere.
The problem states that there are two small insulating spheres separated by a large center-to-center distance. One sphere has a negative charge of -1.50 μC, while the other sphere has a positive charge of 4.15 μC. The charge is uniformly distributed within the volume of each sphere.
To find the electric field at a point between the two spheres, we can use the principle of superposition. This principle states that the electric field due to multiple charges is the vector sum of the electric fields produced by each individual charge.
Here's how we can solve this problem step-by-step:
1. Calculate the electric field due to the negatively charged sphere at the point of interest.
- The electric field due to a single point charge is given by Coulomb's Law:
E = k * (q / r^2)
where E is the electric field, k is the electrostatic constant (9.0 x 10^9 N*m^2/C^2), q is the charge, and r is the distance from the charge to the point of interest.
- In this case, the charge is -1.50 μC and the distance from the negatively charged sphere to the point of interest is the center-to-center distance between the two spheres (0.545 m).
- Plugging in the values, we can calculate the electric field due to the negatively charged sphere.
2. Calculate the electric field due to the positively charged sphere at the point of interest.
- Using the same formula as before, we can calculate the electric field due to the positively charged sphere.
- In this case, the charge is 4.15 μC and the distance from the positively charged sphere to the point of interest is also the center-to-center distance between the two spheres (0.545 m).
3. Find the net electric field at the point of interest by summing the electric fields due to each sphere.
- Since the electric field is a vector quantity, we need to consider both the magnitude and direction of each electric field.
- Since the negatively charged sphere has a negative charge, its electric field points radially inward towards the sphere.
- Similarly, since the positively charged sphere has a positive charge, its electric field points radially outward away from the sphere.
- To find the net electric field, we can add the magnitudes of the electric fields due to each sphere and consider their directions.
By following these steps, you can calculate the electric field at a point between two small insulating spheres with given charges and distances. Remember to use the correct units for charge (Coulombs) and distance (meters) in your calculations.
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the type of spectrum produced by a common light bulb is a ________.
The type of spectrum produced by a common light bulb is a continuous spectrum.A common light bulb emits light in the form of a continuous spectrum.
A continuous spectrum is characterized by a continuous range of wavelengths or colors without any gaps or specific emission lines.In the case of a light bulb, the emitted light is produced by the incandescent process, where a filament is heated to a high temperature, causing it to glow and emit light. This process generates a broad range of wavelengths, resulting in a continuous spectrum. Unlike other light sources such as lasers or specific gases, which produce emission or absorption lines at specific wavelengths, the light bulb's spectrum is smooth and continuous, encompassing a wide range of colors from red to violet.
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What is the hybridization of the xe atom in the xecl4 molecule?
a. sp
b. sp2
c. sp3
d. sp3 d
e. sp3 d 2
Answer:
sp3 d 2
Explanation:
Bio is a root word that means
O heart.
O life.
O cell.
O sugar.
the joints that connect the four fingers with the mother carpal bones are
The joints that connect the four fingers (excluding the thumb) with the carpal bones are called metacarpophalangeal joints (MCP joints).
The metacarpophalangeal joints are located at the base of each finger, where the metacarpal bones of the hand articulate with the proximal phalanges of the fingers. These joints allow for flexion (bending) and extension (straightening) of the fingers and also provide some degree of rotational movement.
There are five metacarpophalangeal joints in total, one for each finger. They are commonly referred to as the knuckles.
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i'm behind a car and wish to pass so you turn to the left and pull into the passing lane without changing speed why does the distance increase between you and the car you're following
Since the component of your velocity along the road decreased slightly as there was a component across the road when you changed lanes, the distance increased.
Which element, which disrupts attention, raises risk when driving a car?Driving while distracted might raise the likelihood of a car accident. Distractions include anything that diverts your focus from operating a vehicle. Distracted driving includes a variety of activities, including as texting, chatting on the phone, using a navigation system, and eating while operating a vehicle.On the left, overtake traffic. Only when the open roadway is clearly signposted for two or more lanes of traffic in your direction are you allowed to pass on the right. You do not drive off the road to pass the vehicle in front of you when they are making a left turn.To learn more about velocity refer to:
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Express 48 m/s in terms of
1.km/h
2.m/min
3.km/s
4.km/minutes
48 m/s in terms of km/h is 720.8 km/h. In terms of m/min is 2880 m/min, in terms of km/s is 0.048 km/s and in terms of km/min is 2.88 km/min.
To solve this question, we need to understand some terms. The unit of velocity is measured in m/s. It can be expressed in different units of velocity.
1 km (kilometer) = 1000 meter
1 h (hour) = 3600 seconds
1 minutes = 60 seconds
To convert m/s into km/h,
48 m/s * 3600/1000 = 172.8 km/h
To convert m/s into m/min,
48 m/s * 60 = 2880 m/min
To convert m/s into km/s,
48 m/s ÷ 1000 = 0.048 km/s
To convert m/s into km/minutes,
48 m/s * 60 / 1000 = 2.88 km/min
Therefore, the 48 m/s expressed is 172.8 km/h, 2880 m/min, 0.048 km/s and 2.88 km/min.
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48 m/s is equivalent to 172.8 km/h, 2880 m/min, 0.048 km/s, and 2.88 km/minute.
To express 48 m/s in different units of velocity:
km/h (kilometers per hour):
To convert m/s to km/h, we can use the conversion factor of 3.6 since 1 m/s is equal to 3.6 km/h.
48 m/s * (3.6 km/h / 1 m/s) = 172.8 km/h
Therefore, 48 m/s is equivalent to 172.8 km/h.
m/min (meters per minute):
To convert m/s to m/min, we can use the conversion factor of 60 since there are 60 seconds in a minute.
48 m/s * (60 m/min / 1 s) = 2880 m/min
Therefore, 48 m/s is equivalent to 2880 m/min.
km/s (kilometers per second):
Since 1 kilometer is equal to 1000 meters, to convert m/s to km/s, we divide the value by 1000.
48 m/s / 1000 = 0.048 km/s
Therefore, 48 m/s is equivalent to 0.048 km/s.
km/minute (kilometers per minute):
To convert m/s to km/minute, we first need to convert m/s to km/s (as calculated in the previous step) and then multiply by 60 to convert seconds to minutes.
0.048 km/s * 60 = 2.88 km/minute
So, 48 m/s is equivalent to 2.88 km/minute.
Hence, 48 m/s is equivalent to approximately 172.8 km/h, 2880 m/min, 0.048 km/s, and 2.88 km/minute.
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Newtons and Coulombs Laws QC
(Look to the bottom for answers 100% correct)
1. Which law gives the force between two objects that is related to their mass and distance?
A. Newton's second law of motion
B. Kepler's law
C. Newton's law of gravitation
D. Coulomb's law
2. What is the property that allows a positive proton and a negative electron to feel an attraction between each other?
A. Mass
B. Weight
C. Charge
D. Spin
3. In which case would there be an electrostatic force between two objects?
A. Two positively charged objects
B. A negatively charged object and a neutral object
C. A positively charged object and a neutral charged objects
D. Two neutral objects
4. Which statement is correct about electrostatic force?
A. It can have a positive or negative value
B. It is only observed between two electrons
C. It depends on the mass if the charges
D. It is independent of the distance between charges
5. In the simulation, two charges are both set to +4 uC. Then one of the charges is charged to -4 uC. Which statement describes the situation?
A. The electrostatic force is originally repulsive and stays repulsive.
B. The electrostatic force is originally attractive and stays attractive.
C. The electrostatic force changes from attractive to repulsive.
D. The electrostatic force changes from repulsive to attractive.
Answers:
1. C
2. C
3. A
4. A
5. D
BE SURE TO CHECK THE ORDER OF YOUR ANSWER CHOICES BECAUSE THEY CAN CHANGE.
100% is guaranteed
1c 2c 3a 4a 5d
Explanation:
I just know.
ur welcome.
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What is equilibrium?
Answer: Equilibrium is the state in which market supply and demand balance each other, and as a result prices become stable. The balancing effect of supply and demand results in a state of equilibrium.
This is the answer please ap mujhe follow kar lo please
How do we define electricity?
Noting that x is position, v is velocity, m is mass, and a is acceleration, which of the following expressions will have units of kg ⋅ m/s^2?
Select all that apply.
m ∫ a dt
m da/dt
m dv/dt
1/2 m dv^2/dx
1/2 m dv^2/dt
m ∫ v dt
m dx/dt
m ∫ x dt
1/2m ∫ v^2 dt
The expressions that have the units of kg ⋅ m/s² are as follows: m da/dt, m dv/dt, and m ∫ a dt.
Given: x is position, v is velocity, m is mass, and a is acceleration.
The unit of force is kg m/s², i.e. Newton.
Using the concept of Force, we can analyze which of the given expressions has the units of kg m/s² as follows:
Using Newton's second law of motion, we have
F = ma or a = F/mor m a = F
Differentiating the equation w.r.t time, we get
m (da/dt) = dF/dt ………………………………………(i)
From Newton's third law, we know that every action has an equal and opposite reaction.
Therefore, dF/dt = dp/dt
Where p is momentum.
So, m (da/dt) = dp/dt
Now, we know that the unit of momentum is kg m/s
So, the unit of dp/dt is kg m/s²
This implies that the unit of (da/dt) is m/s²which further implies that the unit of (m da/dt) is kg m/s²
Hence, m da/dt is the correct option that has the units of kg m/s².
Also, m dv/dt can be rewritten as md/dt (dx/dt).
Using product rule of differentiation we can write,
d/dt (mx') = m d/dt x' + x d/dt m = m d²x/dt² + x dm/dt
where x' = dx/dt
Similarly, d/dt (mv) = m d/dt (dx/dt) + v d/dt m = m d²x/dt² + v dm/dt
So, m dv/dt has the unit of kg m/s²
Next, m ∫ a dt can be differentiated w.r.t. time to get m a.
This implies that the unit of m ∫ a dt is kg m/s².
The other options given do not have units of kg m/s².
Therefore, the correct expressions that have the units of kg m/s² are m da/dt, m dv/dt, and m ∫ a dt.
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