Final answer:
To find the position of the particle when t=7, integrate the velocity function to obtain the position function. Substitute a given position value to determine the constant of integration. Finally, plug in t=7 into the position function and evaluate to find the position of the particle.
Explanation:
To find the position of the particle when t=7, we need to integrate the velocity function from t=6 to t=7. The velocity function v(t) = 5sin(t^2) represents the rate of change of position with respect to time. Integrating this function gives us the position function x(t) = -5cos(t^2) + C, where C is a constant of integration.
We can find the value of C by substituting the given position x(6) = 4.0 into the position function. Plugging in t=6 and x=4.0, we get 4.0 = -5cos(6^2) + C. Solving for C, we find C = 4.0 + 5cos(6^2).
Now we can find the position of the particle when t=7 by plugging in t=7 into the position function x(t) = -5cos(t^2) + C, where C is the value we obtained earlier. Evaluating the expression, we find x(7) = -5cos(7^2) + (4.0 + 5cos(6^2)). Therefore, the position of the particle when t=7 is approximately (0.609, 0).
Final answer:
The position of the particle at t=7 can be determined by integrating the given velocity function v(t) = 5sin(t^2) from t=6 to t=7 and adding the result to the known position at t=6. The integral does not have an elementary antiderivative, so numerical methods are needed for evaluation.
Explanation:
The position of the particle, while it moves along the x-axis, can be found by integrating the velocity function. Since the velocity is given by v(t) = 5sin([tex]t^2[/tex]), we will integrate this with respect to time to find the position function x(t). Given that the particle's position at time t=6 is (4,0), we can use this information to find the constant of integration after integrating the velocity function.
To find the position x(t) at any time t after t=6, we would calculate the integral of the velocity function from 6 to t, and add this to the initial position at t=6:
∫6t 5sin(τ2)dτ + 4
To find the position at t=7, we would evaluate this integral from 6 to 7, which requires a numerical method since the integral of sin(t2) is not an elementary function. Once the integral is evaluated, this value is added to 4 (the position at t=6) to determine the final position of the particle at t=7.
Which element(s) is/are not balanced in this equation?
MgO+2 LiCI → MgCI2+Li2O
A.All elements are balanced
B.Mg
C.CI
D.Li
which nervous system consist of the brain and spine
PLEASE HELP!!!! Scientists launch a rocket, and they monitor its acceleration and the force exerted by its engines. As the rocket gets higher, the monitors show that the acceleration of the rocket is increasing but the force exerted stays the same. How do Newton’s laws explain why the scientists could expect this to happen?
The total force stays the same, but the action force is increasing as the reaction decreases.
The mass of the rocket decreases as fuel is burned, so the acceleration increases.
The inertia of the rocket increases, which reduces the force needed to change its speed.
The reaction force is increasing as fuel is burned, which causes a greater acceleration.
The force exerted is constant because the mass of the rocket decreases as fuel is burned, so the acceleration increases.
What is the relationship between force mass and acceleration?The relationship between force, mass, and acceleration is given by Newton's second law and stated mathematically as follows:
Force = mass × accelerationAs the rocket accelerates, fuel is burnt and the mass of the rocket reduces. Thus, the force exerted remains constant.
Therefore, the mass of the rocket decreases as fuel is burned, so the acceleration increases.
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Answer:
b
Explanation:
A snowmobile has an initial velocity of 3.0 m/s
Part 1: If it accelerates at the rate of 0.5 m/s/s for 7.0 sec, what is the final vel.?
Part 2: If it accelerates at the rate of -0.60m/s/s, how long will it take to reach a complete stop?
Answer:
Part a)
[tex]v_f = 6.5 m/s[/tex]
Part b)
[tex]t = 5 seconds[/tex]
Explanation:
Part a)
As we know that
[tex]v_f = v_i + at[/tex]
here we know that
[tex]v_i = 3 m/s[/tex]
[tex]a = 0.5 m/s^2[/tex]
[tex]t = 7.0 s[/tex]
so we will have
[tex]v_f = 3 + (0.5)(7.0)[/tex]
[tex]v_f = 6.5 m/s[/tex]
Part b)
if finally the snowmobile comes to rest
So here we can say that
[tex]v_f = 0[/tex]
[tex]v_i = 3.0 m/s[/tex]
[tex]a = -0.60 m/s^2[/tex]
so now we have
[tex]v_f = v_i + at[/tex]
[tex]0 = 3.0 - (0.60)t[/tex]
[tex]t = 5 s[/tex]
Which of the following energy forms is associated with an object in motion?
potential energy
elastic potential energy
nonmechanical energy
kinetic energy
Which of the following is not a carbohydrate?
A. Cellulose
B. Sugars
C. Starches
D. Cholesterol
The option that is not a carbohydrate is cholestrol, which is the option D.
D. Cholesterol
What is carbohydrate?Carbohydrate are organic compounds that are made of carbon, hydrogen and oxygen atoms, forming polar hydroxyl groups, (-OH). Carbohydrate are an important source of energy in an healthy diet. There are three main types of carbohydrates, namely; sugars, starch, and fibers.
Cholesterol is a waxy, faty chemical substance that is solid and white or light yellow. The chemical formula for cholesterol is C₂₇H₄₆O, hence cholesterol is a lipid, as it has few hydroxyl groups, (-OH)
The other compounds, cellulose, sugars, and starches are carbohydrates
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A train travels at a velocity of +50 m/s. It takes 80 s to slow down to 5 m/s with constant acceleration. What was its acceleration?
Two cars leave an intersection at the same time. One is headed south at a constant speed of 40 miles per hour, the other is headed west at a constant speed of 30 miles per hour (see the figure). Express the distance d between the cars as a function of the time t. (Hint: At t = 0 the cars leave the intersection.)
d(t)= ...?
The distance between the two cars can be expressed as a function of time using the Pythagorean theorem. At t = 0, the cars are 2 km apart, and as time progresses, their distances increase.
Explanation:The distance between the two cars can be expressed as a function of time using the Pythagorean theorem. Let's consider the time t as the independent variable. At t = 0, both cars leave the intersection, so the distance between them is initially given by:
[tex]d(0) = \sqrt{((2 km)^2 + (0 km)^2)} = \sqrt{(4 km^2)} = 2 km[/tex]
As time progresses, the car headed south travels at a speed of 40 mph, which means its distance from the starting point increases by 40t miles. Similarly, the car headed west travels at a speed of 30 mph, increasing its distance from the starting point by 30t miles.
Using the Pythagorean theorem again, we can find the distance d between the two cars as a function of time:
[tex]d(t) = \sqrt{((40t)^2 + (30t)^2)[/tex]
Is it true that a conductor is a material that doesn't allow electrons to flow through it easily?
The sound produced by touching each button on a touch-tone phone is described by y = sin 2πlt + sin 2πht where l and h are the low and high frequencies (cycles per seconD. in the figure shown.
Use a calculator to find the graph of the sound emitted by touching the 4 key in a [0, 0.01, 0.001] by [-2, 2, 1] viewing rectangle.
A 1700kg rhino charges at a speed of 50.0km/h. What is the magnitude of the average force needed to bring the rhino to a stop in 0.50s?
Enter a one- or two-word answer that correctly completes the following statement.
If the constant force is applied for a fixed interval of time , then the _____ of the particle will increase by an amount at.
What does it mean that a form of energy might take more energy to harness than it provides? Are renewable resources always renewable, or can they become non-renewable? Why aren't renewable resources used for everything that we use energy for? Explain.
Energy that costs more to harness than it provides indicates an energy deficit in the transformation and conversion process. Renewable resources can potentially become non-renewable if their consumption surpasses replenishment. The use of renewable resources is not ubiquitous due to cost, geographical, and technological limitations.
Explanation:When a form of energy takes more energy to harness than it provides, it means that the energy input required to extract or convert the energy is greater than the energy output made available for use. This is a significant factor in evaluating the efficiency of energy sources and plays into the concept of energy transformation and conversion.
Renewable resources, by definition, are replenished naturally over short time scales relative to the lifetime of human civilization. However, the ability to renew does not equate to infinite availability if consumption rates surpass replenishing rates. Thus, although inherently renewable, they may de facto become non-renewable.
While renewable energy resources offer numerous benefits, including lower emissions and a reduced dependence on fossil fuels, they are not used for everything due to several factors. These include cost, geographical limitations, and technology constraints. For instance, the initial costs of renewable energy systems can be high, and not all locations receive enough sunlight or wind to be effective. Additionally, technology has not advanced to a level where renewable energy can fully replace non-renewable sources in all uses.
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Harnessing some energy sources can be inefficient if the energy input exceeds the output. Renewable resources can sometimes become non-renewable if consumed faster than they are replenished. Challenges like intermittency, energy density, infrastructure costs, and location dependency limit the use of renewable energy for all purposes.
When it is said that a form of energy might take more energy to harness than it provides, it means the energy input required to extract, process, and deliver the energy is greater than the usable energy output gained. This scenario is inefficient and often not sustainable.
Renewable resources are typically those that can be naturally replenished within a human lifespan. Examples include solar, wind, and biomass energy. However, they can become non-renewable if their rate of consumption exceeds the rate at which they are replenished, or if environmental conditions change drastically, making them less viable.
There are several reasons why renewable energy sources are not used for all energy needs:
Intermittency: Sources like solar and wind are not always available since they depend on weather and time of day.Energy Density: Renewable energy often has a lower energy density compared to fossil fuels, meaning more space and materials are needed to produce the same amount of energy.Infrastructure Costs: Transforming existing infrastructure to adapt to renewable energy can be costly and complex.Location Dependency: Some regions are more suited to certain types of renewable energy than others, making it impractical or inefficient in some areas.While renewable resources offer many advantages, including lower environmental impact and sustainability, technical and logistical challenges must be addressed for them to replace non-renewable sources completely.
What accounts for an increase in the temperature of a gas that is kept at constant volume ?
The correct answer to the question is : By increasing the pressure.
EXPLANATION:
Before answering this question, first we have to understand Gay lussac's law.
As per Gay lussac's law, the pressure of a gas increases or decreases by 1/273 th of its pressure at zero degree celsius; for every 1 degree celsius rise or fall of temperature at constant volume
In a simple way, the pressure is directly proportional to absolute temperature.
Mathematically P ∝ T. [ P = pressure and T = temperature]
Hence, increase in pressure at constant volume may increase its temperature.
A woman exerts a horizontal force of 1 pounds on a box as she pushes it up a ramp that is 2 feet long and inclined at an angle of 30 degrees above the horizontal. Find the work done on the box in ft -lbs.
...?
IF you are skateboarding and push back with one leg, and, as a result the skateboard moves forward. Which law of motion is being described
Which of the following was NOT an outcome of Bacon's rebellion?
A. A more direct focus on the "Indian Problem"
B. A more focused plain to isolate black slaves from white servants
C. More people where in support of armed expantion to nNative Americans' territory
D. A reformed land policy for thse living in Virgina
Answer: D
Explanation: I took the test
A reformed land policy for these living in Virgina is not an outcome of Bacon's rebellion. Hence, option D is correct.
What Bacon's rebellion?A local conflict with the Doeg Indians on the Potomac River served as the catalyst for Bacon's Rebellion, which was waged between 1676 and 1677. The Indians started assaulting the Virginia frontier after being pursued north by Virginia militiamen, who also assaulted the Susquehannock, who were otherwise uninvolved.
The General Assembly was persuaded to approve a scheme by the governor, Sir William Berkeley, that would have isolated the Susquehannock while enlisting Indian allies on Virginia's side. Others saw the Susquehannock War as a chance to launch a general Indian war that would result in the capture of Indian slaves and lands, as well as the expression of widespread anti-Indian feeling.
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A visitor to the observation deck of a skyscraper manages to drop a penny over the edge. As the penny falls faster, the force due to air resistance increases. How does this affect the acceleration of the penny?
a. The acceleration decreases b. The acceleration remains constant and not zero (my answer)
c. The acceleration remains zero d. The acceleration increases.
Final answer:
The acceleration of the penny decreases as the air resistance increases because the net force acting on it reduces until it reaches terminal velocity, where acceleration becomes zero. So the answer to the question is a.
Explanation:
When a penny is dropped from an observation deck of a skyscraper, initially it accelerates due to gravity. As it gains speed, the force of air resistance increases. This air resistance force acts in the opposite direction to the penny's motion, therefore, as the air resistance increases, it will reduce the net force acting on the penny. According to Newton's second law, acceleration results from forces acting on an object divided by its mass. When the upward air resistance force equals the downward gravitational force, the net force becomes zero, and the penny no longer accelerates and reaches terminal velocity.
Therefore, as the air resistance increases while the penny falls, the acceleration of the penny decreases until it hits terminal velocity, where the acceleration will be zero. So the answer to the question is a. The acceleration decreases.
One end of a rope is fastened to a boat and the other end is wound around a windlass located on a dock at a point 4m above the level of the boat. If the boat is drifting away from the dock at the rate of 2m/min, how fast is the rope unwinding at the instant when the length of the rope is 5m? ...?
As you rise upwards in the atmosphere, air pressure
a. increases.
b. decreases.
c. doesn't change.
d. first increases, then decreases.
Answer:
B
Explanation:
As altitude rises, air pressure drops. In other words, if the indicated altitude is high, the air pressure is low. This happens for two reasons. The first reason is gravity. Earth's gravity pulls air as close to the surface as possible. The second reason is density. As altitude increases, the amount of gas molecules in the air decreases—the air becomes less dense than air nearer to sea level. This is what meteorologists and mountaineers mean by "thin air." Thin air exerts less pressure than air at a lower altitude.
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byeeeee
Which tools would be use to find an irregularly shaped object’s mass and volume?
An electric clothes dryer has a resistance of 16ohms. it draws 15 A of a current. what is the voltage, in volts, of the wall outlet that it is plugged into?
What is Darwin's theory of the origin of species?
what is the half life of a radioactive isotope that decreased to one-fourth its original amount in 100 year
Final answer:
The half-life of a radioactive isotope that decreases to one-fourth its original amount in 100 years is 50 years, as this duration represents two half-lives.
Explanation:
The half-life of a radioactive isotope is the time required for half the atoms of a radioactive sample to decay. If a radioactive isotope decreases to one-fourth of its original amount after 100 years, it means that two half-lives have passed (since one half-life leaves us with half the original amount, and another half-life would then leave us with one-fourth). Therefore, the half-life is 50 years. This exemplifies an exponential decay process, typical for radioactive substances.
An artificial satellite circles Earth in a circular orbit at a location where the acceleration due to gravity is 9.00 m/s2. Determine the orbital period of the satellite.
The orbital period of a satellite depends on the radius of its orbit and the acceleration due to gravity. The mass of the satellite does not affect its orbital period. The calculation assumes a circular orbit and a uniform gravitational field.
Explanation:The orbital period of an artificial satellite is the time it takes the satellite to complete one full orbit around the Earth. Using the given acceleration due to gravity (9.00 m/s2) and the formula for the period of an orbit, we can solve for the satellite's orbital period. The formula for the period (T) of an orbit is derived from the formula for the speed of an orbit: V_orbit = 2πr/T. This formula shows that the orbital speed is equal to the circumference of the orbit divided by the orbital period. By substituting this into the centripetal acceleration equation (a = V²/r), it can be rearranged to get the period of orbit.
The mass is cancelled out in these equations, so the mass of the satellite does not affect the orbital period or speed. Therefore, any satellite at the same altitude will have the same orbital period, regardless of its mass.
A crucial point to remember is that this calculation assumes a circular orbit, which simplifies the calculation. In reality, orbits may not always be perfectly circular. This also ignores the effect of the Earth's nonuniform gravitational field and assumes that the only force acting on the satellite is the Earth's gravity.
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A medieval prince trapped in a castle wraps a message around a rock and throws it from the top of the castle with an initial velocity of 12m/s[42 degrees of above the horizontal]. The rock lands just on the far side of the castle's moat, at a level 9.5m below the initial level. Determine the rock's time of flight. ...?
The rock's time of flight is approximately 2.85 seconds. This is determined by solving a quadratic equation derived from the vertical motion kinematic equation. The initial vertical velocity component and gravitational acceleration are key to finding the solution.
To determine the time of flight of the rock, we need to analyze its vertical motion. The initial vertical velocity is given by:
V₀y = 12 m/s * sin(42°)
Solving for V₀y, we get approximately 8.02 m/s.
Using the kinematic equation for vertical motion,y = V₀yt + 0.5 * a * t²
where y is the displacement (−9.5 m, since the rock falls below its original level), a is the acceleration due to gravity (−9.8 m/s²), and V₀y is the initial vertical velocity.
Substituting the values, we get:-9.5 = 8.02t - 4.9t²
Rearranging and solving the quadratic equation:4.9t²- 8.02t - 9.5 = 0
Using the quadratic formula where a = 4.9, b = -8.02, and c = -9.5:[tex]t= \frac{8.02 \pm \\\sqrt{(8.02^{2} - 4(4.9)(-9.5))}} {(2(4.9))}[/tex]
t ≈ 2.85 s
Therefore, the rock's time of flight is approximately 2.85 seconds.
In an experiment performed in a space station, a force of 60n causes an object to have an acceleration equal to 4m/s s .what is the objects mass?
In an experiment performed in a space station, a force of 60 Newtons causes an object to have an acceleration equal to 4 meters/second², then the mass of the object would be 15 kilograms,
What is Newton's second law?Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
F = mass ×acceleration
As given in the problem In an experiment performed in a space station, a force of 60 Newtons causes an object to have an acceleration equal to 4 meters/second²,
mass = force /acceleration
= 60 Newtons/ 4 meters/second²
= 15 kilograms
Thus, the mass of the object would be 15 kilograms
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How is social status directly related to health care?
a. Wealthy Americans receive adequate medical care.
b. Poor Americans receive adequate medical care.
c. No one receives adequate medical care.
d. none of the above
Answer:
the answer is A) Wealthy Americans receive adequate medical care.
Explanation:
I got a 100 on the test on edge!
Social status can have an influence on access to healthcare, but it does not directly determine whether individuals receive adequate medical care. The most appropriate answer is none of the above.
The relationship between social status and healthcare is complex and multifaceted. Factors such as income, education, employment, insurance coverage, and systemic barriers can impact access to healthcare.
While individuals with higher social status or greater wealth may have more resources and options for healthcare, it does not guarantee that they will receive adequate or optimal medical care.
Conversely, individuals with lower social status or limited financial means may face barriers to accessing quality healthcare, but it does not mean they will not receive any medical care at all. The ability to receive adequate medical care is influenced by various individual and systemic factors, and it is not solely determined by social status.
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(a) Suppose that a NASCAR race car is moving to the right with a constant velocity of +93 m/s. What is the average acceleration of the car? (b) Twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed. What is the average acceleration of the car?
Who invented the electric scoreboard
The electric scoreboard was invented by George A. Baird in 1908.
The electric scoreboard invention was a significant advancement in the way sports scores were displayed during games, making it easier for spectators to follow the progress of the game in real-time.