Answer:
Electric power
Explanation:
Electric power is the rate at which electrical energy is converted to or from another form of energy, such as heat or light. The ratio of power to current is called the voltage.
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Electric power is the rate at which electrical energy is converted into other forms of energy.
What is electrical energy?Electrical energy is the energy derived from electric potential energy or kinetic energy of the charged particles.
Specific examples of electrical energy include:
Alternating current (AC)Direct current (DC)Lightning.Batteries.Capacitors.What is electric power?Electric power is the rate at which work is done or energy is transformed into an electrical circuit. Electric power is measured in watts.
[tex]P = VI[/tex]
Where,
[tex]P[/tex] is the power
[tex]V[/tex] is the potential difference in the circuit.
[tex]I[/tex] is the electric current.
It can also be expressed as
[tex]P = I^{2}R[/tex]
Electric power is the scalar quantity.
Thus, it can be concluded that the rate at which electrical energy is converted into other forms of energy is called electric power.
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Length is fundamental quantity whereas area is derived quantity. Justify
Answer:
A fundamental quantity is something that can only be found by measuring, such as measuring the length of a pencil. We have no other way to find out the length of the pencil other than measuring it in some way.
A derived quantity is something that is calculated and that is not measured directly. Area is found by multiplying two lengths together. We cant find the area other than computing it somehow
A current in a wire increases from 2 A to 6 A. How will the magnetic field 0.01 m from the wire change?
Answer:
It increases to three times its original value. Given the same radius of wire and other constant property. current is directly proportional to the magnetic field.
B1=B2
MoI1/2pir=MoI2/2pir; cancel the same values on both sides
B2/B1=6/2 =3
Explanation:
The magnetic field produced by a current-carrying wire depends on the current and distance from the wire.
Explanation:
The magnetic field produced by a current-carrying wire is given by the formula B = μi / (2πR), where B is the magnetic field strength, μ is the permeability of free space, i is the current in the wire, and R is the distance from the wire.
In this case, the current in the wire increases from 2 A to 6 A. As a result, the magnetic field at a distance of 0.01 m from the wire will also increase. However, the exact value of the magnetic field change can only be determined if the initial distance from the wire is known.
It is important to note that the magnetic field strength is inversely proportional to the distance from the wire, meaning that as the distance increases, the magnetic field strength decreases.
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a man crossed a road 8.25m wide at a speed of 2.01m/s,how long does it take to get man to cross the road
Answer:
t = 4.1 seconds
Explanation:
It is given that,
Width of road which is to be crossed by a man is 8.25 m, it means it is distance to be covered.
Speed of man is 2.01 m/s
We need to find the time taken by the man to cross the road. It is a concept of speed. Speed of a person is given by total distance covered divided by time taken. So,
[tex]v=\dfrac{d}{t}[/tex]
t is time taken
[tex]t=\dfrac{d}{v}\\\\t=\dfrac{8.25}{2.01}\\\\t=4.1\ s[/tex]
So, the time taken by the man to cross the road is 4.1 seconds.
A wire on the left with 9 coils and labeled primary winding. Another coil is near it with 3 coils labeled secondary winding V subscript 2 baseline equals 120. Use the values provided to calculate the initial voltage at the primary winding.
V1 = ? V
Answer:
V1 = 360 V
Explanation:
Applying,
Vs/Vp = Ns/Np................ Equation 1.
Vs = Voltage of the secondary coil, Vp = voltage of the primary coil, Ns = number of coils in the secondary winding, Np = number of coils in the primary winding
make Vp the subject of the equation
Vp = VsNp/Ns............ Equation 2
Given: Vs = 120 V, Np = 9 coils, Ns = 3 coils
Substitute into equation 2
Vp = 120(9)/3
Vp = 360 V.
Hence, V1 = 360 V
Answer:
V1 = 360 V
Explanation:
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A tennis ball has a mass of 0.058 kg and is moving to the right at 40 m/s. What is the momentum
Explanation:
Mass = 0.058Kg
Velocity = 40m/s
Momentum P = ?
P = mv
P = 0.058 × 40
P = 2.32Kgm/s
What are two ways in which you can increase the potential energy of a marble on a ramp?
Answer:
As the marble starts rolling down the roller coaster, the amount of potential energy stored in the marble decreases while its kinetic energy increases. Potential energy is also converted into heat energy due to friction.
Explanation:
As the marble rolls down the hill its potential energy is converted to kinetic energy (its height decreases, but its velocity increases). When the marble goes back up the loop its height increases again and its velocity decreases, changing kinetic energy into potential energy.
The two (2) ways in which the potential energy of a marble on a ramp can be increased are:
I. By placing the marble higher on the ramp.
II. By increasing the mass of the marble.
Potential energy can be defined as a type of energy possessed by an object (body) as a result of its position (height) above the earth.
Mathematically, potential energy (P.E) is calculated by using the following formula:
[tex]P.E = mgh[/tex]
Where:
m is the mass of an object. g is the acceleration due to gravity. h is the height of an object.Hence, potential energy (P.E) is highly dependent on two (2) main factors and these are:
1. Height above the ground.
2. The mass of an object.
In conclusion, the two (2) ways in which the potential energy of a marble on a ramp can be increased are:
Increasing the height of the marble, by placing the marble higher on the ramp.By increasing the mass of the marble such as adding more marbles.Read more: https://brainly.com/question/23153766
A sound wave with a frequency of 510 Hz and a wavelength of 3.5 m is directed toward the bottom of a lake to measure its depth. If the echo of the sound from the bottom is heard 0.39 seconds later, how deep is the lake?
Answer:
Approximately [tex]2.9 \times 10^2 \; \rm m[/tex].
Explanation:
In that [tex]0.39\; \rm s[/tex], this sound wave travelled from the surface of the lake to the bottom, got reflected, and travelled back from the bottom to the surface. The sound wave travelled from the surface to the bottom (without bouncing back) in only [tex]1/2[/tex] that much time. In other words, it took only [tex]\displaystyle ((1/2) \times 0.39)\; \rm s[/tex] for the sound wave to travel from the surface to the bottom of the lake.
The speed [tex]v[/tex] of sound in cold water ([tex]20\; \rm ^\circ C[/tex], [tex]1\; \rm atm[/tex]) is approximately [tex]1.482\times 10^{3} \; \rm m \cdot s^{-1}[/tex].
In [tex]t = ((1/2) \times 0.39) \; \rm s[/tex], that sound wave would have travelled a distance of:
[tex]\begin{aligned}s &= v \cdot t \\ &= 1.482 \times 10^3 \; \rm m \cdot s^{-1} \times \left(\frac{1}{2} \times 0.39 \; \rm s\right) \\ &\approx 2.9 \times 10^2\; \rm m \end{aligned}[/tex].
Therefore, the depth of the lake is approximately [tex]2.9 \times 10^2 \; \rm m[/tex].
A5 cm object is 18.0 cm from a convex lens, which has a focal length of 10.0 cm.
What is the distance of the image from the lens? Round your answer to three significant figures.
cm
What is the height of the image? Round your answer to three significant figures.
cm
Intro
Answer:
answer in picture
Explanation:
An arrow is fired vertically upwards by a bow and reaches an altitude of 134 m. Find the initial speed of the arrow on the ground level.
Answer:
Explanation:
Let the initial speed be u . final speed = 0
v² = u² - 2gh
v is final speed , u is initial speed , h is height .
0 = u² - 2g x 134
u² = 2 x 9.8 x 134
u = 51.25 m /s .
The initial speed of the arrow fired vertically upwards and reaching an altitude of 134m is approximately 51.7 m/s. This was calculated using the second equation of motion and taking into account gravitational acceleration.
Explanation:This physics problem relates to projectile motion and can be solved using the concepts of kinematic equations. The known variables from the question are the final altitude (y = 134m) and the acceleration due to gravity (g = 9.81 m/s^2), which is always acting downward. We're looking for the initial speed (v0) of the arrow when it was released from the ground level.
Due to the arrow being launched upwards and then coming back down, the final velocity would be the negative of its initial velocity. Hence, we can say that v = -v0
According to the second equation of motion, v^2 = v0^2 + 2gy. Replacing known values, we get (-v0)^2 = v0^2 + 2*(-9.81)*134. From which we can solve for v0.
After simplifying the equation, we find that v0 = sqrt(v0^2 - 2*(-9.81)*134), this leads us to find that the initial speed of the arrow was approximately 51.7 m/s.
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I need help with my physics. It’s on waves :(
Answer:
E is the Crest.
What is the main difference between the Schrödinger model and the Bohr atomic model?
A) Schrödinger believed that electrons could only exist in orbits, but Bohr stated that electrons could be found anywhere in the atom.
B) Bohr believed electron orbits were circular, but Schrödinger’s equations represent complex shapes describing the probable locations of electrons.
C) The Bohr model did not explain the emission and absorption spectrum, but the energy levels described by Schrödinger explained this property.
D) Bohr believed that the electrons circle the nucleus because positive particles attract negative particles, while Schrödinger believed that an electron was a wave.
Answer:
the answer is B :Bohr believed electron orbits were circular, but Schrödinger’s equations represent complex shapes describing the probable locations of electrons.
Explanation:
just took the test on edge
The main differences between the Schrödinger and Bohr atomic models are the representation of electron orbits and the explanation of the emission and absorption spectrum.
Explanation:
The main difference between the Schrödinger model and the Bohr atomic model is that Bohr believed electron orbits were circular, while Schrödinger's equations describe complex shapes representing the probable locations of electrons. This means that according to Bohr, electrons could only exist in specific orbits, while Schrödinger's model allows for electrons to be found in a range of locations within an atom.
Another difference is that the Bohr model did not explain the emission and absorption spectrum, whereas the energy levels described by Schrödinger's model successfully explained this property.
Lastly, Bohr believed that electrons circled the nucleus due to the attraction between positive and negative charges, while Schrödinger believed that electrons have wave-like properties.
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Two concave mirrors are kept in a straight line as shown in fig. Mirror A forms 2 times enlarged real image of an object kept in front of it on the same straight line. The focal length of mirror A is given as 10cm.
i. Using sign conventions calculate the object position and image position in the case of mirror A
ii. Mirror B forms a 1/4times diminished real image of the same object. Find the object position, image position and the focal length in this
case.
iii. Draw the ray diagrams in both the cases.
3
Answer:
For mirror A:
Object distance from mirror is 15 cm
Image distance from mirror is 30 cm
For mirror B;
Object distance = 15 cm
Image distance = 3.75 cm
Focal lenght = 3 cm
Explanation:
Detailed explanation and calculation is shown in the images below.
Are quarks and or gluons smaller than photons.
Answer:
V
Explanation:
Photons can be any size that I’d greater than around 6 Planck Lengths. So, technically they take the prize on both ends. We can see since the Higgs has the highest Energy. Therefore it will be smaller than most quarks except the top quark
A truck exerts 2700 N of force on a car that is stuck in the mud, and does not move. How much work has the truck performed?
Answer:
zero
Explanation:
although force was applied as long as there's no movement ,no work has been done
mathematically;work=force×distance
work=2700×0
work=0J
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1) How is chemical energy
transformed into potential
energy?
Answer:
Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction.
Explanation:
A test model for a new experimental gasoline engine does 45 J of work in one cycle for every 76 J of heat it takes in. What is the engines efficiency?
Answer:
The efficiency of the engine is 59.2%.
Explanation:
We have,
Work done by the gasoline engine is 45 J and the for every 76 J of heat it takes in.
It is required to find the efficiency of the engine. Efficiency of the engine is given by the ratio of work done to the heat taken i. Its formula is given by :
[tex]\eta=\dfrac{W}{Q}\\\\\eta=\dfrac{45}{76}\\\\\eta=0.592\\\\\eta=59.2\%[/tex]
So, the efficiency of the engine is 59.2%.
Final answer:
The efficiency of the engine is approximately 59.21%, calculated by dividing the work done by the engine (45 J) by the heat input (76 J) and then multiplying by 100.
Explanation:
The efficiency of a heat engine is the ratio of work output to heat input, expressed as a percentage. To calculate the engine's efficiency, you divide the work done by the engine by the heat energy that was put into the engine, and then multiply by 100 to convert the decimal to a percentage. In the given problem, the engine does 45 J of work and takes in 76 J of heat, which means the efficiency (η) is calculated as:
η = (Work done / Heat input) × 100
η = (45 J / 76 J) × 100
η = (0.59210526315...) × 100 ≈ 59.21%
The engine's efficiency is therefore approximately 59.21%.
¿Por qué si cargas a uno de tus compañeros por cierto tiempo no estás realizando un trabajo mecánico?
Answer:
I will answer this in English, we can translate it to:
Why if you charge a mate by an amount of time you are not doing work?
This happens because work is defined as the displacement done by a force:
W = d*F
where W is work, d is the distance, and F is the force.
This means that the amount of time that you are charging your mate does not affect the mechanical work, the only time that you are doing work is when you are lifting him.
Multiple choice
Which of the following is NOT found in the Milky Way galaxy’s galactic halo?
A. A few lone stars
B. Dark matter
C. Some star clusters
D. The sun
Which of the following is the correct order of the components of the Milky Way galaxy from outermost to innermost
A. Thick Disc, thin disc, extreme disc, galactic halo, black hole
B. Thing disc, extreme disc, thick disc, galactic halo back hole
C. Galactic halo, thick disc, thing disc, extreme disc, black hole
D. Extreme disc, thick disc, thin disc, galactic halo, black hole
Answer:
The correct options are;
D. The Sun
C. Galactic halo, thick disc, thin disc, extreme disc, black hole
Explanation:
1) The Milky Way galaxy consists of a disk, a central bulge and a halo , with the most prominent and visible part of the Milky Way galaxy being the disk
The Sun can be found in the thin disk and not in the Milky Way's galactic halo
2) The structure of the Milky Way galaxy consists of
(1) Galactic halo (2) Spherical component (3) Spiral arms (4) Thick and thin disk (5) Central bulge (extreme disc) (6) Nucleus with black hole
Therefore, the correct order of the components of the Milky Way galaxy from outermost to innermost is as follows
Galactic halo, thick disc, thin disc, extreme disc, black hole.
The Sun is not found in the Milky Way galaxy's galactic halo. The order of components of the Milky Way galaxy from outermost to innermost is: Galactic halo, thick disc, thin disc, extreme disc, black hole.
Explanation:The Milky Way galaxy's galactic halo is a spherical region encompassing the main, disc-shaped structure of the galaxy. It encompasses a few lone stars (Option A), dark matter (Option B), and some star clusters (Option C). However, the Sun (Option D) is not located in the galactic halo; instead, it's positioned within one of the spiral arms of the galaxy's disc. So, the answer is the Sun (Option D) is NOT found in the Milky Way galaxy’s galactic halo.
As for the order of components of the Milky Way galaxy from outermost to innermost: it starts with the galactic halo, followed by the thick disc, thin disc, extreme disc, and finally, at the center, we have the supermassive black hole. Therefore, the correct order is presented in Option C: Galactic halo, thick disc, thin disc, extreme disc, black hole.
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What has more gravity-Earth's moon or the Sun?Why?
Answer:
Even though the sun is much more massive and therefore has stronger overall gravity than the moon, the moon is closer to the earth so that its gravitational gradient is stronger than that of the sun.
Explanation:
Vicente is going to spend the afternoon in his yard. He has the choice to get in the pool, lay on a cotton chaise longue, sit on the porcelain tile bordering the pool, or sit on a plastic chair. The specific heats of these items are:
Water = 4.19 J/g•°C
Cotton = 1.30 J/g•°C
Porcelain = 1.07 J/g•°C
Plastic = 1.67 J/g•°C
Based on the specific heat values given, where is the coolest location for Vicente to be?
pool
cotton chaise lounge
porcelain tile
plastic chair
Answer:
Pool
Explanation:
I just answered it
On the basis of specific heat values, the coolest location for Vicente to be is known as Pool. Thus, the correct option for this question is A.
What is Specific heat?Specific heat may be defined as the quantity of heat that is ultimately required in order to increase the temperature of one gram of a substance by one Celsius degree. The units of specific heat are usually calories or joules per gram per Celsius degree.
According to the question, the specific heat of water is maximum, while the specific heat of porcelain is minimum. This represents that water is the coolest place in the Vicente while porcelain tile is the warmest place in the Vicente.
Therefore, on the basis of specific heat values, the coolest location for Vicente to be is known as Pool. Thus, the correct option for this question is A.
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A tennis ball has a mass of 0.058 kg and is moving to the right at 40 m/s. What is
the momentum of the tennis ball? (p = mv)
2.32
690
1.35
2320
A pinanong ball has a mass of 0 045 ka Approximately how fast must the ping
Answer:
since momentum = mass x velocity
m = 40m/s 0.058kg
m = 2.32
If a force of 3000 N is applied to a large rock, but the rock does not move, how much work is done on the rock?
Answer:
No work was done.
W = 0
Explanation:
Work is said to be done whenever a force of one newton moves a body of one kilogram through a distance of one meter. Meaning the applied force has to move the body from a point of rest through certain distance.
Work = force × distance
So, in the case of this question, we only have the force been applied, but no distance was covered. Hence, no work was done.
W = 3000× 0 meter
W = 0
Based on the solar system, which planet would you expect to have the slowest orbital speed? *
Mercury
Neptune
Jupiter
Earth
Neptune, being the furthest from the Sun, has the slowest orbital speed at approximately 5 kilometers per second, in accordance with Kepler's laws.
Explanation:Based on Kepler's laws of planetary motion, the planet with the slowest orbital speed in our solar system is Neptune. This is because the speed at which a planet orbits the Sun is inversely related to its distance from the Sun. As Neptune is the furthest planet from the Sun with a vast orbital period of 165 Earth-years, it also has the slowest average orbital speed, which is approximately 5 kilometers per second. In contrast, Mercury, with an orbital period of only 88 Earth-days, moves much faster with an average speed of 48 kilometers per second.
If the potential difference across the bulb in a certain flashlight is 3.0 V, What is the potential difference across the combination of batteries used to power it?
Answer:
3.0 V
Explanation:
The voltage across the bulb is the voltage across the batteries, since the batteries are the only source of power for the bulb. So the voltage across the batteries is 3.0 V.
The potential difference should be 3.0 V.
Calculation of the potential difference:In the case when the potential difference for the flashlight is 3.0V so here the batters should be considered as the only source with respect to the power for the bulb. Due to this, the potential difference across the batteries combination that used to power should also be 3.0 V.
Therefore, The potential difference should be 3.0 V.
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In chemical reactions, the products _____.
A. contain fewer atoms than the reactants
B. contain more atoms than the reactants
O c. are found on the left-hand side of the equation for the reaction
D. are found on the right-hand side of the equation for the reaction
In chemical reactions, the products are the substances that are found on the right-hand side of the chemical equation, indicating the outcome of the reaction.
In chemical reactions, the products are the substances that are found at the end of the reaction. The correct answer is D. The reactants, which are the chemical before the reaction starts, are situated on the left side of the chemical equation, represented by a plus sign. An arrow points from the reactants to the products, indicating the direction of the reaction. The products, which are the chemical after the reaction ends, appear on the right-hand side of the equation. For instance, in the combustion of methane, the chemical equation is CH4 + 2O2
ightarrow CO2 + 2H2O, where CH4 and O2 are the reactants and CO2 + 2H2O are the products.
A plane lands at a speed of 38 km/s and comes to rest (0m/s) 36.3 seconds later. What is the acceleration during landing?
20 points!!!!!!!!
Acceleration = (change in speed) / (time for the change)
Change in speed = (speed at the end) - (speed at the beginning)
Change in speed = (0 km/sec) - (38 km/sec) = -38 km/sec
Acceleration = (-38 km/sec) / (36.3 sec) = -1,046.8 m/s²
Now, before we split up our points and go home, let's see what we've actually got here.
-- The plane's landing speed is about 111 times the speed of sound !
-- It rolls to rest 36.3 seconds after it touches down at this speed.
-- In order to do that, it pulls about 107 G's !
It seems to me that during the ground roll, the flight crew's eyeballs fall out, then they get ripped out of their seat belts and crash through the windshield, and the plane continues on with no life forms aboard. Then, maybe 1 second later, the drogue parachute tears off, the tires on the landing gear blow out and get shredded, the remaining fuel sloshes through the walls of the tanks and evaporates catastrophically, the wings fall off and scrape along the ground in a shower of sparks, the cloud of fuel vapor ignites and then erupts in a ball of flame, the people downtown notice it on the horizon and marvel at it, and then any remaining flaming pieces of the plane come to rest in the dense pine forest and the apartment complex 2 miles past the end of the runway.
This is not my business. I only used the numbers you gave me in the question. My math and physics are flawless, I gave you a theoretically bullet-proof answer, and this is a privilege and a pleasure for you and will stand you in good stead. You're welcome.
Cleo stated that light travels through air in straight paths, and when it moves from air to water, light changes direction, speeds up, and bends toward the normal.
Which statement best describes Cleo’s mistake?
Light travels through air and water in angled, scattered paths.
Light does not change direction when it moves from air into water.
Light slows down when it moves from air into water.
Light bends away from the normal when it moves from air into water.
Answer:
Light slows down when it moves from air into water.
Explanation:
It is the property of light that travels faster in a less dense medium.
In a more dense medium, the speed of the light slows down and bends towards the normal.
The air is less dense medium and water is a more dense medium.
When light passes from air to water, the light bends.
This is known as the refraction of light.
Answer:
C is the correct answer on Ed gen uity
The weight of a bicyclist and bicycle together is 51.0kg how much work has been done if the bicyclist slows down the bicycle from a seed of 3.95 m/s to 1.31 m/s
Answer:
The work done is 354.1032 Joules
Explanation:
To answer the question we note that the amount of work done is equivalent to the reduction in the kinetic energy of the bicyclist and bicycle.
Therefore, initial kinetic energy. KE[tex]_i[/tex] of the system is given by the following relation;
[tex]KE_i=\frac{1}{2} mv_{1}^{2}[/tex]
Final kinetic energy [tex]KE_f = \frac{1}{2} mv_{2}^{2}[/tex]
Where:
v₁ = Initial velocity = 3.95 m/s
v₂ = Final velocity = 1.31 m/s
m = Mass of the bicyclist and bicycle = 51.0 kg
Change in kinetic energy ΔKE;
[tex]\Delta KE = KE_f - KE_i[/tex]
[tex]\Delta KE =\frac{1}{2} mv_{2}^{2}-\frac{1}{2} mv_{1}^{2} = \frac{1}{2} m(v_{2}^{2}-v_{1}^{2}) = \frac{1}{2} \times 51 \times (1.31^{2}-3.95^{2}) = -354.1032 \ J[/tex]
Therefore, work done = -ΔKE = 354.1032 Joules.
Need help with Physics. 100 points + Brainliest
1. Two point charges are 10.0 cm apart and have charges of 2.0 µC and –2.0 µC, respectively. What is the magnitude of the electric field at the midpoint between the two charges? (Use G.U.E.S.S.)
Answer:
I wrote down the answer and attached it below.
Explanation:
Hope this Helps!!!!
⬇⬇⬇⬇⬇⬇⬇⬇
Answer:
Every electric charge has a electric field.
The charges in the electric field are affected each other.
As you move away from the electric charge, the intensity of the electric field decreases.
The electric field is a vector quantity.
The electric field of each charge is calculated to find the intensity of the electric field at a point.
The vectorial sum of the vectors are found.
The electric field of the positive charge is directed outward from the charge.
Explanation:
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A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 66 t, at which time the fuel is exhausted and it becomes a freely "falling" body. 15 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -23 ft/s in 5 s. The rocket then "floats" to the ground at that rate.
Determine the position function s and the velocity function v (for all times t).
(x=yt-2)^2(56-tea)^2x10r
Using the given information, we determined the position and velocity functions of the model rocket at different time intervals. The velocity function varies during the rocket's upward acceleration, free fall, and the subsequent parachute slowing. The position function gives the height of the rocket at any time.
Explanation:To determine the position function s(t) and the velocity function v(t), we need to analyze the rocket's motion in different time intervals:
From time t = 0 to t = 3 seconds: The acceleration is given by a(t) = 66t. To find the velocity function, we integrate the acceleration function, v(t) = ∫ 66t dt = 33t2 + C1, where C1 is a constant of integration. We can determine C1 by using the initial condition of the rocket being at rest at t = 0 (initial velocity is 0), which gives us C1 = 0. So, v(t) = 33t2.From time t = 3 to t = 18 seconds: The rocket becomes a freely falling body. This means it is subject to a constant acceleration due to gravity, a(t) = -32 ft/s2. The velocity function can be found by integrating the acceleration, resulting in v(t) = -32t + C2. To determine C2, we use the fact that at t = 3 seconds, the velocity is 0 (since the fuel is exhausted). Plugging in these values, we find C2 = 96. Thus, v(t) = -32t + 96.From time t = 18 to t = 23 seconds: The velocity decreases linearly from -23 ft/s to 0 ft/s in 5 seconds. This means the acceleration is given by a(t) = (-23 - 0) / 5 = -4.6 ft/s2. Integrating the acceleration function, we get v(t) = -4.6t + C3. Using the fact that at t = 23 seconds the velocity is 0, we find C3 = 105.8. Thus, v(t) = -4.6t + 105.8.To find the position function s(t), we integrate the velocity function for each time interval:
From time t = 0 to t = 3 seconds: s(t) = ∫ (33t2) dt = 11t3 + C4. Using the initial condition s(0) = 0, we find C4 = 0. Therefore, s(t) = 11t3.From time t = 3 to t = 18 seconds: s(t) = ∫ (-32t + 96) dt = -16t2 + 96t + C5. Since the rocket is at rest at t = 3 seconds, we have the condition s(3) = 0, which gives us C5 = 1176. Hence, s(t) = -16t2 + 96t + 1176.From time t = 18 to t = 23 seconds: s(t) = ∫ (-4.6t + 105.8) dt = -2.3t2 + 105.8t + C6. Since the rocket starts floating to the ground at t = 18 seconds, we have the condition s(18) = 0, giving us C6 = -685. Thus, s(t) = -2.3t2 + 105.8t - 685.The position function s(t) represents the height of the rocket at any time t, while the velocity function v(t) represents the rate at which the height is changing with respect to time.
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