at time , a particle moving in the xy-plane has velocity vector given by . if theparticle is at the point at time , how far is the particle from the origin at time ?
Answers
The particle is approximately 2.304 units away from the origin at time t=1.
To find the distance from the origin at time t=1, we need to integrate the magnitude of the velocity vector over the interval [0, 1]. The magnitude of the velocity vector is given by:
|v(t)| = √(3² + (2 - t²)²)
Integrating this expression over the interval [0, 1], we get:
distance = ∫[0,1] |v(t)| dt
= ∫[0,1] √(3² + (2 - t²)²) dt
Evaluating this integral gives us the distance:
distance ≈ 2.304
Therefore, the particle is approximately 2.304 units away from the origin at time t=1.
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Related Questions
Students run an experiment to determine the rotational inertia of a large spherically shaped object around its center. Through experimental data, the students determine that the mass of the object is distributed radially. They determine that the radius of the object as a function of its mass is given by the equation r=km^2, where k=3m/kg^2. Which of the following is a correct expression for the rotational inertia of the object?
a) m^3
b) 1.8 m^5
c) 3.6 m^5
d) 6 m^5
e) 9 m^5
Answers
The correct expression for the rotational inertia of the spherically shaped object is \(\(\text{c) } 3.6m^5\)\).
In the given scenario, the students determine that the radius of the object is given by \(\(r = km^2\) with \(k = 3\, \text{m/kg}^2\)\). To calculate the rotational inertia of the object, we need to use the formula for rotational inertia of a spherical object, which is given by \(\(I = \frac{2}{5}mr^2\)\), where m is the mass of the object and r is the radius.
Substituting the given expression for r in terms of m, we have \(\(I = \frac{2}{5}m(km^2)^2\)\). Simplifying this equation, we get \(\(I = \frac{2}{5}mk^2m^4\)\).
Substituting the value of \(\(k = 3\, \text{m/kg}^2\)\), we have \(\(I = \frac{2}{5}(3\, \text{m/kg}^2)^2m^5\)\), which further simplifies to \(\(I = \frac{2}{5} \times 9 \, \text{m}^2/\text{kg}^2 \times m^5\)\).
Finally, multiplying the constants, we get \(\(I = 3.6 \, \text{m}^2/\text{kg}^2 \times m^5\)\), which corresponds to option c) \(3.6 \(m^5\)\).
Therefore, the correct expression for the rotational inertia of the object is \(3.6 \(m^5\)\).
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1. The hydrogen balloons which are used to collect weather information from the atmosphere is made of plastic and never completely filled. Thus the pressure inside and outside are same. The balloon is filled with 150 litres of hydrogen, the air temperature is 27°C and the atmospheric pressure is 98 kPa. The balloon rises to a height where it radios back that the pressure is 30kPa and the temperature is - 33°C. i. What is the Kelvin temperature equivalent to 27°C and -33°C? (1 mark) ii. What is the volume of hydrogen at this height? (2 marks)
Answers
Answer:
Answer:- Volume of the balloon is 5.78 L.
Solution:- There are 0.24 moles of hydrogen gas in a balloon at 35 degree C and 1.05 atm pressure. It asks to calculate the volume of the balloon.
This problem is based on ideal gas law equation:
P = 1.05 atm, n = 0.24 mole, T = 35 + 273 = 308 K
R =
V = ?
The equation could be rearranged for the volume as:
Let's plug in the values and do the calculations to get the volume of the balloon:
V = 5.78 L
So, the volume of the gas balloon is 5.78 L.
What is the formula for principle of moments ?
Answers
Answer:
The Principle of Moments states that when a body is balanced, the total clockwise moment about a point equals the total anticlockwise moment about the same point. Moment =force F x perpendicular distance from the pivot d.
Describe how the pendulum concept is used in the pendulum clock.
Answers
The concept of the pendulum is used in pendulum clocks to keep time. The pendulum swings back and forth in a continuous motion at a fixed rate that is determined by the length of the pendulum and the force of gravity.
This motion is used to regulate the movement of the clock's gears, which control the hands on the clock face.The mechanism of a pendulum clock is such that when the pendulum swings in one direction, it pushes a toothed wheel or gear, which in turn moves the other gears, causing the clock's hands to move forward.
When the pendulum swings back in the opposite direction, it again pushes the gear, causing the hands to move further forward. This cycle continues, with each swing of the pendulum causing the hands to move forward by a set amount. The length of the pendulum determines the rate at which the hands move forward, with longer pendulums causing the hands to move more slowly.
In a pendulum clock, the pendulum swings back and forth in a continuous motion at a fixed rate that is determined by the length of the pendulum and the force of gravity. This motion is used to regulate the movement of the clock's gears, which control the hands on the clock face. The pendulum clock is an improvement on the original verge escapement clocks, which were prone to errors due to the uneven force of the mainspring.The pendulum is a simple yet effective device that can keep accurate time. Its motion is governed by the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another.
When the pendulum is pulled to one side and released, it swings back and forth, converting potential energy into kinetic energy and back again. The period of the pendulum, or the time it takes to complete one full swing, is determined by the length of the pendulum and the force of gravity. By adjusting the length of the pendulum, the rate at which it swings can be altered, allowing it to keep accurate time.
To keep the pendulum clock running accurately, it needs to be adjusted periodically. This is done by altering the length of the pendulum, either by moving a weight up or down along the pendulum rod or by turning a screw at the bottom of the pendulum bob. This alters the period of the pendulum, which in turn changes the rate at which the clock runs.
The pendulum clock is a testament to the ingenuity of humanity. By using the simple yet effective concept of the pendulum, clockmakers were able to create accurate timepieces that revolutionized the way we keep time. Today, the pendulum clock may have been superseded by more advanced technologies, but its legacy lives on in the modern clocks and watches we use every day.
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. A 1.00 kg rock is thrown up into the air from ground level at a speed of 8.00 m/s. The ball travels up
to a maximum height, then returns to the ground. Calculate the rock's momentum as it strikes the
ground.
Answers
Answer:
p = -8 kg-m/s
Explanation:
Given that,
Initial speed of the rock, u = 8 m/s
Mass of the rock, m = 1 kg
The ball travels up to a maximum height, then returns to the ground.
We need to find the rock's momentum as it strikes the ground. Let v be the final speed of the rock. Its final speed is as same as initial speed i.e. 8 m/s but in negative direction. So
p = mv
p = 1 kg × (-8 m/s)
= -8 kg-m/s
So, the rock's momentum as it strikes the ground is (-8 kg-m/s).
8) An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 6.4 cm below the starting point. The mass is then pulled so the spring is stretched to a length of 9.6 cm. How fast will the mass be moving when it reaches the equilibrium position?
Answers
Work is accomplished by stretching or compressing a spring. Elastic potential energy is stored in the spring. It is recommended to expand the spring up to 12.8 cm.
What happens to the elastic potential energy that is stored in a spring when work is done to extend it?Elastic potential energy is stored in the spring as a result of the work required to stretch or compress it. A spring's elastic potential energy is equal to one-half the sum of its spring constant times its deformation squared.
When a spring is stretched or compressed from its initial resting position, where is the elastic potential energy stored?We'll talk about elastic potential energy as the second type of potential energy. The energy that is trapped in elastic materials as a result of their stretching or compression is known as elastic potential energy.
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Calculate how many blocks of ice cream each
10 cm long, 10 cm wide and 4 cm thick can
be stored in the compartment of a freezer
measuring 40 cm deep, 40 cm wide and
20 cm high.
Answers
Answer: 80 blocks
Explanation:
Volume of freezer compartment, V1 = (40 X 40 X 20) cm^3
= 32000cm^3
Volume of ice cream block, V2 = (10 X 10 X 4) = 400 cm^3
No of ice cream blocks = V1/V2 = 32000/400 = 80
consider the gate shown in (figure 1). the gate has a width of 1.5 m. rhow = 1.0 mg/m3. suppose that a = 3 m, b = 1 m, c = 1.3 m.
Answers
Given, Width of gate = 1.5m rhow = 1.0 mg/m3 a = 3m, b = 1m, c = 1.3m. We have to find the force required to open the gate, F.To find the force required to open the gate, we use the following formula F = rhow g (a + b/2) c w where w is the width of the gate.w = 1.5mNow, substituting the given values in the above equation, we get F = 1.0 mg/m³ 9.81 m/s² (3 + 1/2) 1.3m 1.5mF = 69.602 NThus, the force required to open the gate is 69.602 N.
About EquationAn equation is a statement in the form of a symbol that states that two things are exactly the same. Equations are written with an equal sign, as follows x + 3 = 5, which states that the value x = 2. 2x + 3 = 5, which states that the value x = 1. The statement above is an equation.
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Una pelota cae con una energía de 1 J y bota al llegar al suelo. Si tras el bote su energía es de 0,998 J, ¿podemos afirmar que la energía se ha destruido?
Answers
Answer:
The energy is not destroyed, the energy has been transformed into another kind of energy, in this case to heat with energy of 0,002 J
Explanation:
One of the fundamental principles of physics states that energy is neither created nor destroyed, it is only transformed.
In this case, when the ball with an energy of 1 J bounces on the ground, it loses an energy equivalent to 1-0.998 J = 0.002 J. This energy of 0.002 J is not destroyed in the process, but is transformed into another type of Energy. In this case, said energy has been converted to heat. A heat equivalent to 0.002 J of energy.
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Translation to spanish
Uno de los principios fundamentales de la física afirma que la enegía no se crea ni se destruye, sólo se transforma.
En este caso, cuando la pelota con una energía de 1 J rebota en el suelo pierde una energía equivalente a 1-0,998 J = 0,002 J. Esta energía de 0,002 J no se destruye en el proceso, sino que se transforma en otro tipo de energía. En este caso dicha energía se ha convertido en calor. Un calor equivalente a 0,002 J de energía.
What force will cause a displacement of 2m, while doing a work of 50J
Answers
Using the work done relation, the value of force is 25 Newton.
When a force is applied along a displacement, "work" in physics refers to the energy that is transported to or away from an object. The following situations include work: relocating a table. a door being pulled and pushed. Walking. raising a stone.
The work W that a force F traveling across a distance x exerts on an object is calculated using the formula W=Fs. If the object is moving in the opposite direction from how we expect it to, we add a minus sign.
Work done is equal to displacement times force.
50J = force × 2
f=50/2
Force = 25 Newton.
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A pendulum swings back and forth. If the mass of the pendulum is 3kg and it starts from a height of 1m.How much kinetic energy does it have at 0.5m?
Answers
From the principle of energy conservation, the kinetic energy of the pendulum at 0.5 m is 14.7 J.
What is a pendulum?A pendulum swings back and forth and can be used to show the change of potential energy to kinetic energy and vice versa.
Given that the kinetic energy is converted to the potential energy; the potential energy at 0.5 m is 3 * 9.8 * 0.5 = 14.7 J.
Following the principle of energy conservation, the kinetic energy of the pendulum at 0.5 m is 14.7 J.
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At what point of thermometric scale does Kelvin scale reading coincide with Fahrenheit scale
Answers
Answer:
At 574.59 Kelvin, the Fahrenheit temperature will be 574.59 °F.
Explanation:
We first need to find a relation between the Kelvin scale and the Fahranheit scale. We'll use the Celsius scale to relate them.
The Kelvin and Celsius scales are related by the formula:
K = °C + 273.15
Solving for °C:
°C = K - 273.15
Besides, the Kelvin and Celsius scales are related by:
°C = 5 ⁄ 9(°F - 32)
Now we find a temperature, say X, where both scales coincide. Equating both formulas:
X - 273.15=5 ⁄ 9(X - 32)
Multiply by 9:
9X - 2,458.35 = 5X - 160
Simplifying:
4X = 2,458.35 - 160=2,298.35
Solving:
X =2,298.35 / 4 = 574.59
At 574.59 Kelvin, the Fahrenheit temperature will be 574.59 °F.
A 1kg skateboard sits at the top of a ramp 20 fr off the ground . How much potential energy does it have ?
Answers
Answer:
196J
Explanation:
Given parameters:
Mass of skateboard = 1kg
Height off the ground = 20m
Unknown:
Potential energy = ?
Solution:
The potential energy is the energy due to the position of a body above the ground.
It is mathematically expressed as:
Potential energy = mass x acceleration due gravity x height
Potential energy = 1 x 9.8 x 20 = 196J
What is Newton's third law motion answer part a and b
Answers
Answer:
hope it helps
Explanation:
Newtons third law is that objects exert equal and opposite forces on each other.
'every action has an equal and opposite reaction'.
Answer:
to every action there's equal and opposite reaction
Which two structures are not found in animal cells?
A) vacioles and ribosomes
B) chloroplasts and ribosomes
C) cell walls and chloroplasts
D) endoplasmic reticulum and cell walls
Answers
Answer:
C
Explanation:
So, lets start off by thinking about what we know is in both cells, and rule out from there.
There are just some basic things you need in eukaryotic cells, those include the following:
Nucleuscell membranemitochondriacytoplasm(dont get confused with chloroplast)Rough and smooth endoplasmic reticulumGolgi vescileGolci apparatusNucleolus(Dont get confused with nulceus)Here are jsut a few examples of what can be found in both plant and animal cells, however we can already rule out all of the following except for:
C
Because remember, c talks about the chlorplast, which is not the chlorplasm found in both plant anf animal cells, its just the chloroplast found in plant cells.
Although I gave the asnwer to you. Here are some things that are in plant cells that arent in animal cells:
Cell wallvaciolescentral vaciolechlroplastplastidsAnimal cells on the other hand, have a few things that plant cells do not as well:
LysomeCentrolsomeHope this helps! ;)
An object moves in the xy plane in above figure and experiences a friction force with constant magnitude 3.00N, always acting in the direction opposite the objects velocity. Calculate the work that you must do to slide the object at constant speed against the friction force as the object moves along (a) the purple path O to A followed by a return purple path to O, (b) the purple path O to C followed by a return blue path to O, and (c) the blue path O to C followed by a return blue path to O. (d) Each of your three answers should be nonzero. What is the significance of this observation?
Answers
An object moves in the xy plane in above figure and experiences a friction force with constant magnitude 3.00N :Along each step of motion, to overcome friction you must push with, (b) the purple path O to C followed by a return blue path to O.
The value of the pressure is the wide variety that represents the energy of the force. for instance: assume the pressure is = 10 N in the direction of the east. 'towards east' shows route whilst '10' is the magnitude of the force. So basically, value is the 'value' or 'amount' of any physical quantity.
A magnitude is represented by means of a nice actual wide variety. put clearly, a value is the size of a few amount. as an example, the significance of an earthquake, measured at the Richter scale, usually varies between 1 and 10 and represents the scale of the earthquake.
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Light is emitted by electrons when they drop from one energy level to a lower level. Which transition results in the emission of light with the greatest energy?
Answers
Answer:
Level 4 to level 2
Explanation:
Electrons in an atom are contained in specific energy levels (1, 2, 3, and so on) having different distances from the nucleus. When light is emitted by electrons from one energy level to a lower level, level 4 to level 2 has the greatest energy.
Hence, the correct option is "Level 4 to level 2".
Which of the following refers to a force of resistance that acts on an object
when the object moves against other matter?
O A. Balanced force
B. Inertia
C. Friction
D. Contact force
Answers
What is the momentum of a 110 kg football player running north at a speed of 4 m/s?
Answers
Answer:
440kgm/s
Explanation:
Momentum= mass × velocity
= 110× 4
= 440kgm/s
. A man and his son run to the top of a hill and stop. The mass of the
man is bigger than the mass of the boy.
a. Write down who has more kinetic energy while they are both
running at the same speed. Explain your answer.
b. Would it be possible for them to have the same amount of kinetic
energy? Explain your answer.
Answers
The person who would have more kinetic energy between the man and the son, would be the man.
The man and the boy can have the same kinetic energy if the son was running faster than his father.
Who has more kinetic energy ?Since the man has a greater mass than his son and they are running at the same speed, the man will have more kinetic energy. This is because the kinetic energy is directly proportional to the mass when the velocity is constant.
For them to have the same kinetic, the son would have to run at a higher speed than the man, so that the product of 0.5 * mass * speed^2 is equal for both of them. In other words, the smaller mass of the son would need to be compensated for by a higher velocity (speed), resulting in equal kinetic energy.
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relative mass of 5O2 (baby 2)
(oxygens relative mass is 16)
Answers
Answer:
The molar mass and molecular weight of 5O2 is 159.994.
Explanation:
Answer:
It is 15.999
Explanation:
can someone pls help me with this?
Answers
NEED HELP A 400 Ω resistor is connected across 200 V. What current will flow?Single choice.
(2 Points)
0.25 A
0.5 A
2.0 A
4.0 A
Answers
Answer: 0.5A
Explanation:
According to Ohm's law, the Voltage(V) when a current flows through a resistor can be calculated by using the formula:
V = IR
where,
V = Voltage = 200V
I = current in amps (A)
R = resistance in ohms (Ω) = 400Ω
Current = Voltage / Resistance
I = V/R
I = 200/400
I = 0.5A
Therefore, the current is 0.5 Ampere
mosquito buzzing has an intensity level of 40dB, calculate the intensity of this buzzing sound
Answers
The intensity of the buzzing sound of the mosquito will be 10⁻⁸ W/m².
What is the intensity of sound?The intensity of a sound is the power of the sound in the unit of Watts divided by the area which the sound covers in square meters. The loudness of a sound is related to the intensity of any given sound to the intensity at the threshold of hearing capacity. Intensity is measured in decibels (dB).
Intensity level = β = 40 dB
The intensity of this mosquito buzzing sound (I).
The formula to find intensity level is
β = 10 log₁₀ (I/I₁₀)
Here, we have to put the values of β and I₀ (10⁻¹² W/m²)
40 = 10 log₁₀ (I/ 10⁻¹²)
I = 10⁻¹²antilog₁₀(4)
I = 10⁻¹²× 10⁴
I = 10⁻⁸ W/m²
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The middle one please it’s due in 40 min
Answers
Answer:
3240000000 Joules
Explanation:
Individual with homenhigh speed internet access and the tchionolgy and literacy skills to use it are called?
Answers
The individuals with home high-speed internet access and the technology and literacy skills to use it are called “digital citizens”.
Digital citizenship refers to the responsible use of technology by people who have access to digital devices such as computers, tablets, and smartphones, as well as high-speed internet access. It involves using technology to connect with others, conduct research, and stay informed on current events.
Digital citizenship includes the skills necessary to navigate the internet and technology safely and securely. An individual who has access to technology and the internet, as well as the ability to use them efficiently and effectively, is referred to as a “digital citizen.”It is crucial for digital citizens to possess knowledge about the internet and the risks associated with it.
They must know how to keep their personal information safe, avoid online scams and frauds, and protect themselves from cyberbullying. They should also understand the importance of digital etiquette, which involves respecting other people's privacy, property, and intellectual property when using digital technology.Digital citizenship also involves using technology for the greater good. Digital citizens use technology to create positive change, promote social justice, and contribute to their communities.
They have the necessary skills to use technology to collaborate with others, communicate with people from diverse backgrounds, and advocate for important causes. Digital citizenship is an essential component of modern-day life. As our world becomes increasingly connected through technology, digital citizens must take responsibility for their online behavior, stay informed, and use technology in a way that benefits themselves and others.
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How much heat energy does it take to boil 2.35 kg of water at 100oC completely to steam at 100oC ? Show Your WORK! This is Laten Heat
Answers
ANSWER
Q = 5303.95 kJ
EXPLANATION
We are looking for the energy needed to evaporate 2.35kg of water. Since the water is already at evaporation temperature, which is 100°C, we just have to use latent heat. Also, we just want the steam to be at 100°C, so we don't need to find the energy to change its temperature.
The energy needed to evaporate water of mass m is:
\(Q=m\cdot L\)L is the latent heat of the material, in this case water. There are two latent heats, one of fusion and one of vaporization. We have to use the second one, which for water is approximately 2257 kJ/kg
Therefore, to boil 2.35 kg of water at 100°C to steam at 100°C we need:
\(Q=2.35kg\cdot2257\frac{kJ}{\operatorname{kg}}=5303.95kJ\)It is a hot summer day at the beach. From your understanding of specific heat capacity, what can you expect to be the difference between the sand and the water?
The water will gain more thermal energy than the sand
The water will heat up faster then the sand
The sand will heat up faster than the water
The sand will lose its energy more slowly than the water
Answers
Answer:
the sand will heat up faster than the water
Explanation:
water has slow heat conduction
and sand had high heat conduction
A hill that has a 15.5% grade is one that rises 15.5 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal
Answers
The angle of incline of the hill above the horizontal is 8.81°.
Since the hill has a 15.5% grade is one that rises 15.5 m vertically for every 100.0 m of distance in the horizontal direction.
Tangent of the angle of the incline of the hill,The tangent of the angle of the incline of the hill, Ф is
tanФ = vertical rise/horizontal distance = grade of hill
Now, the vertical rise = 15.5 m and the horizontal distance = 100.0 m
So, substituting the values of the variables into the equation, we have
tanФ = vertical rise/horizontal run
tanФ = 15.5 m/100.0 m
tanФ = 0.155
Angle of incline of the hill
Taking inverse tan of both sides, we have
Ф = tan⁻¹(0.155)
Ф = 8.81°
So, the angle of incline of the hill above the horizontal is 8.81°.
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which one is more important in science, qualitative or quantitative
Answers
Answer:
quantitative
Explanation: quantitative research is better for scientist.