A road laid out on an air-hockey table, with a thin coat of ice on the table, and a little bit of oil or lard on top of the ice.
NOTE: The car couldn't actually GO anywhere on this road, because a car needs friction in order to move where you want it to. A car on THIS road would just go wherever the wind blew it.
An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below. (a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second? (b) What is t the first time that the object is at its farthest right? (c) At the time found in part (b), what is the object's velocity? (d) At the time found in part (b), what is the object's acceleration?
Answer:
a.) 10Hz
b.) 0.1 s
c.) 187.4 m/s
d.) -412.6 m/s^2
Explanation:
Given that an object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.
(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?
from the equation given, the angular speed w = 20π
but w = 2πf
where f = frequency.
substitute w for 20π
20π = 2πf
f = 20π/2π
f = 10 Hz
(b) What is t the first time that the object is at its farthest right?
since F = 1/T
T = 1 / f
T = 1/10
T = 0.1 s
Therefore, the t of first time that the object is at its farthest right is 0.1 s
(c) At the time found in part (b), what is the object's velocity?
The velocity can be found by differentiating the equation;
x(t) = 3sin(20πt)
dx/dt = 60πcos(20πt)
where dx/dt = velocity V
V = 60πcos(20π * 0.1)
V = 187.4 m/s
(d) At the time found in part (b), what is the object's acceleration?
to get the acceleration, differentiate equation V = 60πcos(20πt)
dv/dt = -1200πSin(20πt)
dv/dt = acceleration a
a = -1200πSin(20πt)
substitute t into the equation
a = -1200πSin(20π * 0.1)
a = - 412.6 m/s^2
The type of motion the object undergoes that consist of a back-and-forth
movement that is repetitive is a simple harmonic motion.
The correct responses are;
(a) Number of complete back-and-forth motions per second is 10(b) The first time is after 0.025 seconds(c) Velocity is 0(d) Acceleration is approximately -11843.53 m/s²Reasons:
The equation that represents the motion of the object is x(t) = 3·sin(20·π·t)
Where;
t ≥ 0
x(t) is in cm, and t is in seconds.
(a) The general sine function is y = A·sin(B·(t - C) + D
[tex]\mathrm{The \ period \ P} = \dfrac{2 \cdot \pi}{B}[/tex]
By comparison, we have;
B = 20·π
Therefore;
[tex]P = \dfrac{2 \cdot \pi}{20 \cdot \pi} = \dfrac{1}{10} = 0.1[/tex]
The period, which is the time to complete one cycle = 0.1 seconds
The number of cycle completed per second, is the frequency, f
[tex]f = \dfrac{1}{P} = \dfrac{1}{0.1} = 10[/tex]
f = 10 Hz = 10 cycles
The number of cycle completed per second is f = 10 cycles
(b) When the object is at the farthest right, we have;
sin(20·π·t) = Maximum = 1
[tex]\mathbf{sin\left(\dfrac{\pi}{2}\right)} = 1[/tex]
Therefore,
[tex]20 \cdot \pi \cdot t = \dfrac{\pi}{2}[/tex]
[tex]t = \dfrac{\pi}{20 \cdot \pi \cdot 2} = \dfrac{1}{40} = 0.025[/tex]
The first time it is at the farthest right is t = 0.025 seconds after start
(c) [tex]\mathrm{Velocity, \ v, \ is \ given \ by \ v = \dfrac{dx(t)}{dt}}[/tex]
Therefore;
[tex]v = \dfrac{dx(t)}{dt} = \dfrac{dx(t)}{dt} \left(3 \cdot sin \left(20 \cdot \pi \cdot t \right) = 60\cdot \pi \cdot cos \left(20 \cdot \pi \cdot t \right)[/tex]
At t = 0.25 seconds, we have;
[tex]v = \dfrac{dx(t)}{dt} = 60\cdot \pi \cdot cos \left(20 \times \pi \times 0.025 \right) = 0[/tex]
The velocity of the object at the t = 0.025 seconds is v(t) = 0
(d) Acceleration, a, is given by [tex]a = \dfrac{dv(t)}{dt}[/tex]
Therefore;
[tex]a = \dfrac{dv(t)}{dt} = \dfrac{d}{dt} \left( 60\cdot \pi \cdot cos \left(20 \times \pi \times t\right) \right) =-1200 \cdot \pi ^2 \cdot sin(20 \cdot t \cdot \pi)[/tex]
a = -1200·π²·sin(20·t·π)
∴ a = -1200×π²×sin(20×0.025×π)
sin(20×0.025×π) = 1
∴ a = -1200×π²×1 ≈ -11843.53
At the time found in part b the acceleration of the object, a ≈ -11843.53 m/s²
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True or False: The definition of flexibility is the ability of a joint or a series of joints to move through an unrestricted, pain-free range of motion.
Answer:
true
Explanation:
hope I helped a bit
How many significant figures? 53,598 m/sec
Answer:
This has 5 significant figures.
Please help A.S.A.P
If the bands in an igneous rock are dark. What kind of magma was present when it was formed?
Answer:
The magma, molten rock under the surface, and lava (molten rock on the surface) harden into igneous rock. The igneous rock then breaks apart over time through the process of weathering.
Explanation:
Your mother has called you on your cell phone and asked you to pick up a few items at the grocery store on your way home. As you heard your mother state each item, which process transferred this information from your sensory memory to your short-term memory so you could jot each grocery item down?
Answer:
Encoding
Explanation:
Encoding is the initial learning of information. Encoding is the process of passing new information coming from sensory input into our brain so that it can be easily retrievable. In a nutshell, it is the sum total of the processes by which external information such as the list of items your mother asked you to pick up at the grocery store to be converted into a manner that can be stored within the brain and recalled later from long-term memory.
Encoding has to do with transferring external stimuli into short term and subsequently long-term memory.
PLEASE HURRY!
Zach listed the process of how laser beams are produced with crystals.
A flashlamp pumps energy through the crystal.
Atoms in the crystal absorb and then release some of the energy as light.
Light bounces off mirrors and occasionally bounces off crystal atoms, increasing in energy.
Some light escapes the tube through the highly reflective mirror, forming a concentrated beam.
Which best describes Zach’s error?
The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal.
The atoms in the crystal do not release energy; they only absorb energy.
Light does not bounce off mirrors; it focuses through glass lenses.
Light escapes through the partially reflective mirror, not the highly reflective mirror.
The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal best describes Zach’s error.
What is a laser?A device that uses stimulated emission of photons from excited atoms or molecules to produce a strong beam of coherent monochromatic light is a laser.
When electrons in optical materials like glass, crystal, or gas absorb energy from an electrical current or light, a laser is formed.
The increased energy excites the electrons, causing them to migrate from a lower-energy orbit around the nucleus to a higher-energy orbit.
The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal. This statement is incorrect.
Hence Option A best describes Zach’s error.
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Answer:
D. Light escapes through the partially reflective mirror, not the highly reflective mirror.
Explanation:
edge 2022, I took the test.
Joe went to see his Grandmother. He promised his Grandma that he would arrive at her house at 5 pm. He leaves his house at 3:00 and this will allow him 2 hours to get to her house. Joe will need to travel 70 miles to get to her house. How fast will Joe need to drive to make it to Grandma's house on time?
Answer:
35 mph
Explanation:
From the question given above, the following data were obtained:
Time (t) = 2 hours
Distance (d) = 70 miles
Speed (S) =.?
Speed is simply defined as the distance travelled per unit time. Mathematically, it is expressed as:
Speed (S) = Distance (d) / Time (t)
S = d/t
With the above formula, we can calculate how fast (i.e the speed) Joe will need to drive to make it to his Grandma's house on time. This can be obtained as follow:
Time (t) = 2 hours
Distance (d) = 70 miles
Speed (S) =.?
S = d/t
S = 70/2
S = 35 mph
Therefore, Joe will drive at 35 mph in order to get to his Grandma's house on time.
PLEASE HELP
Which object has the least average speed?
A. object A
B. object B
C. object C
D. object D
Answer:
D
Explanation:
I could be wrong, But I'm pretty sure it's D
If the Mass Number is the sum of the protons and neutrons in an atom, what is
the mass number of
Answer:
It's 31
Explanation:
add 15 and 16
To decorate for a party, Simon needs 1,850 centimeters of colorful streamers. If the ratio of meters to centimeters is 1 : 100, how many meters of streamers does he require?
A.
18,500 meters
B.
185 meters
C.
18.5 meters
D.
1.85 meters
A van moves 100 km in 2 1/2 hours.
What is its average speed in kilometers
per hour?
Answer:
0.40km/h
I think.. Hope this helps <3
. Exercises that specifically prepare the muscles for active movements
Answer:
Dynamic Stretching
Explanation:
Dynamic Stretching: Dynamic stretches are controlled movements that prepare your muscles, ligaments and other soft tissues for performance and safety.
define the word prism
Answer:
a polyhedron with two polygonal faces lying in parallel planes and with the other faces parallelograms
a train starting from a distance of velocity of 90 km.h
-1 in 10 minutes assuming that the acceleration is uniform find the acceleration and the distance travelled by the train for attending the velocity
To make this problem solvable and you can get the help you need, I'll complete and arrange some data.
Answer:
Acceleration: [tex]0.0417\ m/s^2[/tex], Distance=7,500 m
Explanation:
Uniform Acceleration Motion
It's a type of motion in which the velocity of an object changes uniformly over time.
Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:
[tex]v_f=v_o+at\qquad\qquad [1][/tex]
The distance traveled by the object is given by:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2][/tex]
Using the equation [1] we can solve for a:
[tex]\displaystyle a=\frac{v_f-v_o}{t}\qquad\qquad [3][/tex]
The problem will be rewritten as follows:
A train starting from rest reaches a velocity of 90 km/h in 10 minutes. Assuming that the acceleration is uniform, find the acceleration and the distance traveled by the train for attending the velocity.
Let's take the relevant data:
vo=0
vf=90 Km/h*1000/3600 = 25 m/s
t = 10 minutes = 10*60 = 600 seconds
Now compute the acceleration by using [3]:
[tex]\displaystyle a=\frac{25-0}{600}=0.0417[/tex]
[tex]a=0.0417\ m/s^2[/tex]
Finally, compute the distance:
[tex]\displaystyle x=0*600+\frac{0.0417\cdot 600^2}{2}[/tex]
[tex]x=7,500\ m[/tex]
Note: We used the value of the acceleration with more precision than shown.
Acceleration: [tex]\mathbf{0.0417\ m/s^2}[/tex], Distance=7,500 m
dimensional formula of energy
Answer:
[M L2 T-2]
Explanation:
hope this is what you're looking for.
Which force is the strongest force inside an atom?
O A. Strong nuclear
B. Electromagnetic
C. Gravity
D. Weak nuclear
Inside an atom, the strongest force is the Strong Nuclear Force, indicated by option A.
The strong nuclear force is one of the fundamental forces of nature and plays a crucial role in binding the subatomic particles, specifically protons and neutrons, within the atomic nucleus.
The strong nuclear force is responsible for overcoming the electrostatic repulsion between positively charged protons in the nucleus. It acts over extremely short distances, on the order of femtometers (10^-15 meters), and is characterized by its strength and short range. It is about 100 times stronger than the electromagnetic force, which is responsible for the interaction between charged particles.
The electromagnetic force, option B, is the second strongest force inside an atom. It is responsible for the interaction between charged particles, such as electrons and protons. The electromagnetic force is involved in holding the electrons in orbit around the nucleus and determines the chemical properties of atoms.
Gravity, option C, is the weakest force among the fundamental forces. While gravity plays a significant role on a macroscopic scale, such as the gravitational attraction between planets or objects on Earth, its influence at the atomic level is negligible compared to the strong nuclear and electromagnetic forces.
The weak nuclear force, option D, is another fundamental force, but it is responsible for processes such as radioactive decay and neutrino interactions. While it is involved in certain nuclear reactions, it is not as strong as the strong nuclear force.
In summary, the strong nuclear force is the strongest force inside an atom, overcoming the electrostatic repulsion between protons and binding the atomic nucleus together. Option A.
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Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/s2.
Explanation:
Acceleration is the rate of change in the speed of an object. If initial and final speed are v₁ and v₂. It changes speed in time t. Its formula is given by :
[tex]a=\dfrac{v_2-v_1}{t}[/tex]
The problem is "A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration? "
In this problem,
v₁ = 2 , v₂ = 10 m/s and t = 3 s
Acceleration of the object,
[tex]a=\dfrac{10-2}{3}\\\\a=2.67\ m/s^2[/tex]
So, the acceleration of the skater is [tex]2.67\ m/s^2[/tex].
In the desert air, sound travels at 358 meters per second (m/s). In the polar air, sound travels at 330 meters per
second (m/s). What can you conclude from this information?
A - The speed of sound is constant.
B - Sound waves travel fastest in a vacuum.
C-The temperature of the air affects the speed of sound.
D-Sound waves travel at the same speed everywhere on Earth.
Please provide your answer below using CER
1. Claim: What is your choice for the correct answer?
2. Evidence: What evidence did you observe from the test-like question that made you decide on your answer?
3. Reasoning: Provide an elaboration on your evidence, possible prior knowledge about your claim.
Answer:
The correct option is;
C. The temperature of the air affects the speed of sound
Explanation:
The information given are;
The speed with which sound travels in the desert air = 358 m/s
The speed with which sound travels in the polar air = 330 m/s
The major difference between the desert air and the polar air is that the temperature of the desert air is hotter than the temperature of the air in the polar region. Therefore the speed of sound is affected by the air temperature.
The equation that gives the relationship of the speed of sound in air, [tex]v_{air}[/tex], to temperature is presented as follows;
[tex]v_{air} = 331\frac{m}{s} \times \sqrt{\dfrac{T_K}{273 K} } = 331\frac{m}{s} \times \sqrt{1 + \dfrac{T_{^{\circ}C}}{273 ^{\circ} C} }[/tex]
Which shows that the speed of sound in air, [tex]v_{air}[/tex], rises as the temperature of the air rises.
Where;
[tex]T_{^{\circ}C}[/tex] = The temperature of the air in degrees Celsius
[tex]T_K[/tex] = The temperature of the air in degrees Kelvin.
How many layers of data can a DVD store?
3
2
4
1
1
Answer:
Capacidad de almacenamiento ofrecida por los DVD
Hay que mencionar que es posible conseguir DVD de una o dos capas. Los DVD que cuentan con una capa son capaces de almacenar aproximadamente 4.7GB de datos, mientras que los de doble capa ofrecen la posibilidad de almacenar alrededor de 8.5GB
Explanation:
Answer:
4 layers
Explanation:
i took the quiz
What creates the solar wind?
Answer:
The solar wind is created by the outward expansion of plasma (a collection of charged particles) from the Sun's corona (outermost atmosphere). This plasma is continually heated to the point that the Sun's gravity can't hold it down. It then travels along the Sun's magnetic field lines that extend radially outward.
PLEASE HELP, WILL MARK BRAINLIEST
What objects exert the attractive force of gravity?
(1 Point)
Anything that has mass
Only planets, moons and stars
Only the Earth and the Sun
Only objects the size of the Earth or larger.
Answer:
Anything that has mass.
Explanation:
Answer: Anything that has mass.
Explanation:
what are some solutions to global temperature changes?
help asap
Answer:
Power your home with renewable energy.
Weatherize, weatherize, weatherize.
Invest in energy-efficient appliances.
Reduce water waste.
Actually eat the food you buy—and make less of it meat.
Explanation:
Please fast ?????????
Answer:
Explanation:
Kinetic
Can someone please help me on this?
Answer:
80
Explanation:
Technological design leads to the development and innovation of new technologies.
Which statements represent innovation? Check all that apply.
Solar panels have increased in efficiency over the past 20 years.
The Sun is the primary source of energy for the solar system.
Alternative energy sources are one method for meeting energy needs.
Amore aerodynamic automobile uses less fuel.
Natural selection ensures that only the fittest survive.
Answer:
Solar panels have increased in efficiency over the past 20 years.
Alternative energy sources are one method for meeting energy needs.
Amore aerodynamic automobile uses less fuel.
Explanation:
Innovation is defined as the introduction or development of something new. Innovation is an idea that is transformed into reality using technology and knowledge.
Statements that represent innovation are:
Using solar panels with more efficiency is an innovation because earlier it was less efficient but using knowledge and technology, they created a solar panel with increased efficiency.The use of alternative energy methods is an innovation because no one has thought before that they can use any other alternative sources of energy. for example: use of water to generate electricity rather than only drinking. Amore aerodynamic automobile uses less fuel. It is innovative to make a device that uses less fuel in comparison to other automobiles and it is an innovation with advantages to natural resources and the environment.Hence, the correct options are: "A, C, and D".
A car moved 40 km north and 90 km south. What is the displacement of the car?
A. 50 km south
B. 50 km north
C. 10 km east
Answer:
A. 50 km south
Explanation:
hope this helps!
The two objects have different masses, the more massive object pulls with a greater force. TRUE OR FALSE?
Answer:
on earth yes, but in space no because there is no gravity
Explanation:
plz can i have some points
The force exerted by an object depends on the mass of the object. Greater mass results in greater force. Hence, the statement is true.
What is force?Force is an external agent acts on a body to change the substance from the state of rest or motion. There are various kinds of force such as nuclear force, magnetic force, frictional force etc.
According to Newton's law of motion force in a moving body is the product of its mass and acceleration. Hence, force is directly proportional to mass and acceleration and an increase in these quantities will increase the force exerted by the body.
Thus, greater force is needed to a move a body with greater mass. If two objects of different masses exerts force each other, the greater force will be exerted by the massive body.
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Forces may cause an object to change ____ if it is unable to move
Answer:
Motion
Acceleration is the change of velocity per unit time, so if there is no force, all we know is that the acceleration is zero. Therefore, the velocity is not changing. If the object was already moving, then it will just keep moving. So, the object can be moving even when there is no force applied to it.
Forces may cause an object to change its state if it is unable to move. The force make the object to move from its state of rest.
What is force?Force is an external agent acting on an object to deform it or to change it state of rest or motion. There are various kinds of forces such as gravitational force, nuclear force, magnetic force, frictional force etc.
Force is a vector quantity thus, it is characterised by its magnitude and direction. According to Newton's first law of motion, an object will continue in its state or motion or rest until an external force acts on it.
Therefore, force changes the state of an object. Force is dependant on the mass of the object. Greater the mass, greater will be the force required to move the object from stationary to stop it from motion.
According to second law of motion, force is the product of mass and acceleration of the object. Hence, force accelerates the body and a change in force changes the acceleration of the object.
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Imagine you are rolling a marble down a wooden ramp for an experiment. What are some variables you can experiment with to increase the velocity of the marble? *
Answer:
Explanation:
In free fall, gravity constantly accelerates an object (increases its velocity)—until it hits terminal velocity. Specifically, gravity increases a falling object's velocity by 9.8 meters per second (m/s) with every passing second. (Whereas velocity is measured in m/s, acceleration is measured in meters per second squared, or m/s2.) How does this constant acceleration affect the distance that an object travels over time? In this experiment you will roll a marble down a ramp to find out.
By adjusting the ramp's height, width, or inclination, you can increase the velocity at which the marble travels down it.
What is ramp?As a tool for lifting or lowering a load, an inclined plane, sometimes referred to as a ramp, is a flat supporting surface that is tilted at an angle from the vertical direction with one end higher than the other.
One of the six traditional simple devices that Renaissance scientists defined is the inclined plane. Heavy weights are transported over vertical obstacles using inclined planes. Examples include a ramp used to load cargo into a truck, a pedestrian ascending a ramp, or an automobile or train ascending an incline.
Less force is needed to push an object up an inclined plane than to lift it straight up, but the distance travelled is greater.
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convert 9.2 km to m
Answer:
9,200 m
Explanation:
1 kilometer = 1000 meters so if there is 9 kilometers then it is 9000 meters, then .2 kilometer is equal to 200 meters. Add the numbers together to get 9,200 meters