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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what is centripetal motion
Answer:
abhi ham logo KO madam ne Padaya nahi hai
Newtons first law of motion states that if the net force on an
object is
then the motion of the
object does not change.
Hurry please!
Answer:
Newton's first law of motion describes inertia. According to this law, a body at rest tends to stay at rest, and a body in motion tends to stay in motion, unless acted on by a net external force.
If the net force on an object is zero, then the motion of the object does not change.
What is Newton's first law of motion?According to Newton's first law, a body will stay at rest or continue to move in a straight line at a constant speed if it is at rest or moving in that direction without being subjected to external forces. In truth, moving uniformly in a straight line and remaining at rest have very little in common, according to classical Newtonian mechanics; they can both be thought of as the same state of motion as seen by different observers, one of whom moves at the same speed as the particle and the other who moves at constant speed in relation to the particle. The law of inertia is a name for this premise.
Newton's first law of motion states that if the net force on an object is then the motion of the object does not change.
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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 has a mass of 1500 kg, how much acceleration is produced by 35000 N of force?
Answer:
The answer is 23.33 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
[tex]a = \frac{f}{m} \\ [/tex]
f is the force
m is the mass
From the question we have
[tex]a = \frac{35000}{1500} = \frac{350}{15} = \frac{70}{3} \\ = 23.33333...[/tex]
We have the final answer as
23.33 m/s²Hope this helps you
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
What defines an element?
energy levels
electrons
neutrons
protons
A ball initially at rest is dropped from a window 24.3 m off the ground. How long does it take for the ball to reach the ground?
Answer:
The ball takes 2.23 seconds to reach the ground
Explanation:
Free Fall Motion
A free-falling object falls under the influence of gravity only. An object being acted upon only by the force of gravity is said to be in a state of free fall. Free-falling objects do not have air resistance.
If an object is dropped from rest in a free-falling motion, it falls with a constant acceleration called the acceleration of gravity, which value is [tex]g = 9.8 m/s^2[/tex].
The distance traveled by a dropped object is:
[tex]\displaystyle y=\frac{gt^2}{2}[/tex]
Knowing the height h from which the object was dropped, we can find the time it takes fo hit the ground:
[tex]\displaystyle t=\sqrt{\frac{2h}{g}}[/tex]
Since y=24.3 m:
[tex]\displaystyle t=\sqrt{\frac{2\cdot 24.3}{9.8}}[/tex]
t=2.23 seconds
The ball takes 2.23 seconds to reach the ground
In the decimal number 40.04672, what number is in the 100th's (hundredths, 1/100s)place?
Answer:
6
Explanation:
because the numbers before the decimal point are whole numbers so that would mean the 4 & 0 before the points the ones and tens place. and anything behind a decimal goes in order as usual ones,tens,hundredths, thousandths, ten thousandths, and so on. so that what makes the 6 be in the hundredths place.
a cup of tea is mixutre true or false
Answer:
this is very true
Explanation:
I I should know I'm a tea fanatic
What is the mass of 5 m3 of cement of 3000 kg/m-3
Answer:
It is 15000 Kgs.
Make a claim about the time interval between lunar phases.
I will mark as BRAINLIEST ✨
just pls help ASAP
due by 4:00pm
plss
Answer:
The Lunar month is the time period for the moon to complete ONE revolution around Earth. SIDEREAL MONTH: 27.3 days SYNODIC MONTH: 29.5 days
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.
Convert 6.6 meters to centimeters
Answer:
660 centimeters
Explanation:
There are 100 cm in 1 m. To convert from m to cm, multiply by 100.
[tex]6.6 \times 100 = 660[/tex]
There are 660 cm in 1 m.
what is measurement ?
Answer: Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of measurement are dependent on the context and discipline. In the natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.
Explanation:
The average speed of a runner in an 800 meter race was 7.0 meters per second. How
long did it take the runner to complete the race?
Answer:
114.29sExplanation:
average speed = distance/Time
Given
speed = 7m/s
distance = 800m
Required
Time taken by the runner to complete the race
From the formula:
Time = Distance/speed
Time = 800/7
Time = 114.29seconds
Hence it took the runner 114.29s to complete the race
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!
Digging downward through a soil profile, how deep would you have to go before you found recognizable fragments of the parent rock for the soil?
Boron (B) has an atomic number of 5 and an atomic mass of 11. Boron has _____.
5 electrons
6 electrons
11 electrons
16 electrons
Answer:
the answer is 5 electrons
Explanation:
because its the same name as the amount of protons
PLEASE HELP !!
In order to describe the velocity of an object, which three pieces of data are needed?
If a bicyclist travels at 15 km/h, how long will it take her to travel 30 km?
17. What is the definition of condensation?
Which of the following is TRUE about velocity?
a if velocity changes the object could be speeding up
b if velocity changes the object could be slowing down
c an object with constant velocity is at rest
d Constant velocity is velocity that doesn’t change
e if velocity changes it is accelerating
Answer:
A
Explanation:
Velocity is when something fast moves
I hope i helped
PLEASE HELP!! ILL MARK BRAINLYEST!!!
A chemical change occurs when a substance changes phase.
True
False
Answer:
False
Explanation:
22. Explain in detail what happens to particles before, during, and after vaporization.
Answer:
Vaporization occurs when a substance changes from a liquid to a gas. The molecules in a liquid are in constant motion while staying relatively close together due to intermolecular forces. When an increase in temperature occurs, the molecules' kinetic energy also increases. If a liquid is heated the particles are given more energy and move faster and faster expanding the liquid. The most energetic particles at the surface escape from the surface of the liquid as a vapor as it gets warmer. Liquids evaporate faster as they heat up and more particles have enough energy to break away.
Mark Me Brainliest If u Found it helpful
Which statement accurately describes a balanced force?
Answer:
a balanced force is when two forces equal each other out and therefor the object is not in motion.
Explanation:
Arrange the following events in the mantle convection process. Use numbers 1-5.
a. Lithospheric plates move in the asthenosphere due to rising and sinking of
materials.
b. The decomposition of radioactive elements causes heat in the interior part of
the Earth
c. Heat slowly rises to the mantle and creates convection current.
d. Heat moves to the core.
e. The process repeats as cycle.
Answer:
1) Lithospheric plates move in the asthenosphere due to rising and sinking of materials is 1.
2) The decomposition of radioactive elements causes heat in the interior part of the Earth
3) Heat slowly rises to the mantle and creates convection current.
4). Heat moves to the core
5) The process repeats as cycle.
Explanation:
Mantle convection is the gradual slow creeping of movement of the Earth's mantle which is as a result of convection current which transfer heat from the interior to the surface of the Earth .
The process of mantle convection start with
1. Lithospheric plates move in the asthenosphere due to rising and sinking of materials is and thus form the two component of the mantle.
2) The decomposition of radioactive elements causes heat in the interior part of the Earth. This is as a result of accretion which is associated to sea flooding
3) Heat slowly rises to the mantle and creates convection current.
4). Heat moves to the core, cools down by conduction and convection of heat.
5) The process repeats as cycle.
The proper and correct arrangement of events in the mantle convection process are:
1. The decomposition of radioactive elements causes heat in the interior part of the Earth.
2. Heat moves to the core
3. Heat slowly rises to the mantle and creates convection current.
4. Lithospheric plates move in the asthenosphere due to rising and sinking of materials.
5. The process repeats as a cycle.
Convection is considered to be one of the most efficient ways through which heat is transported from the interior of planet Earth to the surface.
Mantle convection can be defined as the very slow transfer of heat due to the movement of Earth's solid silicate material within the mantle.
Basically, the slow creeping of the mantle causes a transfer of heat from the white-hot core to the brittle lithosphere during mantle convection.
Furthermore, the heating of the mantle takes place from below (the core) and it rises upward in hotter regions while it sinks down in colder regions.
The proper and correct arrangement of events in the mantle convection process are:
1. Heat is caused in the interior part of the Earth due to the decomposition or decay of radioactive elements.
2. Heat moves to the core.
3. Heat slowly rises from the Earth's core to the mantle and creates convection current in the asthenosphere, which is the plastic layer of the mantle.
4. Lithospheric plates move in the asthenosphere due to rising and sinking of materials.
5. The process is then repeated as a cycle.
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The speed of a river boat is 40 km/h and the rate of flow of the
river is 8 km/h. Moving along the same direction as the flow of
the river, the boat traveled 240 km. Calculate the distance the
boat could travel going against the stream in the same time
period.
Answer:
Distance the boat would travel going upstream = 160 km
Explanation:
First, the time of travel of the boat downstream is calculated.
Time of travel = distance/speed
distance = 240 km;
speed of travel = 40 + 8 = 48 km/h ( since the boat is going downstream)
Time = 240/48 = 5 hours
Therefore, the boat travels for 5 hours.
The distance the boat will travel in 5 hours going upstream is then calculated
distance = speed * time
speed of boat going upstream = 40 - 8 = 32 km/h
Distance = 32 km/h * 5 hours = 160 km
What are three types of electromagnetic waves that can be used to take
photographs??
Answer:
x-rays, Infrared rays, microwaves.
A student is given a 5.4 g mineral sample. She determines that the volume of her sample is 2 cm3. What is the density of her mineral
Answer:
6.7
Explanation:
How much force does a 35 kg child have that is running through the house at an acceleration of 20 m/s^2?
Answer:
The answer is 700 NExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × accelerationFrom the question
mass = 35 kg
acceleration = 20 m/s²
We have
force = 35 × 20
We have the final answer as
700 NHope this helps you
