Let's see
[tex]\\ \rm\Rrightarrow x=Asin(\omega t)\dots(1)[/tex]
Now we know the formula of acceleration
[tex]\\ \rm\Rrightarrow \alpha=-A\omega^2sin(\omega t)[/tex]
[tex]\\ \rm\Rrightarrow \alpha=-Asin(\omega t)\times \omega^2[/tex]
From eq(1)[tex]\\ \rm\Rrightarrow \alpha=-x\omega^2[/tex]
Or
[tex]\\ \rm\Rrightarrow \alpha=-\omega^2x[/tex]
Given that the position x of a particle along X-axis varies with time t by the equation:
[tex]{:\implies \quad \sf x=A\sin (\omega t)}[/tex]
As it defines the position, so x is just displacement here, and we need to find the acceleration first for telling with what if varies, so by definition, the second differential coefficient of displacement is acceleration, so differentiating both sides w.r.t.x of the above equation in accordance with chain rule we have:
[tex]{:\implies \quad \sf \dfrac{dx}{dt}=A\cos (\omega t)\cdot \omega \cdot \dfrac{dt}{dt}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dx}{dt}=A\omega \cos (\omega t)}[/tex]
Differentiating both sides w.r.t.x by chain rule again to get the 2nd order derivative
[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-A\omega \sin (\omega t)\cdot \omega \dfrac{dt}{dt}}[/tex]
[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-A\omega^{2}\sin (\omega t)}[/tex]
Re-write as :
[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-\omega^{2}\{A\sin (\omega t)\}}[/tex]
Can be further written as
[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-x\omega^{2}}[/tex]
This is the Required answer
If they ask you the differential equation for the acceleration of a wave (as the given equation was general equation of a wave), you can simply write:
[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}+x\omega^{2}=0}[/tex]
A 49.0 kg child sits on the top of a slide that is located 1.80 m above the ground. After her descent, the child reaches a velocity of 3.00 m/s at the bottom of the slide. Calculate how efficiently the potential energy is converted to kinetic energy. Round to the nearest tenth.
For the potential energy is converted to kinetic energy is mathematically given as
n=24.44%
What efficiency of the potential energy is converted to kinetic energy?
Generally, the equation for the potential energy is mathematically given as
Ei=mgh
Ei=49.0\*9.81* 1.8
Ei=865.24J
Final total energy
K.E=0.5mv^2
K.E=0.5*49.0* (3.00)^2
K.E=211.5J
In conclusion, efficiency
n=Ef/Ei*100
n=211.5*865.24*100
n=24.44%
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What best describes the relationship between sleep and memory? The quantity of sleep impacts memory, while the quality of sleep does not. The quantity of sleep does not impact memory, while the quality of sleep does. The quantity and quality of sleep have no impact on memory. The quantity and quality of sleep both impact memory.
Answer:
The quantity and quality of sleep both impact memory.
Explanation:
A. A cord passing over an easily turned pulley (one that is both massless and frictionless) has 7kg mass hanging from one end and a 9kg mass hanging from the other end as shown below. G 7.0 kg 9.0 ks This arrangement is known as Atwood's machine. Calculate the (i). acceleration of the masses (ii). tension in the cord. [2.5
Answer:
M g = M a = a (9 - 7) kg with the two masses going in different directions
(7 + 9) kg * g = a * 2 kg 2 kg effective in prducing acceleration
a = 16 / 2 * g = 9.8 m/s^2 / 8 = 1.23 m/s^2
M1 a = T - M1 * g T producing upward acceleration of 1.23 m/s^2
T = 7 (a + g) = 7 * 11 = 77 N
Check:
M2 a = M2 * g - T M2 producing downward acceleration
T = M2 (g - a) = 9 * (9.8 - 1.23) = 77 N
Select the star life cycle that is accurate.
A. Nebula, star of two stellar mass, supernova, black hole
B. Star of three stellar masses, red supergiant, supernova, neutron
star
C. Supernova, star of three stellar masses, black hole, nebula
D. Nebula, white dwarf, red giant, black hole
Answer:
B according to the picture
Explanation:
Star of 3 stellar masses => red supergiant=>supernova=>neutron star
Star of three stellar masses, red supergiant, supernova, neutron star are the star life cycle that is accurate. Therefore, the correct option is option B.
A star's life cycle is as follows: star formation inside a nebula, evolution into a sequence star, sustained nuclear fusion for a long time, exhaustion of fuel at some point, and gravitational core collapse with resulting high pressures and temperatures.
They typically consist of heated plasma held together by a strong gravitational force and are self-luminous. The thermonuclear process between helium and hydrogen that takes place in a star's core causes it to glow brilliantly. Star of three stellar masses, red supergiant, supernova, neutron star are the star life cycle that is accurate.
Therefore, the correct option is option B.
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I
same 7 kg ball.
9. A 10 N force and a 40 N force are acting in opposite direction on the
ball? What is the magnitude of the acceleration of the ball?
Answer:
Here, m=10 kg
The resultant force acting on the body is
F=(98N)2+(6N)2=10N
Let the resultant force F makes an angle θ w.r.t. 8N force.
From figure, tanθ=8N6N=43
The resultant acceleration of the body is
a=mF=10kg10N=1ms−2
The resulatnt acceleration is along the direction of the resulatnt force.
Hence, the resultant acceleration of the body is 1 ms−2 at an angle of tan−1(43) w.r.t. 8N force.

Electromagnetic waves(such as light, gamma rays, microwaves, etc.) exhibit a longitudinal wave form.
True
False
Answer:
False - Electromagnetic waves are transverse waves - they do not need a particular medium for transmission - as sound waves in air (longitudinal waves)
When ocean temperature rises,
a. excess gas is released into the atmosphere.
b. the ocean absorbs and holds carbon dioxide.
c. carbon dioxide is equalized between the ocean and atmosphere. d. no change takes place.
Answer:
see below
Explanation:
Kind of like when yo open a warm soda .....excess gas is released
Which of the following was NOT one of Ghana's chief trading exports?
A. Gold
B. Ivory
C. Horses
Answer:
ivory. ..................
_______is the resistance to motion offered by an object sliding over a surface
friction is the force that resists the sliding or rolling of an object over another.
After a boater runs out of gas a boater considers dropping the motor into the water to create waves describe the resuming motion of the boat and explains why the boaters plan will not help him reach shore ????
The boat will swing back and forth about the same location, never reaching the land. Due to which the boaters plan will not help him reach shore.
Describe boat motion?The ship rocks back and forth as the wind and waves press against it. Similar to swiveling on a chair, yaw spins the ship on an unseen central line.
Waves travelling perpendicular to the ship's motion might create this, changing the ship's heading or direction.
The motion of the motor will be identical to that of water molecules. Because there is a wave on the water surface,The motor will move in lockstep with the water particle.
The particles of the medium only vibrate perpendicular to the wave propagation as the wave travels through the water surface, but they are not moved from their initial position.
As a result, the boat will swing back and forth about the same location, never reaching the land.
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Then, complete the riddle below by finding the matching number and writing the letter.
Newton's Second Law
44k el effe &
forces cause an object to accelerate.
3
10
Acceleration depends on I & I and M a ½ ½.
11 12
13
14 15
16
17
18
19
As the force increases, the
accelera
i on
20
21
29
30 31
increases, too.
Why did the artist paint on cement blocks instead of paper?
"
11
He wanted to create
Answer:
I have no clue I'm just trying to get points
Explanation:
:) sorry
How do you find the range of a data set?
Answer: You take the biggest number and subtract it from the smallest number.
Explanation: Hope this helps.
Answer:
Subtract the minimum data value from the maximum data value to find the data range.
Explanation:
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex]
Q5- Knowing now that your mood might affect your memory, what strategies could you employ to assist your memories and make sure that you forget less information when you are having a good time?
An airplane of mass 270,000 kg that is sitting on a runway has its center of gravity located at 10.0 m in front of the main landing wheels as shown. Find the magnitude of the force exerted by the runway on the nose wheel located 25.0 m from the main landing wheels.
For an airplane of mass 270,000 kg , the magnitude of the force exerted is mathematically given as
N2=1584431.13N
N1=1061568.87N
What is the magnitude of the force exerted by the runway on the nose wheel located 25.0 m from the main landing wheels.?Generally, the equation for the Force balance is mathematically given as
N1+N2=270000*g
Therefore
N2*10=N1*15
N1=10N2/15
N1=0.67N2
Hence
0.67N2+N2=270000*g
N2=1584431.13N
N1=1061568.87N
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A particle has a velocity that is 70 % of the speed of light and weighs 206.8 times the mass of an electron. Find the wavelength of this particle?
For a particle that has a velocity that is 70 % of the speed of light and weighs 206.8 times the mass of an electron, the wavelength of this particle is mathematically given as
W= 739.47
What is the wavelength of this particle?Generally, the equation for the 70 % of the speed of light is mathematically given as
70% of 3x10^8 = 2.1x10^8 m/s
Therefore
206.8*9.11x10^-31 = 1.88x10^-28 kg
In conclusion, The wavelength equation isTThe
wavelength= plancks constant / (mass*velocity)
Where
Plancks constant = 6.62x10^-34 m^2 kg/s
W=6.62x10^-34 / (1.88x10^-28/2.1x10^8)
W= 739.47
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It the mass of the foot is 10kg and it is moving at 5m/s, what is the momentum of the leg?
A sample from a meteorite that landed on Earth has been analyzed, and the result shows that out of every 1,000 nuclei of potassium-40 originally in the meteorite, only 250 are still present, meaning they have not yet decayed. How old is the meteorite (in yr)?
What is the index of refraction of a liquid if the angle of incidence in air is 35 degrees and the angle of refraction is 14 degrees?
A mass of 100kg is acted on by a 400N force acting vertically upward and a 600N force acting at a 45 degrees angle.Calculate the vertical component of the acceleration.The local acceleration of gravity is 9.8 m/s2. A.1.56 B.-1.56 C.-2.43 D.2.43 . E. 3.5
Answer:
A 1.56 see below
Explanation:
I will assume the 45 degree force is upward
vertical component = 600 sin 45 = 424.26 N
added to the other vertical force will total 824.26 N
F = ma
824.26 = 100 * a shows a = 8.24 m/s upward
Now we have to assume the mass is ALSO acted on by gravity and this value is given as 9.8 ( so downward is positive)
9.81 - 8.24 = 1.56 m/s^2
Convert 25 meters per second (m/s) to kilometers per hour (km/hr).
Оа
9.0 x 10^-2 km/hr
Oь
9.0 x 10^-1 km/hr
Ос
9.0 x 10^1 km/hr
Od
9.0 x 10^2 km/hr
Answer:
9 x 10^1 km/hr
Explanation:
25 m/s x 3600 sec / hr x 1km / 1000 m = 90 km/hr
A(n) __________ __________ is made with an electromagnet that is free to spin between two permanent magnets
Answer:
Like a galvanometer, an electric motor contains (a switch, an electromagnet) that is free to rotate between the poles of a permanent, fixed magnet. 9.
PLEASE HELP!! Lab: Electromagnetic Induction
Answer:
I think this is the answer
Explanation:
A sound wave is produced when a medium begins to
Answer:
when a medium begins to vibrate
When you think about and describe the characteristics of a giraffe, what type of model are you using?
Answer:
The giraffe is the tallest of all mammals. It reaches an overall height of 18 ft (5.5 m) or more. The legs and neck are extremely long. The giraffe has a short body, a tufted tail, a short mane, and short skin-covered horns
Which is an example of radiation?
Answer:
A burning candle emits radiation in the form of heat and light. The Sun emits radiation in the form of light, heat, and particles. Uranium-238 decaying into Thorium-234 emits radiation in the form ofalpha particles.
Answer:
the sun
Explanation:
the sun emits radiation
How long it take to change the velocity of a car from 100m/s to 250m/s if it accelerates at 5m/s^2
Answer:
30 seconds
Explanation:
The formula for calculating acceleration is
( final velocity - inital velocity) ÷ time
If we enter the values, it would be (250 - 100) ÷ t = 5m/s^2
Now we need to know 't'
So we rearrange the equation to make t the subject.
(250-100) ÷ 5 = 30s
The atmosphere has mass and produces friction as objects move through it.
true or false
true
Explanation:
It has friction when objects move through it.
what is kinematics ?
explain ~
Kinematics is the branch of physics and a subdivision of classical mechanics concerned with the geometrically possible motion of a body or system of bodies without consideration of the forces involved. :)
Answer:
Kinematics is a branch of mechanics that deals with pure motion, without reference to the masses or forces involved in it.
Explanation:
Ex. X=2t+1 here x is related to t which is time(function of time)
What is the angular acceleration experienced by a uniform solid disc of mass 5-kg and radius 20 cm when a net
torque of 50 N.m is applied? Assume the disc spins about its center.
Answer:
7.07 radians per second
How do landforms and rock layers support the plate tectonic theory