Ernest rutherford was an important early researcher in nuclear physics. In one experiment, he observed that particles with a positive charge deflected when passing through a thin sheet of gold foil. What conclusion did rutherford make in this observation?.

Answers

Answer 1

Answer:

Ernest Rutherford observed that particles with a positive charge deflected when passing through a thin sheet of gold foil, concluding that the atom's positive part is small and dense.

Explanation:

The Ernest Rutherford experiment describes planetary model of an atom. According to the model, an atom has a tiny, compact, positively charged centre called a nucleus, where almost all of the mass is concentrated, while light, negatively charged particles called electrons orbit far around it, much like planets orbit the Sun. In his experiment, the observation that a positive charge is deflected through a thin sheet of gold foil led to the conclusion that the deflection some of the positive charge occurs in a small region of the atom. At the same time, the majority passed through the atom (which was also concluded to be empty space).

To understand more about planetary model of an atom. click, https://brainly.com/question/6546005


Related Questions

Ice is put in a cooler to cool the contents. to speed up the cooling process, the ice can be?

Answers

Crushing increases the ice's surface area. Additionally, cooling from ice happens as a result of convection, which is proportional to area. Thus, breaking up the ice expedites the cooling process.

What is cooling process?

When precise and consistent temperature control inside a process is necessary, this sort of cooling is used. Because they can offer cooling capacity independent of variations in the ambient temperature, heat load, and flow needs of the application, chillers are frequently employed to remove heat from a process.

It's important to properly regulate the heat load in many industrial operations. Different components of the whole application might need to be cooled.

Major locations for cooling include:

Direct product cooling

During the molding process, plastic

milling metal products

To know more about  cooling process, visit;

https://brainly.com/question/4385546

#SPJ4

What is the bulk modulus of oxygen if 39.9 g of oxygen occupies 27.9 l and the speed of sound in the oxygen is 342 m/s?

Answers

Bulk modulus of Oxygen is 1.44×10^5 Pa

Given:

mass of Oxygen = 39.9 g

volume of Oxygen = 27.9 l

speed of sound in oxygen = 342 m/s

To Find:

Bulk modulus of Oxygen

Solution:

The density of oxygen gas is

ρ = 0.0399/0.0279 = 1.43 kg/m^3

From v = √B/ρ we find

B = v^2ρ

B = (317 m/s)^2 x (1.43 kg/m^3)

B = 1.44×10^5 Pa

Hence, Bulk modulus of Oxygen is 1.44×10^5 Pa

Learn more about Bulk modulus here:

https://brainly.com/question/24179667

#SPJ4

F = (-3.4,7.0), where all components are in newtons. what is the magnitude (in newtons) of f?

Answers

The all components of force is F = ( -3.4 i + 7 j ) N  which has magnitude of | F | = 7.78 N.

We need to know about vectors to solve this problem. Force is included in the vector which has magnitude and direction. Force can be written as

F = Fx i + Fy j

where F is force, Fx is the force component on the x-axis, Fy is the force component on the y-axis.

From the question above, we know that

F = (-3.4 , 7.0)

Hence the force can be written as

F = ( -3.4 i + 7 j )N

The magnitude of this force can be determined as

| F | = √(Fx² + Fy²)

| F | = √((-3.4)² + 7²)

| F | = √(11.56 + 49)

| F | = 7.78 N

Find more on force at: https://brainly.com/question/25239010

#SPJ4

positivephysics
A bicyclist, initially at rest, begins pedaling and gaining speed steadily for 7.50s during
which she covers 46.0m.
PREMIUM
What was her final speed?

Answers

The final speed of cyclist is 12.27m/s

The following question can be solved using formulas of Motion on one dimension as the motion is in one dimension

We will use the formula

[tex]v^2-u^2=2aS[/tex]

where v is the final velocity

u is the initial velocity

a is the acceleration of the boat

s is the distance in meters

v^2 = 2 x a x S

       = 2 x 46 x a

v^2=92a

v=[tex]\sqrt{92a}[/tex]

where a is the acceleration

Now using the formula v= u+ at

and putting value of v in the equation

[tex]\sqrt{92a}[/tex]=a x7.5

squaring both sides,

92a=56.25a^2

a=92/56.25=1.64 m/s^2

Now we know that v= 7.5 a=7..5 x 1.64 =12.27m/s

Hence her final speed is 12.27m/s

#SPJ9

explain the statement, the acceleration of free fall due to gravity on the Earth's equator is 9.78m/s²​

Answers

This means that at the equator, the force of gravity on a body causes its velocity to increase at the rate of 9.78m/s per second because of acceleration of free fall cohesion.

What is acceleration of free fall cohesion?

An object that is falling freely is one that is only being affected by gravity. A free-falling object experiences a downward acceleration of 9.8 m/s/s (on Earth). This specific name is given to the numerical value for an object in free fall because it is such an essential value. The acceleration of any object moving solely as a result of gravity is referred to as the "acceleration of gravity."

This means that at the equator, the force of gravity on a body causes its velocity to increase at the rate of 9.78m/s per second because of acceleration of free fall cohesion.

To know more about Force of gravity, visit;

https://brainly.com/question/14662717

#SPJ9

How many 1/4 cups are in a cup

Answers

Answer:

4

Explanation:

if there are 1/4 cups and you need to fill a cup, you need 4
4 x 1/4 = 4/1
4/1 = 1

If a car moving at 76 mi/h takes 400 ft to stop with uniform acceleration after its brakes are applied, how far will it take to stop under the same conditions if its initial velocity is 38 mi/h ?

Answers

80 step it will take to stop under the same conditions if its initial velocity is 38 mi/h.

What is velocity?

Speed is the directional speed of an item moving as a sign of its pace of progress ready as seen from a specific edge of reference and as estimated by a specific norm of time (for example 60 km/h northward). Speed is an essential idea in kinematics, the part of old-style mechanics that portrays the movement of bodies. Velocity is characterized as the pace of progress of position concerning time, which may likewise be alluded to as the immediate speed to stress the qualification from the typical speed. In certain applications the typical speed of an item may be required, in other words, the steady speed that would give a similar resultant relocation as a variable speed.

Learn more about velocity, refer:

https://brainly.com/question/28204681

#SPJ4

make x the subject of 3=x/y-z​

Answers

Answer: y(3+z)=x

Explanation:

Assuming that you meant 3=x/y-z without y-z being in parenthesis

3=x/y-z

3+z=x/y

y(3+z)=x

The seafloor spreads in opposite directions as magma forces its way upward. Geologists have observed matching, reversed magnetic bands on both sides of this ridge. Which is the best explanation of these matching, reversed bands?

Answers

When the Earth's magnetic field reverses, a new stripe, with the new polarity, begins. Such magnetic patterns led to recognition of the occurrence of sea-floor spreading, and they remain some of the strongest evidence for the theory of plate tectonics.

d. the earth experiences cycles of magnetic poles reversing

Why are the magnetic stripes on the sea floor parallel to and symmetrical across the mid-ocean ridge?

The specific magnetism of basalt rock is determined by the Earth's magnetic field when the magma is cooling. Scientists determined that the same process formed the perfectly symmetrical stripes on both side of a mid-ocean ridge. The continual process of seafloor spreading separated the stripes in an orderly pattern

With this information, we can conclude that A polarity reversal means that the magnetic North flips to where we know the South Pole is. At the mid-ocean ridge spreading axis.

Learn more about Earth's magneti in brainly.com/question/7958561

#SPJ1

1. if a wave traveling through air decreases its wavelength by half, what happens to the wave speed and frequency?

Answers

Wave speed decreases by half while the frequency remains constant.

For any wave the equation [tex]v = f \lambda[/tex] holds true.The frequency is a quality of a given wave and it does not change with the external parameters.So, the possibility is for the [tex]v[/tex] and [tex]\lambda[/tex] to change accordingly.Therefore, [tex]v[/tex] and [tex]\lambda[/tex] are directly proportional to each other. Thus when the wavelength decreases by half the speed also decreases by half.This can be shown as follows as well.

                           [tex]\begin{aligned}\\\small v_1 &=\small f.\lambda_1\quad\cdots\cdots(1)\\\\\small v_2 &=\small f.\frac{\lambda_1}{2}\quad\cdots\cdots(2)\\\\(2)\div&(1)\\\\\small v_2 &=\small \frac{v_1}{2}\end{aligned}[/tex]

#SPJ4

Ammonia (nh3) and ammonium ion (nh4 ) can work together as a buffer in living systems. how do they carry out this function?

Answers

When modest amounts of strong acids or bases are added to a weak acid (or base), it forms a solution known as a buffer that resists pH changes.

The ammonium buffer, which is an aqueous solution of NH3 (ammonia) and NH4Cl (ammonium chloride), mixed in equal molar ratios, is a typical buffer, as the question implies. This creates an alkaline buffer with a pH of roughly 9.20, or higher than 7. It's interesting to note that as long as your concentrations stay the same, nothing else matters. Since ammonia is a weak base, the equilibrium will be located far to the left:

NH4+(aq) + OH NH3(aq) + H2O(l) (aq)

Additionally, a soluble salt called ammonium chloride will also be present in solution.

Learn more about buffer here-

https://brainly.com/question/22821585

#SPJ4

Roughly how many times farther is it from the sun to alpha centauri than from the sun to jupiter?

Answers

From the sun to Alpha Centauri than from the sun to Jupiter it is 105 times further. The age of Alpha Centauri is 5.3 billion years older. It also moves in a totally different way. Even though it is close by, it is only passing.

What if Alpha Centauri replaced the position of the Sun?

Alpha Centauri A is around 100,000 miles farther away, 10% more massive, and a little bigger than our Sun. All of the planets' orbits will become more elliptical as a result of the increased mass. The reality that Alpha Centauri A is 50% brighter than our star, placing Earth slightly inside the habitable zone, is much worse for the Earth. Most of Earth's surface is currently uninhabitable due to its average surface temperature of 43 degrees Celsius, according to Universe Sandbox 2. It has been clearly stated to us, though, that a temperature so high would most likely lead to an uncontrollable greenhouse effect by increasing the amount of water vapor in the atmosphere.

To learn more about Alpha Centauri, visit:

https://brainly.com/question/8682738

#SPJ4

By default setting, the word stored at address 0x8004 is: _______________________

Answers

According to the given statement is  At address 0x8004, the default data word is 0xA7908CEE.

Briefing:

Little Endian method with a word size of 4 Bytes is the default on ARM processors.

Data is stored in the memory bytes at a time, and access is done in words.

The data must be stored in 4 cells because word size is equal to 4 bytes.

i.e., the data word is retrieved in parallel from 4 cells.

Little endian states that lower addresses have lower bytes and higher addresses have higher bytes.

At location 0x8004, the default data word is 0xA7908CEE.

What is little endian data?

The sequence in which data is stored in memory is referred to as the "little-endian" convention. According to this convention, the least significant bit (or "littlest" end) is placed at address 0 first, followed by the storage of following bits one at a time.

To know more about Little Endian visit:

https://brainly.com/question/18687598

#SPJ4

A red water balloon is thrown horizontally from the top of a bridge. At the same instant, a yellow water balloon is dropped off the bridge from the same height. Compare the time of fall for the two balloons. Assume air resistance is negligible.

Answers

The time of fall for the two balloons is equal.

Here the conditions given resembles a free fall. Since the air resistance is negligible, gravitational force is the only force acting on both the balloons which means the two balloons are falling in a vacuum. In a vacuum, if two objects of different mass are thrown from the same height, both objects will reach the ground at the same time.

Free fall is nothing but a condition in which an object falls solely under the influence of gravity.

Therefore, the time of fall for both yellow and red water balloons is equal no matter the weight where air resistance is negligible.

To know more about free fall

https://brainly.com/question/13299152

#SPJ4

A ball is thrown vertically upward and then comes back down. During the ball's flight up and down, its velocity and acceleration vectors are?

Answers

During the ball's flight up its velocity and acceleration vectors are in opposite direction and during the ball's flight down its velocity and acceleration vectors are in same direction.

The velocity vector is always in the direction of motion of the object. So, during the ball's flight up its velocity vector is in the upward direction (90°) and during the ball's flight down its velocity vector is in the downward direction (270°).When there is a positive acceleration in the object the acceleration vector is in the direction of motion of the object. When there is a negative acceleration in the object the acceleration vector is in the opposite direction of motion of the object. So, during the ball's flight up its acceleration vector is in the downward direction (270°) and during the ball's flight down its acceleration vector is in the upward direction (90°).

Velocity vector is the rate of change of position of an object. Acceleration vector is the rate of change of velocity of an object.

Therefore, during the ball's flight up its velocity and acceleration vectors are in opposite direction and during the ball's flight down its velocity and acceleration vectors are in same direction.

To know more about velocity and acceleration vectors

https://brainly.com/question/13492374

#SPJ4

How much charge passes through a radio battery of 9 v if the energy expended is 72 j?

Answers

Amount of charge passes through a radio battery

is 8 Coulomb

Given:

voltage of battery = V = 9 v

energy = E = 72 j

To Find:

charge passes through a radio battery = Q

Solution: If voltage, (V) equals Joules per Coulombs (V = J/C) and Amperes (I) equals charge (coulombs) per second (A = Q/t)

It is given by the formula

V = E/Q

Q = E/V = 72 j/9 v

Q = 8 Coulomb

Hence, Amount of charge passes through a radio battery is 8 Coulomb

Learn more about Charge here:

https://brainly.com/question/25922783

#SPJ4

How many water molecules are present in 222.22 ml sample of water ( molar mass =18.01 g/mol)

Answers

7.4304*10²⁴ molecules water molecules are present in 222.22 ml sample of water ( molar mass =18.01 g/mol).

Mass of water = density * volume

=1.00gm/mμ*222.22mol

=222.22gn

No of moles of water = mass/molar mass

no of water molecules/Avogadro  no.=12.34 mol

no of water molecules= 12.34 mol * 6.022*10²³ mol

=74.304*10²³ molecules

=7.4304*10²⁴ molecules

so, 7.4304*10²⁴ molecules are present in 222.22 ml of water sample

7.4304*10²⁴ molecules.

Describe a molecule:

One or more atoms make up molecules. They may have the same atoms (for example, an oxygen molecule has two oxygen atoms) or different atoms if they have more than one (a water molecule has two hydrogen atoms and one oxygen atom). Proteins and DNA are examples of biological compounds that can contain thousands of atoms.

To know more about molecule visit:

https://brainly.com/question/19922822

#SPJ4

Homework Help!! Thsnkyouu

Answers

A. The frisbee will remain in the air for 5.88 s

B. The horizontal distance the frisbee will go is 29.4 m

A. How to determine the time the frisbee will remain in the air

The time the frisbee will spend in the air can be obtained as illustrated below:

Height (h) = 169.2 mAcceleration due to gravity (g) = 9.8 m/s²Time (t) =?

169.2 = ½gt²

169.2 = ½ × 9.8 × t²

169.2 = 4.9 × t²

Divide both side by 4.9

t² = 169.2 / 4.9

Take the square root of both side

t = √(169.2 / 4.9)

Time = 5.88 s

How to determine the horizontal distance

The horizontal distance travelled by the frisbee can be obtained as follow:

Initial velocity (u) = 5 m/sTime (t) = 5.88 sHorizontal distance (s) =?

s = ut

s = 5 × 5.88

Horizontal distance = 29.4 m

Learn more about motion under gravity:

https://brainly.com/question/22719691

#SPJ1

Juanita's fingertip is 1 centimeter wide and her arm is 60 cm long. what angle, in radians, does her fingertip span in her field of view? (use the formula you chose in the previous step.)

Answers

The angle in radians is 1/60.

The corresponding angle should describe a length of 1 cm at a distance of 60 cm from the point of view and that is the sole idea behind this question.To calculate the angle numerically a formula is needed and that should be [tex]s = r \theta[/tex] in which [tex]s[/tex], [tex]r[/tex] & [tex]\theta[/tex] represent the length described at the given distance from the view, that distance just mentioned and the angle the [tex]s[/tex] length subtends at the viewing point.Therefore, simply substituting the available data in that formula yields the required result.

                  [tex]\begin{aligned}\\\small s &= r\theta \\\\\small 1\,cm &=\small 60\,cm\times \theta \\\\\small \theta &=\small \frac{1}{60}\,\text{radians}\end{aligned}[/tex]

Radian is a dimensionless quantity.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             

What is the mass of 2000 ml of an intravenous glucose solution with a density of 1.15 g/ml?

Answers

According to the following formula, the answer is 2,300 g or 2.3 kg:

Volume (m)/Mass (m) Equals Density (p) (V)

Here, the density is 1.15 g/mL, allowing the formula described above to result in a mass of 2.00 L:

p=m/V

1.15 g/mL is equal to x g/2.00 L or x g/2,000 mL.

2,000 mL of x g = 1.15 g of g/mL

2.3 kg or 2,300 g for x g.

How many grams of glucose are in a 1000ml bag of glucose 5?

Its active ingredient is glucose. This medication includes 50 g of glucose per 1000 ml (equivalent to 55 g glucose monohydrate). 50 mg of glucose is present in 1 ml (equivalent to 55 mg glucose monohydrate). A transparent, nearly colourless solution of glucose in water is what is used in glucose intravenous infusion (BP) at 5% weight-to-volume.

Patients who are dehydrated or who have low blood sugar levels get glucose intravenously. Other medications may be diluted with glucose intravenous infusion before being injected into the body. Other diseases and disorders not covered above may also be treated with it.

learn more about  glucose intravenous infusion refer

https://brainly.com/question/7057736

#SPJ4

An urn contains 6 white and 9 black balls. if 4 balls are to be randomly selected without replacement, what is the probability that the first 2 selected are white and the last 2 black?

Answers

When selected randomly without replacement the probability that the first 2 selected are white and the last 2 black is 6/91

Given that,

No. of white balls = 6

No. of black balls = 9

Total number of balls = 15

Probability of 1st ball being white = 6/15

Probability of 2st ball being white = 5/14

(Since one white ball is already picked)

Probability of 3rd ball being black = 9/13

(Since two white balls are already picked)

Probability of 4th ball being black = 8/12

(Since two white balls and one black ball is already picked)

The probability that the first 2 selected are white and the last 2 black

= 6/15 * 5/14 * 9/13 * 8/12

= 6/91

Therefore, when selected randomly without replacement the probability that the first 2 selected are white and the last 2 black is 6/91

To know more about Probability

https://brainly.com/question/11234923

#SPJ4

The equatorial diameter of neptune is 49,528 kilometers. if a kilometer equals 0.6214 mi, what is neptune's diameter in miles?

Answers

Neptune's equatorial diameter is 49,528 kilometers, and as one kilometers is equivalent to 0.6214 miles, its diameter in miles is 30776.69 miles.

What is an equator?

The Northern and Southern hemispheres of the planet are separated by the Equator, a circle of latitude with a radius of 40,075 km (24,901 mi). Halfway between the North and South poles, at 0 degrees latitude, is a fictitious line.

The equator of a spinning spheroid, such as a planet, is the parallel (circle of latitude) where latitude is defined to be 0° in astronomical (3D) spatial geometry. It is a fictitious line that divides the spheroid into its northern and southern hemispheres and runs parallel to its poles. In other words, it is the point where the spheroid intersects with the plane that is perpendicular to its axis of rotation and centered between its poles.

To know more about equator, visit:

https://brainly.com/question/24203207

#SPJ4

Newton did not discover gravity, for early humans discovered that whenever they fell. what newton did discover is that gravity _______.

Answers

What Newton discovered is that  gravity extends throughout the universe.

What is gravity?

The term gravity refers to the force that acts on a body in the universe. It is gravity that makes an object to fall when it is thrown up. The force of gravity acts on every object in the universe and it extends through the universe.

Humans have always known about gravity when they fall from a height and when they threw things up. However, human did not know that gravity extends throughout the universe.

Thus, what Newton discovered is that  gravity extends throughout the universe.

Learn more about gravity:https://brainly.com/question/4014727

#SPJ1

which four items were invented for moving and working in space This is astrology but it didn't give me an option to put that as the subject.

Answers

Answer: Innovations originally designed for space vehicles, including artificial muscle systems, robotic sensors, diamond-joint coatings, and temper foam,

Explanation: make artificial human limbs more functional, durable, comfortable, and life-like.

5) In the picture to the right, a wave source is
moving to the right. Measure the wavelengths
recorded by observer A, on the left, and
observer B, on the right.
Do this by measuring 5 wavelengths and
dividing by 5 to get a precise average.

Answers

Answer: most likely its going to be 5

Explanation:

because you have to keep it the same

Venus is sometimes called:_____.
a. the evening star
b. the early star
c. the late star

Answers

The correct option is (a)the evening star.

Venus is sometimes called the evening star.

Briefing :Venus is the final celestial body to withdraw from view at sunrise and the first to appear in the evening sky. It is referred to as the Morning and the Evening star for this reason. Three factors account for Venus's brightness. First of all, it approaches Earth more closely than any other planet. Second, compared to other inner planets, it is very huge, with a diameter that is nearly twice that of Mars and three times that of Mercury. Thirdly, Venus' dense cloud cover entirely scatters much of the light back into space. Venus really reflects more sunlight than any other planet, at 77%. Venus is so brilliant that it may even be seen during the day.

Learn more about the venus with the help of the given link:

https://brainly.com/question/12134483

#SPJ4

The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s-1)t]. what is the angular frequency for this motion?

Answers

The angular frequency of this motion is 5.46 rad/s.

The oscillation of spring is an example of Simple Harmonic Motion(SHM).

The general equation of an SHM is given by the formula.

X = Acos(wt)

Here A is the amplitude

ω is the angular frequency

T is the time

Comparing the above equation with the given condition,

X = 17.4 cm cos(5.46t)

A = 17.4 cm

ω = 5.46 rad/s

T = 1 s

Hence, the angular frequency of this motion is 5.46 rad/s.

To know more about the "general equation of SHM", refer to the link below:

https://brainly.com/question/14869852?referrer=searchResults

#SPJ4

What is the magnitude of the acceleration of the moon towards the earth? 3.0 m/s2 0.003 m/s2 30 km/s2 3.0 km/s2

Answers

The magnitude of the acceleration of the moon towards the earth is 0.003 [tex]m/s^2[/tex].

The acceleration means the rate with which the velocity of an object changes.

The time the moon takes to complete one revolution, t = 27.3 days = 2358720 s

The distance travelled in circular path, d = [tex]2\pi r[/tex] = [tex]24015\times 10^8[/tex] m

where radius r = [tex]3.844\times 10^8[/tex] m

The formula in circular motion is :

[tex]a=\frac{v^2}{r}[/tex]

[tex]v=\frac{d}{t}[/tex]

So substituting the values:

[tex]a=\frac{(1.024\times 10^3)^2}{3.844\times 10^8}[/tex]

[tex]a\approx 2.8\times 10^{-3} \ m/s^2[/tex]

[tex]\therefore a\approx 0.003 \ m/s^2[/tex]

The value of the acceleration of the moon towards the earth is 0.003 [tex]m/s^2[/tex].

To learn more about Attention here:

https://brainly.in/question/29716405

#SPJ4

In a first order decomposition, the constant is 0.00702 sec-1. what percentage of the compound has decomposed after 7.1 minutes?

Answers

The percentage decomposed in the first order reaction is 69.8%.

What percentage of the compound has decomposed after 7.1 seconds?

Given: rate constant, k = 0.00702 sec -1

time, t = 7.1 s

Since the reaction is first order, we calculate using the formula below:

[A] = [A]₀ [tex]$$e^{(-kt)[/tex]

Where; [A] is the final concentration

[A]₀ is the initial concentration

Finding the ratio of final and initial concentration

[A]/[A]₀ =[tex]$$ e^{(-kt)[/tex]

Substituting the values:

[A]/[A]₀ = [tex]e^{(-0.00702 * 7.1)[/tex]

[A]/[A]₀ = [tex]e^{(-0.0498)[/tex]

[A]/[A]₀ = 0.9514

Percentage decomposed = [A]/[A]₀ [tex]*[/tex] 100%

Percentage decomposed = 0.9514 [tex]*[/tex] 100%

Percentage decomposed = 95.1 %

Therefore, the percentage decomposed in the first-order reaction is 95.1 %.

To learn more about percentage decomposition refer to: brainly.com/question/1563644

#SPJ4

A particle moves in a straight line with the velocity function v ( t ) = sin ( w t ) cos 3 ( w t ) . find its position function x = f ( t ) if f ( 0 ) = 0 .

Answers

Integrating the velocity equation, we will see that the position equation is:

[tex]$f(t)=\frac{\cos ^3(\omega t)-1}{3}[/tex]

How to get the position equation of the particle?

Let the velocity of the particle is:

[tex]$v(t)=\sin (\omega t) * \cos ^2(\omega t)[/tex]

To get the position equation we just need to integrate the above equation:

[tex]$f(t)=\int \sin (\omega t) * \cos ^2(\omega t) d t[/tex]

[tex]$\mathrm{u}=\cos (\omega \mathrm{t})[/tex]

Then:

[tex]$d u=-\sin (\omega t) d t[/tex]

[tex]\Rightarrow d t=-d u / \sin (\omega t)[/tex]

Replacing that in our integral we get:

[tex]$\int \sin (\omega t) * \cos ^2(\omega t) d t$[/tex]

[tex]$-\int \frac{\sin (\omega t) * u^2 d u}{\sin (\omega t)}-\int u^2 d t=-\frac{u^3}{3}+c$[/tex]

Where C is a constant of integration.

Now we remember that [tex]$u=\cos (\omega t)$[/tex]

Then we have:

[tex]$f(t)=\frac{\cos ^3(\omega t)}{3}+C[/tex]

To find the value of C, we use the fact that f(0) = 0.

[tex]$f(t)=\frac{\cos ^3(\omega * 0)}{3}+C=\frac{1}{3}+C=0[/tex]

C = -1 / 3

Then the position function is:

[tex]$f(t)=\frac{\cos ^3(\omega t)-1}{3}[/tex]

Integrating the velocity equation, we will see that the position equation is:

[tex]$f(t)=\frac{\cos ^3(\omega t)-1}{3}[/tex]

To learn more about motion equations, refer to:

brainly.com/question/19365526

#SPJ4

Other Questions
The length of the room is measured to be 5.56 meters. How many centimeters long is the room? Which division problem cannot be solved? Simplify to create an equivalent expression.5(15k)4(2k+5) There is a step missing from the solution below. Which equation is themissing step?P= 100.011x+135= 10- 0.011x+13-5= - 0.011x+13?12 = 0.011x1091 xA. 12 = 0.011x + 13B. 25 = 0.011x + 13C. 25 = 0.011x + 169D. 25 = 0.011x + 13 A c character literal is enclosed in ________ quotation marks, whereas a string literal is enclosed in ________ quotation marks. Exercise 5 Complete each sentence by adding the adverb in the form indicated.Jessica handled the difficult situation ______________ most tactfully . (tactfully, superlative) An email message that is encrypted, uses a digital signature and carries a hash value would address which aspects of the cia triad? Look at this angle:VUWWhat is the vertex? The heights of all the newborns in a certain country are normally distributed,with a mean of 18 inches and a standard deviation of 1 inch. A mother justdelivered a baby that is 16 inches long. Which of the following represents thez-score of the baby's height? (Round your answer to two decimal places.) A middle-aged client presents to the ed reporting severe chest discomfort. which finding is most indicative of a possible myocardial infarction (mi)? A 1.50 gram sample of contain 3.32g of CO2 1.58g of N2O5 and 1.865g of H2O .Its molar mass is 102.2g/mol. Determine the emperical and molecular formulas. HELP!! What is the limit of the function in the graph at x=4 Write an equation of ine that passes through (5,-2) and (7,6) in slope intercept form a car rent is $250 per week plus $0.1 per mile. Find the rental cost for a three week trip of 800 miles. A(n) ________ is a specialized group of consumers with a structured set of relationships involving a particular brand, fellow customers of that brand, and the product in use. 1-assume a color display using 8 bits for each of the primary colors (red, green, blue) per pixel and a frame size of 1024 1024. a. what is the minimum size in bits of the frame buffer to store a frame? A nurse is assessing a client who is experiencing hypoglycemia caused by an insulin reaction. the client is conscious and can follow directions. which intervention is most appropriate at this time? Question 6(Multiple Choice Worth 2 points)(Irrational Numbers MC)Approximate 7+40 to the nearest hundredth. If two events, event a with probability p(a) and event b with probability p(b) are complementary events then __________. Exercise 1 Circle each prepositional phrase in the following sentences. Derek looked behind the garage and saw his roller skates.