URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS

The diagram below shows a portion of the electromagnetic spectrum. Which of the following statements correctly explains the relationship between FM and AM radio waves?

The athlete is 7.5 km North east from the starting point.

According to Pythagoras theorem,

[tex]AD^{2}[/tex] = [tex]6^{2}[/tex] + [tex]4.5^{2}[/tex]

AD = √ 36 + 20.25

AD = √ 56.25

AD = 7.5 km

Therefore, the athlete is 7.5 km North east from the starting point.

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You can move in some direction to reduce this distance to zero if the body remains at rest position.

The distance can be zero when the object is present at rest position. Distance is defined as the length covered by a body. The distance can also be defined as the length of the path between two points. Displacement and distance are used for the measurement of length covered by a body. There is one difference between distance and displacement which is displacement can be zero but distance cannot be zero until it stops moving because distance is the total path covered by a body but displacement is the shortest distance between two points. If the distance is not covered by a body means the body can't move then the distance will  be zero.

So we can conclude that You can move in some direction to reduce this distance to zero if the body remains at rest position.

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Answer:

SEE below

Explanation:

MASS is a measure of the amount of matter in an object....it will remain the same ....

  WEIGHT is a measure of gravitational pull on the object and is inversely dependent on the square of the distance between the two bodies...so weight will be LESS than on the surface of the planet

The waves that differ is:

Δx = 2λ

The constructive interference is equal: ΔΦ = 2nπ

If

n = 0, central bright fringe

n = ±1, first maxima on both fringes

n = ±2, second maxima on both fringes

What is maxima?

The maxima and minima of a function, collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.

Therefore,

identify the fringe or fringes that result from the interference of two waves whose path difference differs by exactly 2λ2λ . enter the letter(s) indicating the fringe(s) in alphabetical order. for example, if you think that fringes a and c are both correct,

The waves that differ is:

Δx = 2λ

The equation for phase difference is:

The constructive interference is equal: ΔΦ = 2nπ

If

n = 0, central bright fringe

n = ±1, first maxima on both fringes

n = ±2, second maxima on both fringes

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The ear is composed of outer, middle, and inner parts. The large external auricle gathers sound waves of air and directs them into the external acoustic meatus to the tympanic membrane.

What is tympanic membrane?

A second name for the tympanic membrane is the eardrum. It divides the middle ear from the outer ear. The tympanic membrane vibrates as sound waves enter it. The middle ear's minuscule bones are thus exposed to the vibrations. The vibrating signals are then sent from the middle ear bones to the inner ear.

Therefore,

The ear is composed of outer, middle, and inner parts. The large external auricle gathers sound waves of air and directs them into the external acoustic meatus to the tympanic membrane.

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Answer:According to Coulomb's law, the electrostatic force between two bodies is proportional to the product of their two charges. If the charge on A is increased this product increases in size (it must have been non-zero to begin with, since there was a force between them at first). Thus, the force between them rises.

Explanation:

Elastic potential energy is initially at rest, making it move.

Elastic potential energy is what causes a ball to bounce or rebound because it is transformed into kinetic energy and used to raise the ball back up. However, because some of the ball's energy was transferred to the ground or changed into sound (in the noise it makes upon impact) and heat energy, the ball won't go as high as it did at first (friction with the table). Additionally, even though we cannot see it, the ball alters once it strikes the ground or a table, energy is needed to take shape for a brief period of time.

Because of this, each bounce has a slightly lower height than the one before it. The ball has some kinetic energy when it hits the floor, but some of it is changed, so it loses some of it each time it bounces. After a few bounces, the ball has so little kinetic energy remaining that it stops bouncing.

Thus the correct answer is option A.

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The inertia with the speed of 2.9 m/s has moved a distance of 3.6 kilometers in the west direction and 2.35 kilometers in the north direction.

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Given:

Speed of the speed 2.9 m/s

The direction in which the inertia change is moving = 43° north west.

Time taken to travel the distance = 30 minutes

According to the question that is moving in a Northwest direction with a velocity of 2.9 m per second.

If you want to find the distance it has moved in either North or west direction you will first have to find the total distance that kayak has moved in 30 minutes.

The distance travel by the kayak in 30 minutes = speed of person × time taken

The distance travel by the person in 30 minutes = 2.9 × 30 × 60

The distance travel by the person in 30 minutes = 5220 metre

The distance travel by the person in 30 minutes = 5.22 km

The distance traveled in the west direction can be find using trigonometric ratio.

5.2 × sin 43 = The distance traveled in the west direction

The distance traveled in the west direction = 3.6 kilometers

The distance traveled in the west = cos 43 × 5.2

The distance traveled in the west = 2.35 km

Therefore, The person with the speed of 2.9 m/s has moved a distance of 3.6 kilometers in the west direction and 2.35 kilometers in the north direction.

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Answer: its B hence "An object with a higher mass has more inertia which causes it to speed up less quickly."

Explanation: i took the test

The force constant of the spring that compresses a distance of 2.28 cm when a 4.62 kg object is placed on top is 1.59 kN/m.

When the object comes to equilibrium, we have

∑[tex]F_{y}[/tex] = -k(-[tex]y_{0}[/tex]) -mg =0

The force constant

k=[tex]\frac{mg}{y_{0} }[/tex] = [tex]\frac{4.25*9.80}{2.62*10^{-2} }[/tex]

=1.59 x [tex]10^{3}[/tex] N

=1.59 KN/m

Spring constant is used to identify whether a spring is stable or unstable, and consequently, what system it should be employed in. It is stated mathematically as k = - F/x, which reworks Hooke’s Law.

Where x is the displacement caused by the spring in N/m, F is the force applied over x, and k is the spring constant.

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The energy of a photon with wavelength of 410nm can be calculated as 4.85 x [tex]10^{-19}[/tex] j

Any energy unit, such as the electron volt (eV) or the joule (J), can be used to express photon energy.

P = F × E (equation 3)

P = F × hc/l (equation 4)

P (mW) is equal to 1.989 10-10 F/l (nm)

Ensure that your wavelength is expressed in meters.

The wavelength is multiplied by the speed of light, which is roughly 300,000,000 m/s, to determine the wave’s frequency.

Add the Planck constant, 6.626 1034 J/Hz, to the frequency.

The resulting figure represents a photon’s energy.

[tex]\lambda[/tex] = 410nm = 410 x 10^(-9).

E = hc/[tex]\lambda[/tex]  = [6.626 x 10^(-34) x 3 x 10^(8) ] / 410 x 10^(-19)

= 0.0485 x 10^(-17)

= 4.85 x 10^(-19)

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If a score in a distribution change in numerical value, it will necessarily change mean.

Increasing a current score: Changing one score into another will change the mean since every score in a distribution affects the mean’s value.

The mean will increase in value if an existing score is valued higher. The value of the mean will fall if an existing score’s value is reduced.

There are 50% of observations on either side of the median value, which divides the distribution in half.

The median value is the midpoint in distribution with an odd number of observations.

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The distance has the proton been deflected sideways when it reaches the far edge of the capacitor is [tex]1.08 * 10^-3[/tex].

What is parallel-Plate Capacitor:

When two parallel plates are connected across a battery, the plates are charged and an electric field is established between them, and this setup is known as the parallel plate capacitor.

The parallel plate capacitor formula is given by:

C = k∈0 A / d.

Now,

The electric field is, E = sigma/epsilon_{o} = (1 * 10 ^ - 6)/(8.85 * 10 ^ - 12) = 1.129 * 10 ^ 5 * N / C

The force on the proton is (F) = q E = 1.6 * 10 ^ - 19 * 1.129 * 10 ^ 3 = 1.81 * 10 ^ - 14 * N

So, the acceleration of the proton is,

a = F/m = (1.81 * 10 ^ - 14)/(1.67 * 10 ^ - 27) = 1.084 * 10 ^ 13 * m / (s ^ 2)

Time taken to cross the plate is (t) = d/u = (2.4 * 10 ^ - 2)/(1.7 * 10 ^ 6) = 1.41 * 10 ^ - 8

Therefore, the required distance travelled distance is,

d = u t + 1/2 * a * t ^ 2

d = 0 + 1/2 * 1.084 * 10 ^ 13 * (1.41 * 10 ^ - 4) ^ 2

d = 1.08 * 10 ^ - 3 * m

Therefore, the distance is 1.08*10^-3 m

A parallel-plate capacitor has 2.4 cm × 2.4 cm electrodes with surface charge densities ±1.0×10^−6C/m2. A proton traveling parallel to the electrodes at 1.4×10^6 m/s enters the center of the gap between them.

By what distance has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the field is uniform inside the capacitor and zero outside the capacitor

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Gravity is the sole force acting on the body during free fall motion.

The student should launch the sphere at 2v0 because it will land in the 3 point zone at a distance of around 1.41D.

The variables mentioned are;

the sphere's travel distance when thrown from a height, H = D

The speed at which the ball travels to D = v0

The launcher's current available height is H/2.

The available speeds are v0 and 2v0.

Using the formula H = ut + (1/2)gt2, where u is the beginning velocity of the ball's vertical motion, the following is obtained:

H = (1/2)·g·t²

The time it takes for the ball to fall from H is given by t = ((2H/g)).

The length, D = v0 (2H/g),

we obtain when the height is H/2;

t = √(2·H/(2·g)) = √(H/g)

D1 = v0 (H/g) is the distance traveled.

D = (2) v0 (H/g) = ((2)) D1 follows.

D₁ = D/(√2) ≈ 0.71·D

D₁ ≈ 0.71·D

We have at pace 2v0;

D2 = 2v0 (H/g) = 2 v2 v0 (H/g) = 2 v0 (2H/g) = 2D1 1.41D

D₂ ≈ 1.41·D

The 2 point zone is equal to D/2 x D = 0.5 D x D. (This is where position D1 0.71D is placed)

The 3 Point Zone is located at position D2 1.41D and is defined as D x 3D/2 = D x 1.5D.

The student should launch the sphere at the speed, 2v0, such that the ball will land at D2 1.41D, which is in the 3 Point Zone, given that the ball lands at D2, where it is in the 3 Point Zone.

A group of students prepare for a robotic competition and build a robot that can launch large spheres of mass M in the horizontal direction with variable speed and from a variable vertical position and a fixed horizontal position x=0.

The robot is calibrated by adjusting the speed at which the sphere is launched and the height of the robot’s sphere launcher. Depending on where the spheres land on the ground, students earn points based on the accuracy of the robot. The robot is calibrated so that when the spheres are launched from a vertical position y=H and speed v0, they consistently land on the ground on a target that is at a position x=D. Positive directions for vector quantities are indicated in the figure.

When the students arrive at the competition, it is determined that the height of the sphere launcher can no longer be adjusted due to a mechanical malfunction. Therefore, the spheres must be launched at a vertical position of y=H2. However, the spheres may be launched at speed v0 or 2v0.

Question: In a clear response that may also contain diagrams and/or equations, describe which speed, v0 or 2v0, the students should launch the sphere at so that they earn the maximum number of points in the competition.

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The average speed of the rolled marble across the floor is 1.5 m/s.

We need to know about the average speed to solve this problem. The average speed can be determined as the total distance divided by the total time. It can be written as

v = d / t

where v is average speed, d is distance and t is time.

From the question above, we know that

d = 15 m

t = 10 s

By substituting the given parameter, we can calculate the average speed

v = d / t

v = 15 / 10

v = 1.5 m/s

Hence, the average speed of the marble is 1.5 m/s.

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It is true that as soon as the marble is launched out of the cannon it is in the free fall (provided that there is no air resistance). The value of acceleration will be -10 m/s² for upward motion and 10m/s² for downward motion.

Free fall is defined as the condition in which the body moves under the influence of gravity alone. In the case of free fall, there is no air resistance.

Given in the question is a marble launched out of cannon.

Yes, as soon as the marble is launched out of the cannon it is in the free fall (provided that there is no air resistance) since it moves under the influence of gravity only. As soon as the marble is launched out of the cannon, it will follow a parabolic path. Now, it will move upwards and reach maximum height. From the launch to the maximum height, the marble will move opposite to that of gravity and hence the value of acceleration due to gravity will be g = - 10 m/s². After the maximum height is achieved, it starts to descend towards the ground such that the velocity vector and acceleration vector are both directed in the same direction. In this case, the acceleration due to gravity will be g = 10 m/s²

Therefore, it is true that as soon as the marble is launched out of the cannon it is in the free fall (provided that there is no air resistance). The value of acceleration will be -10 m/s² for upward motion and 10m/s² for downward motion.

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Answer:The sentence can have several meanings depending on how a person chooses to see it. Two sentences explaining the meaning of the pun in this sentence are given below:

The pun used in this sentence is meant to indicate that the person being spoken about has a place in the speaker's heart. Just as a pizza is shared into several portions, so does the person being spoken of, occupy a portion of the speaker's heart.

Pun is the humorous usage of a word in order to make use of its several meanings. Pun is a way of playing with words.

In the sentence above, the speaker plays with the word pizza as a replacement to the word, 'place'. When sharing pizza, it is usually divided into parts.

In the same way, the person who the speaker was referring to occupied a place in his heart.The sentence can have several meanings depending on how a person chooses to see it. Two sentences explaining the meaning of the pun in this sentence are given below:

The pun used in this sentence is meant to indicate that the person being spoken about has a place in the speaker's heart. Just as a pizza is shared into several portions, so does the person being spoken of, occupy a portion of the speaker's heart.

Pun is the humorous usage of a word in order to make use of its several meanings. Pun is a way of playing with words.

In the sentence above, the speaker plays with the word pizza as a replacement to the word, 'place'. When sharing pizza, it is usually divided into parts.

In the same way, the person who the speaker was referring to occupied a place in his heart.The sentence can have several meanings depending on how a person chooses to see it. Two sentences explaining the meaning of the pun in this sentence are given below:

The pun used in this sentence is meant to indicate that the person being spoken about has a place in the speaker's heart. Just as a pizza is shared into several portions, so does the person being spoken of, occupy a portion of the speaker's heart.

Pun is the humorous usage of a word in order to make use of its several meanings. Pun is a way of playing with words.

In the sentence above, the speaker plays with the word pizza as a replacement to the word, 'place'. When sharing pizza, it is usually divided into parts.

In the same way, the person who the speaker was referring to occupied a place in his heart.The sentence can have several meanings depending on how a person chooses to see it. Two sentences explaining the meaning of the pun in this sentence are given below:

The pun used in this sentence is meant to indicate that the person being spoken about has a place in the speaker's heart. Just as a pizza is shared into several portions, so does the person being spoken of, occupy a portion of the speaker's heart.

Pun is the humorous usage of a word in order to make use of its several meanings. Pun is a way of playing with words.

In the sentence above, the speaker plays with the word pizza as a replacement to the word, 'place'. When sharing pizza, it is usually divided into parts.

In the same way, the person who the speaker was referring to occupied a place in his heart.The sentence can have several meanings depending on how a person chooses to see it. Two sentences explaining the meaning of the pun in this sentence are given below:

The pun used in this sentence is meant to indicate that the person being spoken about has a place in the speaker's heart. Just as a pizza is shared into several portions, so does the person being spoken of, occupy a portion of the speaker's heart.

Pun is the humorous usage of a word in order to make use of its several meanings. Pun is a way of playing with words.

In the sentence above, the speaker plays with the word pizza as a replacement to the word, 'place'. When sharing pizza, it is usually divided into parts.

In the same way, the person who the speaker was referring to occupied a place in his heart.The sentence can have several meanings depending on how a person chooses to see it. Two sentences explaining the meaning of the pun in this sentence are given below:

The pun used in this sentence is meant to indicate that the person being spoken about has a place in the speaker's heart. Just as a pizza is shared into several portions, so does the person being spoken of, occupy a porti

In the same way, the person who the speaker was referring to occupied a place in his heart.

Explanation:

The stopping distance s from an initial speed of 80 mi∕hr will be 219 ft.

Here we can define the value t = 0s as the moment when the car starts decelerating.

At this point, the acceleration of the car is given by the equation:

A(t) = -10 ft/s^2

Where the negative sign is because the car is decelerating.

To get the velocity equation of the car, we integrate over time, to get:

V(t) = (-10 ft/s^2)*t + V0

Where V0 is the initial velocity of the car, we know that this is 88 ft/s

Then the velocity equation is:

V(t) = (-10 ft/s^2)*t + 88ft/s

To get the position equation we need to integrate again, this time we get:

P(t) = (1/2)*(-10 ft/s^2)*t^2 + (88ft/s)*t + P0

Where P0 is the initial position of the car, we do not know this, but it does not matter for now.

We want to find the total distance that the car traveled in a 3 seconds interval.

This will be equal to the difference in the position at t = 3s and the position at t = 0s

distance = P(3s) - P(0s)

= ( (1/2)*(-10 ft/s^2)*(3s)^2+ (88ft/s)*3s + P0) - ( (1/2)*(-10 ft/s^2)*(0s)^2 + (88ft/s)*0s + P0)

=  ( (1/2)*(-10 ft/s^2)*9s^2+ (88ft/s)*3s + P0) - ( P0)

=  (1/2)*(-10 ft/s^2)*9s^2+ (88ft/s)*3s = 219ft

The car advanced a distance of 219 ft in the 3 seconds interval.

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The radius of Earth to have the same mass density as matter in a nucleus is 1.80 x 10^3 m.

The density of a body is given by the following expression;

Density = Mass/Volume

Let the radius of Earth be r.

As the earth is a sphere, hence its volume will be 4/3 x π x r^3

So, the equation becomes

Density = Mass/(4/3 x π x r^3)

The mass of the earth is given as 5.98 x 10^24 kg and the density of the nucleus is given to be 2.4 x 10^14 m.

2.4 x 10^14 = 5.98 x 10^24/ (4/3 x 3.14 x r^3)

On Solving the above equation, the radius r comes out to be

r = 1.80 x 10^3 m.

Hence, The radius of Earth to have the same mass density as matter in a nucleus is 1.80 x 10^3 m.

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From the total plate count assay, the  colony forming units/ml (CFU/ml) of the original sample is 2.1 * 10⁸ CFU/mL.

The the Colony Forming Units/ml (CFU/ml) of a given sample of of cultured bacteria is a measure of the number of colonies formed per given mL f the final diluted sample of the cultured bacteria.

The formula for calculating the Colony Forming Units/ml (CFU/ml) of a given cultured bacteria sample is given as follows:

Where:

FDF is the final dilution factor

The final dilution factor is the product of all the dilution factors from the original sample to the countable plate.

From the dat provided:

FDF = 1 * 10⁻⁶

number of colony forming units on the countable plate = 210

The colony forming units/ml (CFU/ml) of the original sample = 210 * 1/1 * 10⁻⁶

The colony forming units/ml (CFU/ml) of the original sample = 2.1 * 10⁸ CFU/mL

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Answer:

In general, a falling barometer indicates the approach of a storm. If the mercury is over 30.20 inches but falling quickly, warmer, cloudier weather is coming. If the mercury continues to fall, the weather will worsen. When the mercury level is between 30.20 and 29.80 inches and dropping rapidly, expect precipitation

Answer:

When cold air encounters warm air, the warm air rises over the cold air and makes surface air pressure drop. As a result, a low-pressure system forms, and winds begin to blow. This is how storms form in response to changes in air temperature.

Explanation:

To a stationary observer, a man jogs east at 6 m/s and a woman jogs west at 2 m/s. From the man's frame of reference, the woman's velocity is 4 m/s.

Velocity is a term that defines that how much a particle covered the distance in a particular time. Velocity is a vector quantity. It can be measured in m/s or cm/s.

To calculate the velocity we are using the formula, Δv= v₁-v₂

Here we are given,

v₁= According to a stationary observer, velocity of a man=6 m/s East.

v₂=According to a stationary observer, velocity of a woman= 2 m/s West.

We have to calculate the woman's velocity, from the man's frame of reference=  Δv

Now we put the values in the above equation, we get

Δv= v₁-v₂

Or, Δv= 6-2

Or, Δv=4m/s.

According to the calculation we can say that, From the man's frame of reference, the woman's velocity is 4 m/s.

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The shot was released at a height of 2.20 m, and he is 1.80 m tall t ac=2.66s is long is he have to get out of the way.

What is velocity?

When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.

Therefore,

a very strong, but inept, shot putter puts the shot straight up vertically with an initial velocity of 11.0 m/s. how long does he have to get out of the way if the shot was released at a height of 2.20 m, and he is 1.80 m tall?

t AC=2.66s

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The  best represent the size of visible light will be C. Protozoa

The electromagnetic spectrum, gives the overall distribution of electromagnetic radiation by the  frequency or wavelength. All EM waves travel at the speed of light in a vacuum, but over a wide range of frequencies, wavelengths, and photon energies.

Visible light wavelengths cover the range of approximately 0.4 to 0.7 μm. electromagnetic spectrum that the human eye can see is the Visible light. Visible light is a form of electromagnetic (EM) radiation, along with radio waves, infrared, ultraviolet, X-rays, and microwaves. the wavelengths that are visible to most human eyes is generally known as Visible light

the best represent the size of visible light is Protozoa, According to the diagram of the electromagnetic spectrum shown,

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The exact form of this dependence of period is given as T = 2π√(L/g).

The time period of a simple pendulum is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”.

The equation for the period of pendulum oscillation is determined as;

T = 2π√(L/g)

where;

Thus, the exact form of this dependence of period is given as T = 2π√(L/g).

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Answer:c

Explanation:

Answer: twice as much

Explanation:

you're welcome!

Option A) Since the p-value is greater than 0.05, we have no evidence that the sandwiches are not purchased similarly across all the four different states as per the statistical data.

A statistic, according to the Longman Dictionary of Contemporary English, is a person who has perished as a result of a specific type of accident or illness and is merely another statistic.

These things cannot be reduced to a statistic data.

In conclusion, there are a total of five reasons to study statistics. These are, to be able to conduct research efficiently, to read and evaluate journal articles, to further develop critical thinking and then also develop proper analytical skills, to act as an informed consumer, and to then recognize the times whenever you get the need to hire outside statistical help.

As per the question,

p = 0.7682

and thus, we have p > 0.05

And if p > 0.05 then we fail to reject the null hypothesis and results are not significant.

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L = 24 + 12 + 6 + 3 + 1.5 + 0.75 + 0.375 + 0.1875 + ......+ 0.5X(n-1) expression gives the total length the monkey swings in her first n swings.

The first swing's length was 24 meters.

The monkey only covers half of the arc's length in each swing.

First, n swings' cumulative length equals?

Total swing length is equal to the initial swing's length plus 0.5 times that amount plus the next number of swings.

i.e., Total length of n swings = length of first swing + 0.5 X length of first swing + .....+ length of n swings

L = 24 + 12 + 6 + 3 + 1.5 + 0.75 + 0.375 + 0.1875 + ...

Therefore, the expression is

L = 24 + 12 + 6 + 3 + 1.5 + 0.75 + 0.375 + 0.1875 + ......+ 0.5X(n-1)

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A solar system is a system in which the sun serves as the parent star and everything revolves around it. Everything also includes all planets, all moons, all asteroids, and all comets.

The gravitationally system comprising the Sun and the satellites in its orbit is referred to as the Solar System. The gravitational collapse of a massive interstellar molecular cloud gave it birth 4.6 billion years ago. The Sun has the great majority of the system's mass, with Jupiter holding the majority of the remaining mass.

The first four plants are referred to as terrestrial/Inner planets in our solar system. The asteroid belt is ahead of them. Mars, Venus, Mercury, and Earth are the planets.

Jovian/giant/outer planets are the planets that follow the asteroid belt in the solar system. Their atmosphere is dense and primarily made of hydrogen and helium. Jupiter, Saturn, Uranus, and Neptune are the planets after asteroid belt.

Hence, the sun, 8 planets, 63 moons, as well as millions of other minor bodies like asteroids and comets, as well as enormous amounts of dust and gases, make up the solar system.

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The acceleration of the stalled car is 0.5 m/ s^2 forward.

By the formula of force we know that F = m X a

so in this question, mass = 1000kg , and F = 2000N

so acceleration of the car = 2000N= 1000kg X a

a = 1000kg / 2000N, = 0.5 m/ s^2 forward.

Force is a factor that has the power to alter an object's motion. An object with mass can change its velocity, or acceleration, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

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Acceleration of the stalled car is 2 m / s ² in forward direction .

Force is defined as the rate of change of momentum or as the product of mass and acceleration .

F = m ( v - u ) / t

F = m x a

F  = Force

m = Mass

a = Acceleration

It is given that ,

F = 2,000 N

m = 1,000 kg

Since , F = m x a

So ,

a = F / m

a = 2,000 N / 1,000 kg

a = 2 m / s ² Forward

Hence , Acceleration of the stalled car is 2 m / s ² in forward direction .

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The magnitude of the force needed to supply 100 N m of torque to the bolt is 417 N

Here r = < 0, 0.3, 0 >

F = F < 0, 3, -4 >

T = r F sin θ

If v = < 0, 3, -4 >, θ is the angle between r and v

r . v = r v cos θ

0.9 = ( 0.3 ) ( 5 ) cos θ

Cos θ = 0.6

Sin θ = 0.8

T= r F sin θ

100 = 0.3 F ( 0.8 )

F = 417 N

Torque is a type of force which causes an object to rotate about an axis. Torque is represented as τ. Its unit is N m

Therefore, the magnitude of the force needed to supply 100 N m of torque to the bolt is 417 N

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