how do the age and size of our solar system compare to the universe?

Answers

Answer 1

The age and size of our solar system are significantly smaller when compared to the age and size of the universe.

Age

The estimated age of our solar system is around 4.6 billion years. This age is based on scientific evidence and dating techniques that provide insights into the formation and evolution of our Sun and the planets.

In contrast, the age of the universe is estimated to be approximately 13.8 billion years. This age is determined through observations of cosmic microwave background radiation, the expansion of the universe, and other astrophysical measurements.

Size

The size of our solar system is relatively small compared to the vast expanse of the universe. The solar system consists of the Sun, eight planets, their moons, asteroids, comets, and other celestial bodies. The extent of the solar system is often measured by the farthest orbiting object, which is currently considered to be Voyager 1, about 22 billion kilometers away from the Sun.

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Related Questions

the ____ metacharacter is used to allow a string to contain an alternate set of substrings.

Answers

The vertical bar (|) metacharacter is used to allow a string to contain an alternate set of substrings. It is also known as the "pipe" character and it functions as an "OR" operator in regular expressions.

This means that when the vertical bar is used between two strings, the regular expression engine will look for either one of the strings in the target string. For example, the regular expression "cat|dog" will match either "cat" or "dog" in the target string. The vertical bar is a useful tool for creating flexible regular expressions that can match different variations of a pattern.
This pattern would match any of the three colors "red", "blue", or "green" in a given string. By incorporating the "|" metacharacter, you can efficiently search for and match various substrings within a larger string, making it a powerful and versatile tool in pattern recognition and text processing tasks.

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Please help fast I don’t understand

Please help fast I dont understand

Answers

The pickup truck with changing velocity can accelerate faster than the other pickup trucks.

option A.

What causes a change in velocity of a pickup truck?

A change in velocity of a pickup truck can be caused by several factors, including:

Acceleration:  Acceleration is the rate of change of velocity over time, and it can result in an increase in velocity.

External forces: Other external forces, such as air resistance or friction from the road surface, can also cause a change in velocity of a pickup truck.

It's important to note that according to Newton's first law of motion, an object will maintain its velocity unless acted upon by an external force.

Therefore, any change in velocity of a pickup truck must be caused by the application of an external force.

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What two things determine whether a molecule is polar?
Check all that apply.
A. If there is an anion and a cation
B. If the molecule is easily ionized
C. If the bonds are polar
D. The molecular shape

Answers

Answer:

c

Explanation:

Answer:C&D

Explanation:

I just did it

How many distinct angles from the vertical axis can the orbital angular momentum vector L make for an electron with = 5? b)Calculate the smallest possible angle the L can make with respect to the vertical axis. (Hint: The smallest angle occurs when m takes the maximum allowed value. Sketch L in that case and compare the vertical component, which is related to m, to the magnitude of L, which is related to .)

Answers

The smallest possible angle that L can make with respect to the vertical axis is 0 degrees.

The orbital angular momentum vector L of an electron can take on distinct angles from the vertical axis depending on the allowed values of the magnetic quantum number (m).

For an electron with principal quantum number n, the allowed values of m range from -l to +l, where l is azimuthal quantum number. In this case, since = 5, azimuthal quantum number l have values ranging from 0 to 4. Therefore, total of 2l + 1 distinct angles.

For l = 5, there are 2(5) + 1 = 11 distinct angles that L can make with the vertical axis.

The smallest possible angle L can make with respect to vertical axis, consider the maximum allowed value of m, which is +l. In this case, m = 5.

When m takes the maximum allowed value, the orbital angular momentum vector L is aligned parallel to the vertical axis. The vertical component of L, related to m, is equal to the magnitude of L, which is related to .

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In a real pully system the work supplied must be _____ the work accomplished​ and no links plz​

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us the link or will help you

a collection of hydrogen atoms in the ground state is illuminated with ultraviolet light of wavelength 75.0 nm. find the kinetic energy of the emitted electrons.

Answers

The kinetic energy of the emitted electrons is 11.24 eV.

What is kinetic energy?

The following is the physics definition of kinetic energy:

The amount of effort that a moving object may accomplish is measured by its kinetic energy.

Kinetic energy is a scalar quantity that can only be fully explained by its magnitude.

Given parameters:

Wavelength of ultraviolet light : λ = 75.0 nm.

Energy of the ultraviolet light: E = hc/λ = 1242/75.0 eV= 22.84 eV

Potential energy of a electron of   hydrogen atoms in the ground state is -13.6 eV.

This energy of light supplies required potential energy to the emitted electron and kinetic energy of electron.

So,  the kinetic energy of the emitted electrons = 22.84 eV - 13.6 eV = 11.24 eV.

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Q2: Find the average autocorrelation function and the spectrum of the following signal, then find the signal energy: x(t) = 50 ^ (0.05(-2)) A

Answers

The average autocorrelation function of the signal x(t) is E = ∫_0^∞ |x(t)|² dt = 50, the spectrum and the signal energy is 50.

The average autocorrelation function of the signal is:

Rxx(τ) = 50 ^ (0.05(-2τ)) A²

The spectrum of the signal is:

Sxx(f) = 50 ^ (0.05(-2πf)) A²

The signal energy is:

E = ∫_0^∞ |x(t)|² dt = 50

The signal energy can be found using the following formula:

E = ∫_0^∞ |x(t)|² dt

In this case, the signal is a constant, so the integral can be simplified as follows:

E = ∫_0^∞ |50A|² dt = ∫_0^∞ 2500A² dt = 50

Therefore, the signal energy is 50.

The average autocorrelation function of a signal is a measure of how similar the signal is to itself at different time lags. In this case, the average autocorrelation function is a decreasing exponential function, which means that the signal is more similar to itself at small time lags than at large time lags.

The spectrum of a signal is a measure of the distribution of the signal's energy over different frequencies. In this case, the spectrum is an exponential function, which means that the signal has more energy at low frequencies than at high frequencies.

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the total energy of a system is 300j. if the potential energy is 40j what is the kinetic energy if the object started 300m above the ground?

Answers

Answer:

43.3 m/s.

Explanation:

Assuming the potential energy is due to the gravitational potential energy, we can use the conservation of energy to find the kinetic energy:

Total energy = Potential energy + Kinetic energy

Kinetic energy = Total energy - Potential energy

Kinetic energy = 300 J - 40 J = 260 J

However, we need to know the mass of the object to convert the kinetic energy to velocity. We can use the potential energy to find the mass:

Potential energy = mgh

40 J = m(9.81 m/s^2)(300 m)

m = 0.137 kg

Now we can use the kinetic energy to find the velocity:

Kinetic energy = (1/2)mv^2

260 J = (1/2)(0.137 kg)v^2

v^2 = (2*260 J) / 0.137 kg

v = 43.3 m/s (rounded to one decimal place)

Therefore, the kinetic energy is 260 J and the velocity of the object when it reaches the ground is 43.3 m/s.

What is your hypothesis (or hypotheses) for this experiment? (kinetic energy)

Answers

Kinetic energy of any object is always positive. This should be  hypothesis for any experiment.

What is hypothesis?

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.

Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge. Despite the frequent confusion between the terms "hypothesis" and "theory," a scientific hypothesis differs from a scientific theory.

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a power loss ride through function is limited to _____ seconds.

Answers

A power loss ride through function is limited to 1-2 seconds.

Power loss function

Typically, the length of the power loss ride-through function is created to offer a long enough buffer time to bridge the gap between the power loss and the power restoration. It enables the system or gadget to securely shut down without causing a sudden disruption to operations.

The application requirements, system criticality, energy storage or backup power capacity, and the time needed for power restoration or alternative power source activation can all be used to establish the precise duration of the ride-through function.

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For a convex lens to produce a real, enlarged, inverted image which of the following must be true?1) The object’s distance must be greater than one focal length but less than twice the focal length.2) The object’s distance must be greater than twice the focal length.3) The object’s distance must be equal to the focal length.4) The object’s distance must be less than one focal length.

Answers

For a convex lens to produce a real, enlarged, and inverted image, the following must be true.

The object's distance must be between F and 2F.

In other words, the object’s distance must be greater than one focal length but less than twice the focal length.

Therefore, the 1st option is the correct answer.

"The object’s distance must be greater than one focal length but less than twice the focal length."

could you help me pleaseeeeeeee " if a car starts from a stop and speeds up to 15 m/s in a time frame of 5 seconds calculate the acceleration

Answers

Answer:

\(vf=vi+at\\vf=15\\vi=0\\a=?\\t=5\\\\15=0+a5\\a=\frac{15}{5} \\a=3\)

Therefore the acceleration is 3m/s^2

Explanation:

We will be using the kinematics big five equations. Specifically, the one without displacement (d).

Write out your values and substitute the, into the equation.

Solve for a.

Note. Starts from stop so vi=0

Which phrase describes the idea that heat is transferred as thermal energy by the interaction of moving particles?.

Answers

Explanation:

Nasa picture po ang answer

Which phrase describes the idea that heat is transferred as thermal energy by the interaction of moving

A block of weight W is pushed to the right across a level surface at a constant velocity by a force P acting at an angle above the horizontal, as shown. The magnitude of the normal force exertedon the block by the surface is

A block of weight W is pushed to the right across a level surface at a constant velocity by a force P

Answers

ANSWER:

(a)

\(w+P\cdot\sin \theta\)

STEP-BY-STEP EXPLANATION:

The first thing is to make the force diagram to be able to determine the answer, just like this:

Therefore, in the y-direction, we can determine the value of the normal force as follows:

\(N=w+P\cdot\sin \theta\)

A block of weight W is pushed to the right across a level surface at a constant velocity by a force P

what is the balance equation for the chemical equation h2o+so2=h2o+s​

Answers

Answer:

2H₂S + SO₂ —> 2H₂O + 3S

Explanation:

From the question given above, the following equation were obtained:

H₂S + SO₂ —> H₂O + S

The equation can be balance as illustrated below:

H₂S + SO₂ —> H₂O + S

There are 2 atoms of O on the left side and 1 atom on the right side it can be balance by writing 2 before H₂O as shown below:

H₂S + SO₂ —> 2H₂O + S

There are 2 atoms of H on the left side and 4 atoms on the right side. It can be balance by writing 2 before H₂S as shown below:

2H₂S + SO₂ —> 2H₂O + S

There are 3 atoms of S on the left side and 1 atom on the right side. It can be balance by writing 3 before S as shown below:

2H₂S + SO₂ —> 2H₂O + 3S

Now, the equation is balanced.!

bioprocessing
1. Validation is not needed for single-use systems in a
bioreactor. Would you agree with this statement? Explain your
answer.

Answers

In general, the statement that validation is not needed for single-use systems in a bioreactor is not accurate. Validation is an essential process in bioprocessing that ensures the reliability, consistency, and safety of the manufacturing process. Single-use systems, which are increasingly used in bioreactors, can introduce unique challenges and considerations.

Validation of single-use systems involves assessing their performance, integrity, and compatibility with the process requirements. Factors such as material integrity, sterile connections, and proper functioning of sensors and control systems should be evaluated to ensure the system's suitability for use.

While single-use systems offer advantages in terms of cost, flexibility, and minimizing cross-contamination risks, they still require validation to demonstrate their reliability and performance. It is essential to follow industry standards, regulatory guidelines, and good manufacturing practices to ensure the quality and safety of bioprocessing operations, regardless of the system being used.

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Fighter jets on aircraft carriers are accelerated down a 270 foot "runway" in two seconds when they are taking off. A fully loaded, combat ready F-15 has a maximum take-off weight of 62,000 pounds. To ensure the pilot can reach sufficient velocity within 2 seconds a pneumatic cannon propels the plane down the runway. If this same cannon was used to launch your Toyota Corolla (mass is 2646lbs), how fast in miles per hour would you be going after reaching the end of the runway?

Answers

The speed of the  Toyota Corolla would have  been 143.9 mph.

What is the acceleration of the F-15?

The acceleration of the F-15 can be calculated as follows:

Acceleration = Velocity Change / Time = (Take-off Speed) / Time

where;

Take-off Speed = √(2dg /t²)

Take-off Speed = √(2 x  (270 ft)  x 32.2 ft/s² / (2 s)²)

T  = √(17496) = 131.6 ft/s

Acceleration = Velocity Change / Time

= (131.6 ft/s) / (2 s) = 65.8 ft/s²

We can use the same acceleration to launch the Toyota Corolla, and calculate its final velocity:

Final Velocity = Initial Velocity + Acceleration x Time

where;

Initial Velocity = 0 (because the car is not moving initially), Time = 2 s

Final Velocity = 0 + (65.8 ft/s²) * (2 s) = 131.6 ft/s

Finally, we can convert the velocity from feet per second to miles per hour:

Velocity (mph) = Velocity (ft/s) x (1 hour/3600 s) x (5280 ft/mile)

= 131.6 ft/s x  (1 hour/3600 s)  x (5280 ft/mile)

= 143.9 mph

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F PHY112 Chapter 29 Homework Question 2 of 4 > -/1 View Policies Current Attempt in Progress An incident X-ray photon of wavelength 0. 2019 nm is scattered from an electron that is initially at rest. The photon is scattered at an angle of 0 = 180. 0° in the drawing and has a wavelength of 0. 2068 nm. Use the conservation of linear momentum to find the momentum gained by the electron. E. X e E, Photon scattering from stationary electron Number Units וח​

Answers

The momentum gained by the electron in this scattering process is approximately \(6.91 * 10^{-24} kg m/s\).

In this scenario, an incident X-ray photon of wavelength 0.2019 nm is scattered from a stationary electron, resulting in the photon being scattered at an angle of 180 degrees with a wavelength of 0.2068 nm. The conservation of linear momentum can be used to find the momentum gained by the electron in this process.
The momentum of the photon can be calculated using the formula p = h/λ, where h is Planck's constant and λ is the wavelength of the photon.

Using this formula, we find that the initial momentum of the photon is approximately \(3.093 * 10^{-22} kg m/s\).
The final momentum of the photon can be calculated in the same way, using its new wavelength of 0.2068 nm.

The final momentum is approximately \(3.024 * 10^{-22} kg m/s\).
Since momentum must be conserved in this process, we can find the momentum gained by the electron by subtracting the final momentum of the photon from its initial momentum.

Doing so, we find that the momentum gained by the electron is approximately \(6.91 * 10^{-24} kg m/s\).

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Five particles are shot from the left into a region that contains a uniform electric field. The numbered lines show the paths taken by the five particles. A negatively charged particle with a charge –3q follows path 2 while it moves through this field. Do not consider any effects due to gravity. In which direction does the electric field point?.

Answers

Five particles are shot from the left into a region that contains a uniform electric field.  A negatively charged particle with a charge –3q follows path 2 while it moves through this field. The electric field point towards the bottom of the page.

What are electric fields?

An electric field is a physical field around a charged particle or object which has the ability to surround electrically charged particles and exerts force on all other charged particles that are present in the field.

This force exerted upon them is either attracting or repelling them. This electric field also refers to as the physical field for a system of charged particles.

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Why can videos be streamed from one computer to another with excellent
quality?
A. They are received using both analog and digital signals.
B. They are transmitted using analog signals.
C. They are received using either analog or digital signals.
D. They are transmitted using digital signals.
SUBMIT

Answers

the answer should be d) they are transmitted using digital signals

A 2kg box has a speed of 10m/s at the bottom of a 37 degree inclined ramp
A)how far up the ramp does the box slides if the ramp was friction less
B)how far does it slides if the coefficient of kinetic friction is 0.2

Answers

The box travels 3.33 meters up the ramp with no friction and 1.56 meters with friction.

Calculation-

Frictionless ramp:

K_i = (1/2)mv_i^2 = (1/2)(2 kg)(10 m/s)^2 = 100 J

K_f = 0

U_f = mgh

Since energy is conserved, we have:

K_i = U_f

(1/2)mv_i^2 = mgh

h = (1/2)(v_i^2)/g * sin^2(theta) = (1/2)(10 m/s)^2 / (9.81 m/s^2) * sin^2(37 degrees) = 3.33 m

Ramp with friction:

f_friction = μ_k * f_norm

W_friction = f_friction * d = μ_k * f_norm * d

K_i = U_f + W_friction

(1/2)mv_i^2 = mgh + μ_k * f_norm * d

d = (v_i^2 - 2gh)/(2μ_kf_norm) = ((10 m/s)^2 - 2*(9.81 m/s^2)sin(37 degrees)(3.33 m))/(20.22 kg*cos(37 degrees)*9.81 m/s^2) = 1.56 m

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Which electrical component is used for detecting light levels in digital cameras?

Answers

The electrical component that is used for detecting light levels in digital cameras is the light meter.

What are light meters?

A light meter is a device used to measure the amount of light. In photography industry, a light meter is used to determine the proper exposure for a photograph.

A digital camera is a camera that captures photographs in digital memory.

Most digital cameras can be grouped into four main types which includes:

digital SLR (or DSLR), point-and-shoot, bridge cameras, and camera phones.

Each type of these digital cameras has advantages and disadvantages, and some the types are more expensive than their counterparts.

There are two different kinds of light meters which are:

incident and reflective.

-An incident light meter measures all the light falling onto a subject. Incident light meters help a camera focus on a subject regardless of how light or dark the surrounding background is.

- Reflective light meters  on the other hand do the opposite by measuring the light reflected by or bouncing off a subject.

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communications satellites would fly off in a straight line never to be see again if it were not for a force from the earth compelling them to constantly change their direction. this tendency to fly off in a straight line is a statement of the

Answers

Communications satellites would fly off in a straight line never to be see again if it were not for a force from the earth, The moon "falls" from a straight line because there IS some attraction toward the Earth.

What would happen if forces were suddenly removed from the satellite?

The satellite will tend to move tangential to the initial orbit without the assistance of centripetal force at the same speed as it did just before the gravitational field vanishes. As a result, the spacecraft will veer off course and leave its orbit.

Do people gravitate toward one another?

The combined gravitational force of acts on the mass in your body. What gives you weight is that. Additionally, you would weigh less than you do now if you were on a planet with a lower mass than Earth. You make the same gravitational force on Earth that it does on you.

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Consider the modified Atwood machine shown in Figure 13.11. The two weights on the left have equal masses m and are connected by a massless spring of force constant k. The weight on the right has mass M = 2m, and the pulley is massless and frictionless. The coordinate x is the extension of the spring from its equilibrium length; that is, the length of the spring is l. + x where is the equilibrium length (with all the weights in position and M held stationary). (a) Show that the total potential energy

Answers

In the modified Atwood machine shown in Figure 13.11, the two weights on the left have equal masses m and are connected by a massless spring of force constant k. The weight on the right has mass M = 2m, and the pulley is massless and frictionless. The coordinate x is the extension of the spring from its equilibrium length. We need to find the total potential energy of the system.

Let us first consider the potential energy of the spring. The potential energy of a spring is given by the equation U = 1/2 kx^2, where k is the force constant of the spring, and x is the displacement of the spring from its equilibrium position. In this case, the extension of the spring is x, so the potential energy of the spring is U_spring = 1/2 kx^2.

Next, we need to consider the gravitational potential energy of the weights. The gravitational potential energy of an object of mass m at a height h above the ground is given by U_gravity = mgh, where g is the acceleration due to gravity and h is the height of the object above the ground. In this case, the height difference between the two masses on the left and the mass on the right is l - x, so the potential energy of the left weights is U_left = 2mgl - 2mgx.

The mass on the right has a height of zero, so its gravitational potential energy is U_right = 0.

Therefore, the total potential energy of the system is given by U_total = U_spring + U_left + U_right = 1/2 kx^2 + 2mgl - 2mgx.

In conclusion, we have derived an expression for the total potential energy of the modified Atwood machine. This expression shows that the potential energy of the system is dependent on the extension of the spring, the acceleration due to gravity, and the masses of the weights.

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. What was the problem in Redi's experiment?
a. How do maggots appear in meats?
b. How do worms appear in wood?
c. Is spontaneous generation a valid
explanation formaggots in meats?
d. All of the above are examples of problems

Answers

Answer:

I say that the answer is D all of the above hope this helps ‍♂️

Is the daughter or the science teacher correct? And why?

Is the daughter or the science teacher correct? And why?

Answers

Answer:

The daughter. I can't really explain but practically, it happens as the daughter has stated.

A ball collides with a vertical, unmovable wall_ There is no friction between the wall and the ball (the only force acting on the ball during the collision is the normal force from the wall). 0f 1) What is the direction of the X-component of the impulse imparted to the ball during the collision? to the right to the left zero Submit 2) What is the direction of the Y-component of the impulse imparted to the ball during the collision?

Answers

The X-component of the impulse imparted to the ball during the collision is zero. The Y-component of the impulse imparted to the ball during the collision is downward.

Impulse is the change in momentum that occurs over a period of time. During a collision between two objects, such as a ball and a wall, the impulse can be calculated by multiplying the force of the collision by the time duration. If the duration of the collision is very short, the average force of the collision can be very large.

In this case, the ball collides with a vertical, unmovable wall. There is no friction between the ball and the wall, so the only force acting on the ball during the collision is the normal force from the wall. The normal force acts perpendicular to the surface of the wall, so it has no component in the X direction. Therefore, the X-component of the impulse imparted to the ball during the collision is zero.

The Y-component of the impulse can be calculated using the equation:

Impulse = Change in momentum

where momentum is the product of mass and velocity. Since the wall is immovable, the velocity of the ball in the X direction does not change during the collision. However, the velocity of the ball in the Y direction changes direction because the ball bounces off the wall.

We can assume that the ball is thrown towards the wall with some initial velocity in the Y direction. The ball then collides with the wall and bounces off with the same magnitude of velocity in the opposite direction. During this time, the Y-component of the velocity changes from positive to negative, causing a change in momentum.

Since there are no other forces acting on the ball during the collision, the impulse must be equal to the change in momentum. Since the Y-component of the velocity changes sign, the change in momentum has the same magnitude but opposite direction as the initial momentum, giving a downward impulse.

In conclusion, the X-component of the impulse imparted to the ball during the collision with a vertical, unmovable wall is zero because the only force acting on the ball during the collision is the normal force from the wall, which is perpendicular to the surface of the wall. The Y-component of the impulse is downward because the wall causes the velocity of the ball in the Y direction to change sign during the collision, leading to a change in momentum in the opposite direction.

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I NEED THE RIGHT ANSWER ASAP IT NEEDS TO BE 100% ACCURATE NO LINKS !!!
What happens when multiple forces act on an object?
1: The object will move if the forces are unbalanced.
2: The object will always stay in place.
3: The object will always move.
4: The object will move if the forces are balanced.

Answers

Answer:

The object will move if forces are unbalanced

Newton’s second law: The acceleration (a) of an object is directly proportional to the force on the object (F) and inversely proportional to its mass (m).

F < The greater the force, the greater the acceleration
a = -- OR F=ma
M< The greater the mass the less the acceleration

Answers

Answer:

there is the answer

Explanation:

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

Newtons second law: The acceleration (a) of an object is directly proportional to the force on the object

A train started from a station and accelerated at 0.5 m s−2 to reach its top speed of 50 m s−1 and maintained this speed for 90 minutes. As the train approached the next station the driver applied the brakes uniformly to bring the train to a stop in a distance of 500 m. Calculate how long it took the train to reach its top speed.

Answers

Answer:

(a) The train took 100 seconds (1.667 minutes) to reach its top speed.

(b) The train travelled a distance of 270000 meters (270 kilometers) at top speed.

(c) The train decelerates at a rate of 2.5 meters per square second.

Explanation:

Statement is incomplete. Complete description is presented below:

A train started from a station and accelerated at \(0.5\,\frac{m}{s^{2}}\) to reach its top speed of \(50\,\frac{m}{s}\) and maintained this speed for 90 minutes.

When the train approached the next station the driver applied the brakes uniformly to bring the train to a stop in a distance of 500 meters.

(a) Calculate how long it took the train to reach its top speed.

(b) Calculate how far it travelled at its top speed.

(c) Calculate the acceleration experienced by the train when the brakes were applied.

(a) Let suppose that train accelerates uniformly. Then, the time needed by the vehicle (\(t\)), measured in seconds, is described by the following equation of motion:

\(t = \frac{v-v_{o}}{a}\) (1)

Where:

\(a\) - Acceleration, measured in meters per square second.

\(v_{o}\), \(v\) - Initial and final speed, measured in meters per second.

If we know that \(a = 0.5\,\frac{m}{s^{2}}\), \(v_{o} = 0\,\frac{m}{s}\) and \(v = 50\,\frac{m}{s}\), then the time needed by the train is:

\(t = \frac{50\,\frac{m}{s}-0\,\frac{m}{s}}{0.5\,\frac{m}{s^{2}} }\)

\(t = 100\,s\)

The train took 100 seconds (1.667 minutes) to reach its top speed.

(b) Let suppose that train travels at constant speed, the distance travelled by the train (\(s\)), measured in meters, is:

\(s = v\cdot t\) (2)

Where:

\(v\) - Top speed, measured in meters per second.

\(t\) - Time, measured in seconds.

If we know that \(v = 50\,\frac{m}{s}\) and \(t = 5400\,s\), then the distance travelled by the train at top speed is:

\(s = \left(50\,\frac{m}{s} \right)\cdot (5400\,s)\)

\(s = 270000\,m\)

The train travelled a distance of 270000 meters (270 kilometers) at top speed.

(c) Let suppose that train decelerates at constant rate. We can calculate the acceleration from the following expression:

\(a = \frac{v^{2}-v_{o}^{2}}{2\cdot s}\) (3)

Where:

\(v_{o}\), \(v\) - Initial and final speed, measured in meters per second.

\(s\) - Travelled distance, measured in meters.

If we know that \(v_{o} = 50\,\frac{m}{s}\), \(v = 0\,\frac{m}{s}\) and \(s = 500\,m\), then the acceleration of the train is:

\(a = \frac{\left(0\,\frac{m}{s} \right)^{2}-\left(50\,\frac{m}{s} \right)^{2}}{2\cdot (500\,m)}\)

\(a = -2.5\,\frac{m}{s^{2}}\)

The train decelerates at a rate of 2.5 meters per square second.

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