(i) The wavelength of y = 4 sin (1000πt/λ + 0. 5x), where y and x are in cm and t is in second = 12.56 m
(ii) The speed of the wave = 6280 ./s
(iii) The frequency of the wave = 500 Hz
The wave function y(x,t) = A sin(ωt−Kx), the equation itself can be used to read the amplitude, which equals A. The angular frequency can be used to calculate the wave's period.
A = 4
ω = 1000π
k = 0.5
Hence,
(i) The wavelength:
λ = 2π / k
= 2π / 0.5
= 12.56 m
(i) The speed of the wave:
v = f λ
= (500 Hz x 12.56m)
= 6280 m/s
(iii) The frequency of the wave:
f = ω / 2π
= (1000π) / 2π
= 500 Hz
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what is the best definition of electric charge
Answer:
B. It is the flow of electrons that have a negative charge to protons that have a positive charge.
Explanation:
Electric charge is a fundamental property of matter that arises from the presence or absence of electrons in an object. Electrons have a negative charge, while protons have a positive charge. When an object has an excess or shortage of electrons, it creates an electric charge. This charge can be measured and is used to explain various electrical and electronic phenomena, including the flow of electric current, the behavior of electric circuits, and the interaction of charged objects with each other. The flow of electrons from one charged object to another is what creates an electric current, which is a flow of electric charge. Thus, the best definition of electric charge is the flow of electrons that have a negative charge to protons that have a positive charge.
1. A student carries a 12 kg box up a flight of stairs at a slow constant speed in 4. 5 seconds. The height
of the flight of stairs is 3. 6 meters.
a. What is the weight of the box? (in other words, its force in Newtons)
Want:
Given:
Can someone help me which this physic homework please?
Formula:
Solve:
b. How much work does the student do on the box? Draw a problem solving box!
c. What is the student's output power? Draw a problem solving box!
can someone help me with this physic homework pleas?
The weight of the box is 120N and work done is 432J.
We know that weight is just the force.
Weight = F = mg
where, m = mass of the body = 12kg
g = acceleration due to gravity = 10 m/s^2
Putting these values in above equation we get : F = 120 N
So, the weight of the box is 120N.
We know that work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
Now Work done by an object is given by : W = F.d
where,
F = force acting
d = displacement = 3.6 m
Putting these values in above equation we get: W = 120 * 3.6 = 432J
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A truck travels on a straight road at a velocity of 17 meters per second. Over 20 seconds, it accelerates uniformly to 27 meters per second. What was the acceleration of the truck in m/s2?.
A truck travels on a straight road at a velocity of 17 meters per second. Over 20 seconds, it accelerates uniformly to 27 meters per second. The acceleration of the truck was 0.5 m/s^2
The velocity of the truck after 20 seconds is 27 m/s and its initial velocity was 17 m/s, so the change in velocity is:
Δv = 27 m/s - 17 m/s = 10 m/s
The acceleration can be calculated as the change in velocity divided by the time it took to change, so:
a = Δv / t = 10 m/s / 20 s = 0.5 m/s^2
Acceleration is a measure of the rate of change of velocity over time. It is a vector quantity, meaning it has both magnitude and direction, and is defined as the derivative of velocity with respect to time. In other words, acceleration is the rate at which an object's velocity is changing. If an object is moving in a straight line and its velocity is increasing, then it is accelerating. If the velocity is decreasing, then the object is decelerating.
Acceleration has units of meters per second squared (m/s^2). Positive acceleration means an increase in velocity, while negative acceleration means a decrease in velocity. For example, when an object is accelerating upwards, its acceleration is positive, while when it is falling, its acceleration is negative.
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describe the relationship between the wavelength and the frequency of a wave.
The relationship between wavelength and frequency of a wave is well established in physics and is described in the provided search results. According to the frequency of a wave multiplied by its wavelength gives the speed of the wave. In 2, the relationship is described using the equation frequency x wavelength = speed of light, where frequency (v) and wavelength (λ) are related to the speed of light (c).
The relationship between frequency and wavelength is also described in 3, where the wave speed is equal to the product of its frequency and wavelength. This is expressed as v = f * λ, where v is the wave speed, f is the frequency, and λ is the wavelength. In summary, the wavelength and frequency of a wave are directly proportional to each other, and the product of their values gives the speed of the wave.
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how to get real and imaginary parts of permittivity from refractive index and extinction coefficients
The refractive index and the extinction coefficient of a material can be used to calculate its complex permittivity, which is a measure of the material's ability to store electric energy.
It is defined as the ratio of the electric flux density (D) to the electric field strength (E) in a vacuum and has units of farads per meter (F/m). In a material, the electric field is partially screened by the material's electrons, leading to a reduction in the effective electric field. The complex permittivity is given by the following equation:
ε = ε' - jε'' = n^2 - jk,
where ε' is the real part of the permittivity, ε'' is the imaginary part of the permittivity, n is the refractive index, and k is the extinction coefficient.
So, to obtain the real and imaginary parts of the permittivity, one can simply use:
ε' = n^2
ε'' = k
where n and k are the known refractive index and extinction coefficient, respectively.
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According to the second law of thermodynamics, the entropy of a system will always __________.
According to the second law of thermodynamics, the entropy of a system will always increase over time.
define thermodynamics ?
Thermodynamics is a branch of physics that deals with the relationships between heat, work, and energy in a system. It is concerned with understanding how energy is transformed and transferred between different forms, such as heat and mechanical energy. The laws of thermodynamics describe the basic principles that govern the behavior of energy and heat in a system and provide a basis for the understanding of thermodynamic processes.
According to the second law of thermodynamics, the entropy of a system will always increase over time.
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What is the final velocity of an object that accelerates from rest at 3, point, 5, m, slash, s, squared,3.5m/s
2
for 8, point, 5, s,8.5s?
The final velocity of the object is 29.75 m/s.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
The acceleration of the object = 3.5 m/s²
The initial velocity of the object = 0 m/s.
Time interval = 8.5 second.
Hence, form basic kinematics, we can write the final velocity becomes = initial velocity + acceleration × time interval
= 0 + 3.5 × 8.5 m/s
= 29.75 m/s
Hence, the final velocity of the object is 29.75 m/s.
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Your question is incomplete but most probably the question was:
What is the final velocity of an object that accelerates from rest at 3.5m/s² for 8.5 s?
A 60 g tennis ball with an initial speed of 39 m/s
hits a wall and rebounds with the same speed. See attachment for graph
(a) The impulse experienced by the ball is 4.68 kgm/s.
(b) The maximum force of the ball is 1,170 N.
What is the impulse of the tennis ball?The impulse of the tennis ball is calculated by applying the following formula as shown below.
J = Ft
where;
F is the applied forcet is the time of motion of the ballThe impulse experienced by the ball is the area of the force time graph.
J = area of trapezium
J = ¹/₂ x ( 2 + 6 ) x Fmax
J = 4 Fmax
Fmax = J / 4ms
J = ΔP
where;
ΔP is the change in the momentum of the ballΔP = m ( v - u )
ΔP = 0.06 kg ( 39 m/s - - 39 m/s )
ΔP = 0.06 kg ( 39 m/s + 39 m/s )
ΔP = 4.68 kgm.s
The maximum force of the ball is calculated as;
Fmax = ( 4.68 ) / ( 4 x 10⁻³ )
Fmax = 1170 N
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The complete question is below;
A 60 g tennis ball with an initial speed of 39 m/s
hits a wall and rebounds with the same speed. See attachment for graph. find the impulse experienced by the ball and the maximum force Fmax.
A 0. 16 kg pool ball sliding to the right at 8. 0 m/s has an elastic head-on collision with another 0. 16 kg pool ball initially at rest. If the first ball stops after the collision, what is the velocity of the second pool ball after the collision?
To find the velocity of the second pool ball after the collision, we need to apply the law of conservation of momentum.
Let's call the velocity of the first ball before the collision as v1, and the velocity of the second ball after the collision as v2. The momentum of each ball before the collision is given by m1v1 and m2v2, respectively, where m1 and m2 are the masses of the balls.
Since the first ball stops after the collision, its velocity becomes 0, so we can write the equation as:
m1v1 + m2v2 = m1 * 0 + m2 * v2
Simplifying and substituting the given values, we get:
0.16 * 8.0 + 0.16 * v2 = 0.16 * 0 + 0.16 * v2
v2 = 8.0 m/s
So the velocity of the second ball after the collision is 8.0 m/s.
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what two measurements are necessary for calculating speed?
The two measurements that are necessary for calculating speed are distance and time. To find the average speed, you divide the distance by the time.
[tex]speed=\dfrac{distance}{time}[/tex]
what is the ratio of deprotonated to protonated histidines at ph 7.40
The pKa of histidine is approximately 6.0, which means that at a pH of 7.4, the majority of histidine residues would be in their deprotonated (negative) form. The exact ratio depends on various factors such as the protein context and local environment, but a rough estimate is that at pH 7.4, histidine would be about 90-99% deprotonated.
What is pKa?pKa is a measure of the acidity or basicity of a chemical species, such as an amino acid or a small molecule. It is defined as the pH at which the species is equally likely to exist in its protonated (acidic) and deprotonated (basic) forms. The pKa value is an important parameter in biochemistry and biophysics because it determines the charge state of a molecule and influences its interactions with other molecules. In general, a molecule with a low pKa is more acidic, while a molecule with a high pKa is more basic.
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What is 2km in miles?
A mile is 1.609 kilometers long. Both the mille and the kilometer are units of measurement. A mile is larger than a kilometer, nevertheless.
Is a 2 km stroll too far?Approximately 125 calories are burned by walking for thirty min at a quick pace for a distance between 2.0 to 2.5 kilometres (520 kiloJoules). This may not appear to be much, but if if walked for a whole year, five days a week, you would have burned more than 32,000 calories, or more than 5 kg, of fat.
Does a brisk stroll burn fat?Conclusions Walking at any speed results in the loss of total body fat, however in overweight individuals the reduction is more pronounced, immediate, and initially larger with slow walking. a stronger, deeper exercise impulse.
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calculate the kinetic energy (in ev) of a nonrelativistic neutron that has a de broglie wavelength of 9.9 × 10−12 m. (h = 6.626 × 10−34 j • s, mneutron = 1.675 × 10−27 kg, 1 ev = 1.60 × 10−19 j)
The Kinetic energy of the nonrelativistic neutron which has a De Broglie wavelength of [tex]9.9 * 10^{-12}[/tex] m is [tex]8.375 * 10^{4}[/tex] Eu.
A moving item or particle might have power of a certain type called kinetic energy. An item gains kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving item or particle's mass and motion speed determine its kinetic energy.
The energy an object has as a result of motion is referred to as kinetic energy. It is defined as the effort needed to move a body of a particular mass from rest to the desired velocity. Unless its speed changes, the body retains the kinetic energy it gained during acceleration.
[tex]lambda D=9.9[10^{-12} ]\\h=6,626[10^{-34} ]\\m= 1.675[10^{-27} \\KE= \frac{h^{2} }{2m[lambda D^{2} } ]\\=13.4[10^{-15} ] joule\\KE = 8.375[10^{4} ]eu[/tex]
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An electron is located 4. 22 mm away from an isolated proton. If the distance between the two particles is increased to 8. 44 mm, what happens to the electrical potential energy of the electron and why?.
If the distance between the two particles is increased to 8.44 mm, the electrical potential energy will increase because work must be done to separate two particles that attract one another. Hence option(A) is correct.
The square of the distance between the charges has an inverse relationship with the potential energy. Additionally, it depends on whether the two charges have the same sign or the opposite sign; if they have the same sign, potential energy will decrease, but if they have the opposite sign, it will increase.
Which energy has potential?The energy that a thing retains due to its position in relation to other objects, internal tensions, electric charge, or other variables is known as potential energy.
Common examples of potential energy include the gravitational potential energy of an object, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field. The International System of Units uses the joule as its unit of energy, represented by the letter J. (SI).
It takes effort to separate two particles because the positive and negative charges are attracted to one another. Thus, there will be an increase in electrical potential energy.
your question is incomplete but most probably your full question was An electron is located 4.22 mm away from an isolated proton. If the distance between the two particles is increased to 8.44 mm,
what happens to the electrical potential energy of the electron and why?
A. The electrical potential energy will increase because work must be done to separate two particles that attract one another.
B. The electrical potential energy will remain the same because the electron and proton are both fundamental particles and their
charge cannot be changed.
C. The electrical potential energy will increase because larger energies are associated with greater distances.
D. The electrical potential energy will decrease because no work is necessary to increase the distance between particles that
demonstrate attraction.
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does the hanging a-tape have a stronger, weaker, or identical interaction with the partially neutralized a-tape?
The interaction between partially neutralized U-tapes may also be weaker compared to only one tape being neutralized, hence both tapes have reduced charge, which reduces the electrostatic between them.
To the correlation of the cooperation between two to some extent killed U-tapes and just a single U-tape being killed. Killing a U-tape includes lessening its charge by running a finger over piece of its length on the non-tacky side. At the point when one U-tape is somewhat killed, it debilitates the electrostatic power among it and another tape or a hand. In the event that both U-tapes are to some degree killed, the association between them is additionally liable to be more vulnerable contrasted with if by some stroke of good luck one tape was killed. This is on the grounds that decreasing the charge on the two tapes debilitates the electrostatic power between them. The power between tapes or a tape and a hand relies upon how much charge on each tape, with a more grounded charge bringing about a more grounded electrostatic power.
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The figure shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. What force (magnitude and direction) must you apply to the third rope to keep the knot from moving?
A total force of 8.0 units would be applied in the opposite direction of both ropes as a result.
What force is it?An influence known as force can alter an object's motion, direction, shape, or resting state. It is one of physics' fundamental ideas. Contact forces and field forces are the two types of forces.
The normal force, air resistance, and friction are all examples of contact forces. Gravity, the electric force, and the magnetic force are all examples of field forces. The magnitude, direction, and duration of a force can all be measured.
A force's magnitude indicates its strength, and its direction indicates its direction of action. The amount of time a force is applied is its duration.
The knot must have zero net force in order to remain stationary. To put it another way, all of the forces must add up to zero. As a result, you will need to apply forces of 3.0 units in the first rope's opposite direction and 5.0 units in the second rope's opposite direction.
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Two forces F1and F2act on the screw eye. If their lines of action are at an angle θapart and the magnitude of each force is F1=F2=F. Determine the magnitude of the resultant force FRand the angle between FRand F1.Parallelogram Law Of Vector Addition:If two vectorsF1and F2are acting at angle θbetween them , the resultant of these two vectors is given asR=√F21+F22+2F1F2cosθ
The resultant between two vectors will be given by the formula, R= √(2(F^2) + 2(F^2)cosθ)
In order to solve the equation for resultant between the two vectors F1 and F2 at an angle of θ, the following steps have to be followed:
The diagram for this problem is attached below
It is given in the problem that the magnitudes of forces F1 and F2 are equal,
F1= F2= F
In order to find the resultant force, the Parallelogram Law of Vector Addition comes into play.
This law states that if two vectors have the same initial point, and are dawn into a parallelogram, the summation of the two vectors will be the directed diagonal that starts at the initial point of the vectors.
Therefore, R= √(F1^2 + F2^2 + 2F1F2cosθ)
Now, since F1= F2= F,
R= √(F^2 + F^2 + 2(F^2)cosθ)
R= √(2(F^2) + 2(F^2)cosθ)
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What is the final speed of an object that starts from rest and accelerates uniformly at 4. 0 meters per second 2 over a distance of 18. 0 meters?.
Answer:
12 m/s
Explanation:
The final speed of an object that is subjected to uniform acceleration can be calculated using the equation:
v^2 = u^2 + 2as
where v is the final speed, u is the initial speed (in this case, 0 m/s since the object starts from rest), a is the acceleration (4.0 m/s^2 in this case), and s is the distance traveled (18.0 m in this case).
Plugging in the values, we have:
v^2 = 0 + 2 * 4.0 * 18.0
v^2 = 144
v = √(144)
v = 12 m/s
So the final speed of the object is 12 meters per second.
dr. ensign ran the top of utah half marathon in a time of one hour, 21 minutes and 19 seconds in august 2012. a half marathon is 13.1 miles. what was his average speed in units of km/h? assume the number of significant figures is limited by the distance (13.1 miles). conversion factors: 1 mile
15.555 km/h was his average speed in units of km/h.
What is speed ?
The rate of a directionally changing object's location. The SI unit of speed is created by combining the fundamental units of length and time. Meters per second (m/s) is the unit of speed in the metric system.
What is distance ?Distance is an object's overall movement, regardless of direction. Distance refers to the length of an object's real route as a whole. The displacement of an object between two points is defined as the straight line distance (shortest distance), measured from one position to the other.
Using the conversion units given
1 mile = 1.609347 km
13.1 miles = 21.0824457 km
1 hour, 21 minutes and 19 seconds
1 + (21/60) + (19/60 × 60)
1.35527 hours
So he ran 21.0824457 km in 1.35527 hours
Speed = 21.0824457/1.35527
= 15.555 km/h
Thus, 15.555 km/h was his average speed in units of km/h.
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Two point in a rectangular coordinate ytem have the coordinate (5. 0, 2. 7) and (−3. 1, 5. 5), where the unit are centimeter. Determine the ditance between thee point
8.57cm is the distance between thee point
Define distance .
The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The length of the entire journey taken to get from one point to another is the distance traveled.
Displacement is just the distance between the object's initial location and its final location. The amount of distance an object travels in a specific length of time is measured in terms of velocity.
d is [tex]\sqrt{x} (x2-x1)^2 + (y2-y1)^2[/tex]
x1 ,y1 is 5.0, 2.7
x2, y2 is -3.1, 5.5
d will be sqrt.(--3.1-5)^2 + (5.5-2.7)^2 i.e. 8.57cm
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A certain cylinder has a diameter that is twice the length of its height. If the volume of the cylinder is 64π cubic inches. What is the radius?
If the cylinder seems to have a 64 cubic inch volume, its radius becomes R = 8/2, as well as 4.
What is called cylinder?The three-dimensional shape of a cylinder is made up of two equal circular bases connected by a curved surface. The correct cylinder is created when the vertices of the round bases cross each other. The axis, which represents the height of a cylinder, has been the line segment that connects the two centres.
A cylinder's volume (V) is equal to the sum of its base's area (B) and height (H) (H)
Given V = 64(π)
B = (π) * [diameter(D)/2]^2 * (H)
Given D = 2 * H
V = π * (D/2)^2 * H, then
V = π * (2 * H/2)^2 * H = π * H^3
π * H^3 = 64π
H^3 = 64
H = 4
D = 8
Radius(R) = D/2
R = 8/2 = 4
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what is the formula that you use for, How many miles did a plane travel if it flew 455 miles per hour in 3 hours?
Answer: 1365 miles.
Explanation: Good evening.
There is no formula to determine how many miles a plane flies in a certain set of time. If it gives you the time, and distance, all you have to do is multiply. It tells you to find how many miles it traveled in total.
A cylindrical 4. 31 kg pulley with a radius of 0. 294 m is used to lower a 6. 27 kg bucket into a well. The bucket starts from rest and falls for 3. 55 s. The acceleration of gravity is 9. 8 m/[tex]s^{2}[/tex]
What is the angular acceleration of the cylindrical pulley?
Answer in units of rad/[tex]s^{2}[/tex]
The net torque on the pulley can be calculated as follows:
T = I * alpha
where
I = (1/2) * m * r^2 (moment of inertia of a cylinder)
m = 4.31 kg (mass of pulley)
r = 0.294 m (radius of pulley)
alpha (angular acceleration)
The gravitational force on the bucket creates a tension in the rope, which provides the torque on the pulley.
T = (m_bucket + m_pulley) * g * r
Equating the two expressions for T and solving for alpha, we get:
alpha = (m_bucket + m_pulley) * g * r / ((1/2) * m_pulley * r^2)
m_bucket = 6.27 kg
Substituting the values, we get:
alpha = (6.27 + 4.31) * 9.8 * 0.294 / ((1/2) * 4.31 * 0.294^2)
alpha = 11.58 rad/s^2
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a dc motor draws a current of 50 a at 230 v, and 1200 w of power is dissipated as heat by the motor. how much power is left for mechanical work?
The required amount of power left for mechanical work by the DC motor is calculated to be 10300 w.
The current drawn by the motor = 50 A
Voltage of the DC motor = 230 v
Power dissipated as heat = 1200 w
The formula to calculate power dissipated by the motor;
P = V I
where, P is power
V is voltage
I is current
So, putting the known values into the above equation, we have,
P = V I = 230 × 50 = 11500 w
As some amount of power is dissipated as heat, the power left for mechanical work is;
⇒ 11500 - 1200 = 10300 w
Thus, the required amount of power is 10300 w.
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Which two have the same magnitude of electric charge? (Select all that apply.)
(a) neutrons
(b) electrons
(c) protons
The electrons and protons have the same electric charge but of opposite nature.
What do you mean when you say "electric charge"?
Subatomic particles have a characteristic known as "electric charge" that makes them experience force while in an electric and magnetic field. Protons and electrons are the two main charge carriers for both positive and negative electric charges.
The quality of matter known as the electric charge is what causes it to create and feel the electric and magnetic effects.
Does the electric charge of protons and neutrons differ?
Neutrons lack charge, while protons and electrons have opposite charges. The size and direction of the charges on the proton and electron are the same.
In a neutral atom, protons and electrons exactly balance one another out in the same number.
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the cedula personal was optional during the spanish period
The cédula personal was optional during the Spanish period.
The cédula personal was a document used during the Spanish colonial period in the Philippines to keep track of the population and to collect taxes. It was a personal identification document that contained the holder's name, occupation, and tax status.
However, the requirement for a cédula personal was not strictly enforced during the Spanish period. While the Spanish government encouraged people to obtain one, it was not a mandatory requirement, and many people lived and worked without one.
This lack of strict enforcement was due to a number of factors, including limited resources for collecting taxes, the large size of the Philippines, and the limited number of government officials available to enforce the regulations.
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Complete Question:
Is the cedula personal was optional during the spanish period?
true or false all rhythm originating from the sinus node have matching p waves that are upright in most leads
The given statement about “all rhythm originating from the sinus node have matching p waves that are upright in most leads” is true because that is the most basic criterion for sinus rhythms.
A sinus rhythm is present when the sinus node is acting as the primary pacemaker and directing impulse production (waveform 1 and waveform 2). Activation of the atrium occurs in this context from right to left, superior to inferior, and front to back.
Since the right atrium is activated before the left, the usual P wave in sinus rhythm can look a little notched when this activation pattern is present. Lead II always has a positive (upright) P wave, while lead aVR always has a negative one. Lead I typically displays a positive P wave, but lead III can be any of these or more. Lead aVL has an ambiguous polarity. There is typically a terminal negative component of the P wave in the precordial (chest) leads V1 and V2, which reflects the left atrium's posterior location (relative to the right atrium) and later activation. In the other precordial leads, the P wave is frequently positive.
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Which of the following does not require good reaction time?
Select one:
A. Moving out of the way of a falling shelf
B.Removing your hand from a hot burner
C. Stopping while driving when you see the brake lights on the
car in front of you
D. Going to sleep
if the water is cooled at constant-specific volume to a pressure of 30 bar, determine the quality at the final state.
The quality at the final state is 2.96%.
Given,
m = 1 Kg p₂ = 30 bar
Water is cooled at a constant specific volume from p₁ to p₂
At first, water is at a critical point. The final quality will be determined if the water is cooled at a constant specific volume. The precise volume must be determined if the water expands at a constant temperature.
The critical pressure and critical temperature of the water are
[tex]p_c = 220.9 bar\\T_c = 647.13 K[/tex]
The specific volumes of the saturated liquid and saturated vapor corresponding to the saturation pressure of 30 bar are:
[tex]v_f = 1.2165 \times 13^{-3}\frac{m^3}{kg} \\v_g = 0.06668 \frac{m^3}{kg}[/tex]
Then the quality of state is:
[tex]v = v_f + x(v_g-v_f)\\\implies x = \frac{v - v_f}{v_g - v_f} \\\implies x = \frac{0.0031555-1.2165\times10^{-3}}{0.06668-1.2165\times10^{-3}}[/tex]
⇒ x = 0.0296
⇒ x = 2.96%
Therefore, the quality at the final state is 2.96%.
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a 747 jet needs to attain a speed of 180 mph to take off. it can accelerate from 0 to 180 mph in 12 seconds, how long must the runway be, assuming acceleration is constant?
The runway must be 482.4 m long. The result is obtained by using the equations in uniformly accelerated motion.
What are equations in uniformly accelerated straight motion?The equations apply in uniformly accelerated straight motion in horizontal dimension are
v₁ = v₀ + at
v₁² = v₀² + 2ax
x = v₀t + ½ at²
Where
v₀ = initial velocityv₁ = final velocitya = accelerationt = timex = distanceA 747 jet needs to attain a speed of 180 mph to takeoff. With
v₀ = 0v₁ = 180 mpht = 12 sa is constantFind the length of the runway!
The length of the runway here is equal to the minimum distance the jet must travel before takeoff.
Let's convert the unit of speed!
v₁ = 180 mph
v₁ = 180 × 1609.34 × 1/3600 m/s
v₁ = 80.5 m/s
The acceleration is
v₁ = v₀ + at
80,5 = 0 + a(12)
80.5 = 12a
a ≈ 6.7 m/s²
The minimum distance will be
x = v₀t + ½ at²
x = 0 + ½ (6.7)(12)²
x = ½ (6.7)(12)²
x = 482.4 m
Hence, the length of the runway must be 482.4 m.
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