By orthogonality, vectors tj < Vj, Vi> = 0.
Given,
v₁, v₂, and v₃ are mutually orthogonal vectors in r³.
Let v₁, v₂,...vₓ ∈ V form an orthogonal set if and only if
<Vi, Vj> = { 1 if i = j ; and 0 if i ≠ j}
Now, let v₁, v₂, and v₃ are non-zero vectors that form an orthogonal set.
Suppose t₁v₁ + t₂v₂ + t₃v₃ = 0; for some t₁, t₂, t₃∈ R
Then for any index t ≤ i ≤ 3, we have
< t₁v₁ + t₂v₂ + t₃v₃, Vi> = < 0, Vi> which equals to 0.
t₁<v₁,Vi> + t₂<v₂,Vi> + t₃<v₃, Vi> = 0
By orthogonality, tj < Vj, Vi> = 0
Or, tj = 0
Where, i = j = < 1, 2, 3>
Hence proved.
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How much energy is required to bring a 122g block of ice at -45 to steam at 190
degrees?
Answer:
Explanation:
[tex]The amount of the water, m = 200 L = 2.0×105 gThe initial temperature of the water, T1 = 18∘CThe final temperature of the water, T2 = 60∘CThe specific heat of the water, C = 4.184 J/g−∘CThe energy required by the water can be given asE = mC(T2−T1)→E = 2.0×105 g×4.184 J/g−∘C×(60−18)∘C→E = 2.0×105×4.184×42 J∴E = 3.51×107 JHence the energy required for this process is 3.51×107 J.[/tex]
a radar station detects an airplane approaching directly from the east. at first observation, the range to the plane is 385.0 m at 41.0 °
An airplane flying directly toward it from the east is spotted by a radar station. The distance to the plane at initial observation is 385.0 m at 41.0 °. 302.26m is the displacement.
What is displacement?Displacement is defined as a shift in an object's position. It is a vector quantity with direction and magnitude. An arrow pointing from the starting location to the finishing position is used to represent it. For instance, if an object moves from position A to position B, its position changes. The term used to describe this change in an object's position is displacement.
The instantaneous velocity of the item is the rate at which the displacement changes as a function of time when studying the motions of objects across time. Therefore, the instantaneous speed is different from the velocity, or the rate at which the distance traveled along a particular path changes over time. The temporal rate of change can also be used to define the velocity. The velocity of P (for example, a point representing the position of a passenger walking on the train) may be referred to as a relative velocity as opposed to an absolute velocity, which is computed with respect to a point which is considered to be "fixed in the space," if one takes into consideration a moving initial position or, equivalently, a moving origin (e.g., an initial position or the origin which is fixed to a train wagon, which in turn moves on its rail track) (such as, for instance, a point fixed on the floor of the train station).
Therefore,
d1= 385.0m
∅ = 41°
and ∅=124° , d2= 795.0m
r1= d1sin∅j+d2cos∅i
=385sin41°j+795cos41°i
=252.59j+599.98i
|r1|= [tex]\sqrt{63801.70+359976.00} ( r=\sqrt{a^{2}+b^{2} }[/tex] if |r| = ai+bj)
=650.98m
similar for r2,
=d1sin124°j+d2cos124°i
=319.16j+(-444..40)i
|r2|=[tex]\sqrt{101863.10+19749.36}[/tex]
=348.72m
so displacement |r2-r1| = 302.26m
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At which location could another charge be placed so that the net force on it would be zero? another way to ask the same question: at which location, a->h, is the electric field zero?
Between a negative and positive charge along the line connecting the two charges, the electric field may be zero. if the two charges have the same size. When there is no longer any net force between the two charges, the third charge should be positioned between the two charges.
The internet pressure is the vector sum of all forces acting on an item.
When an item is in equilibrium, whether it is at rest or moving at a constant speed, there is no net force acting on it. A vector can only have magnitudes of zero when all of its components are zero.
In mechanics, the term "net force" refers to the vector sum of all forces acting on a particle or object. The internet pressure, which is a single pressure, replaces the influence of the real forces on the particle's motion. The net pressure is the sum of all forces acting on an item.
Newton's second regulation, which says that F = ma, wherein F represents the net force, can be used to compute the net force. The item's mass is given with the aid of m. Acceleration is a.
The internet force performing on an object is 0 whilst it is in equilibrium, whether it's far at rest or moving at a consistent pace.
handiest whilst all of a vector's components are 0 can a vector have magnitudes of zero. the general pressure acting on an item is referred to as the net force. while the forces are equal and cancel every different out, it will become zero. If there may be a internet force performing on an object, it's going to accelerate in that direction; but, except the object is shifting simple, this is not the same as the path of movement.
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100 points pls help
With what will a car hit a tree if the car has a mass of 3,000 kg acceleration of m/s^2
What force would be needed to make 10kg bowling ball acceleration of 3m/s^2
What would be the mass of a truck if it is accelerating at a rate of 5m/s^2 and hits a parked car with a force of 14000 N
What is the acceleration of a softball if it has a mass of 0.50 kg and hits the catcher's glove with a force of 25 N
How much does a suitcase weigh if has a mass of 22.5 kg
What would the mass of a rock falling from the sky if it hits the ground with the force of 147N
Find the acceleration of the stacks of books pictured if the stack has a total mass 1.5 kg
A kg model airplane is traveling at a speed 33m/s.
The operator than increases the speed up to 45 m/s in seconds
How much force did the engine need in order to make this change.
Answer:
According to Newton's second law of motion, the acceleration of a body is directly proportional to the force acting on the body and inversely proportional to its mass. The formula for this law is
a
=
F
m
, from which we get the formula
F
=
m
a
. When mass is in kg and acceleration is in
m/s/s
or
m/s
2
, the unit of force is
kgm/s
2
, which is read as kiligram-meter per second squared. This unit is replaced with an N in honor of Isaac Newton. Your problem can be solved as follows:
Known/Unknown:
m
=
3000kg
a
=
2m/s
2
Equation:
F
=
m
a
Solution:
F
=
m
a
=
3000kg
x
2m/s
2
=
6000kgm/s
2
=
6000N
Explanation:
ikikikiki
Answer:
6000
Explanation:
a car is moving forward at 55 mi/hr . what is the direction of the velocity vector?
a, forward
b, backward
c, right
d, left
pls help
an object moving with uniform acceleration has a velocity of 11.0 cm/s in the positive x-direction when its x-coordinate is 2.91 cm. if its x-coordinate 3.25 s later is −5.00 cm, what is its acceleration?
The acceleration of the object is 5.3 cm/[tex]s^{2}[/tex] and is directed towards the negative x - axis.
We have an object moving with uniform acceleration along the + x axis.
We have to determine of the acceleration of object after 3.25 seconds.
According to the question -
initial velocity = u = 11 cm/s along +x axis.
Now, using the second equation of motion -
[tex]$S=ut +\frac{1}{2}at^{2}[/tex]
S = x(2) - x(1) = - 5 - 2.91 = - 7.91 = 7.91 cm along -x axis.
u = 11 cm/s
Substituting the values -
7.91 = 11 x 3.25 + 0.5 x 3.25 x 3.25 x a
7.91 = 35.75 + 5.3a
a = - 5.3 cm/[tex]s^{2}[/tex]
Hence, the acceleration of the object is 5.3 cm/[tex]s^{2}[/tex] and is directed towards the negative x - axis.
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Two cars travel along a straight road. When
a stopwatch reads t = 0.00 h, car A is at
XA= 48.0 km moving at a constant speed of
36.0 km/h. Later, when the watch reads
t = 0.50 h, car B is at XB = 0.00 km moving
at 48.0 km/h. Answer the following
questions, first graphically by creating a
position-time graph, and then algebraically
by writing equations for the positions XA
and XB as a function of the stopwatch
cime, t.
The equation for position of car A is [tex]x_{a}[/tex] ( t ) = 36 t + 48.
The equation for position of car B is [tex]x_{b}[/tex] ( 0.5 ) = 36 ( 0.5 ) + c.
The position function in one dimension is written as x ( t ) = vt + c. This equation is for a function starting at t = 0.
x = Distance
t = Time
v = Initial Velocity constant
c = Initial position constant
For car A ,
t = 0
c = 48 km
v = 36 km / h
[tex]x_{a}[/tex] ( 0 ) = 36 ( 0 ) + 48
[tex]x_{a}[/tex] ( 0 ) = 48 km, which is the distance at which car A starts to move from.
For car B,
t = 0.5 hr
c = 0
v = 48 km / h
[tex]x_{b}[/tex] ( 0.5 ) = 48 ( 0.5 ) + 0
[tex]x_{b}[/tex] ( 0.5 ) = 24 km
[tex]x_{b}[/tex] ( 0 ) = 48 ( 0 ) + c
[tex]x_{b}[/tex] ( 0 ) = c
Therefore,
The equation for position of car A is [tex]x_{a}[/tex] ( t ) = 36 t + 48.The equation for position of car B is [tex]x_{b}[/tex] ( 0.5 ) = 36 ( 0.5 ) + c.To know more about position equation as a function of time
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Infrared light, though it may be invisible, has many of the same characteristics of visible light. true or false?
True, infrared light, though it may be invisible, has many of the same characteristics as visible light.
They both travel at the speed of light i.e, 3 x 10^8 m/s.
They both follow the rules of reflection and refraction.
Infrared light and visible light are types of electromagnetic waves.
As shown in the adjoining image, in an electromagnetic wave, the electric field and the magnetic field are perpendicular to each other. Also, the direction of the propagation of the wave is perpendicular to both electric and magnetic fields.
Other than the two kinds of waves mentioned above i.e visible and infrared, the electromagnetic spectrum includes other waves also like X-rays, gamma rays, radio waves, microwaves, and ultraviolet rays.
The waves that are a part of the electromagnetic spectrum have different wavelengths and frequencies, as shown in the adjoining image but they share some common characteristics like:
They travel at the speed of light i.e, 3 x 10^8 m/s.
They obey the rules of reflection and refraction.
Hence, infrared light, though it may be invisible, has many of the same characteristics as visible light.
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True, infrared light, though it may be invisible, has many of the same characteristics as visible light.
They both travel at the speed of light i.e, 3 x 10^8 m/s. They both follow the rules of reflection and refraction. Infrared light and visible light are types of electromagnetic waves.
As shown in the adjoining image, in an electromagnetic wave, the electric field and the magnetic field are perpendicular to each other. Also, the direction of the propagation of the wave is perpendicular to both electric and magnetic fields.
Other than the two kinds of waves mentioned above i.e visible and infrared, the electromagnetic spectrum includes other waves also like X-rays, gamma rays, radio waves, microwaves, and ultraviolet rays.
The waves that are a part of the electromagnetic spectrum have different wavelengths and frequencies, as shown in the adjoining image but they share some common characteristics like:
They travel at the speed of light i.e, 3 x 10^8 m/s.
They obey the rules of reflection and refraction.
Hence, infrared light, though it may be invisible, has many of the same characteristics as visible light.
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What type of semiconductor is prepared by doping as into si?
a) p-type
b) n-type
c) intrinsic
d) e-type
e) none of these
N- type of semiconductor is denoted by positive ion and free electron.
What is semiconductor?An object known as a capacitor is one that uses an electric field to store electrical energy. There are two terminals on this passive electrical component.
Capacitance is the name for a capacitor's result. A capacitor is a component made to increase the capacitance in a circuit, even though there is some capacitance between any two electrical conductors that are close to one another in a circuit. Condensers and condensators were the previous names for capacitors. Although condenser microphones, sometimes known as capacitor microphones, are an important exception, this word and its cognates are still often used in many other languages outside English.
Practical capacitors come in a wide variety of physical shapes and constructions, and they are used in a variety of ways. A minimum of two electrical conductors are typically found in a capacitor.
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What force must the compressed air exert to lift a car weighing 13,300 n? give your answer in newtons.
The compressed air must exert a force of 1318.14 N on the small piston in order to lift the car weighing 13300 N.
What is force?
The concept of force is commonly explained in terms of Newton’s three laws of motion.
According to Newton’s first principle, a body that is at rest or moving at a uniform rate in a straight line will remain in that state until some force is applied to it.
The second law says that when an external force acts on a body, it produces an acceleration in the direction of the force. The magnitude of the acceleration is directly proportional to the magnitude of the external force and inversely proportional to the quantity of matter in the body.
Newton’s third law states that when one body exerts a force on another body, the second body exerts an equal force on the first body.
Because force has both magnitude and direction, it is a vector quantity.
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Lance is working in a library using a trolley to carry books. As he stacks books from the trolley on shelves, it gets easier to push or pull the trolley. Which part of Newton’s laws of motion explains the increased ease of moving the trolley?
Answer:
It is the law of f=ma because the lighter the trolley is, the easier it is to push it, because it doesn't have as much mass,
Explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
How are earthquake epicenters active volcanoes and mountain ranges distributed on the map?
Answer:
Volcanoes and earthquakes are not randomly distributed around the globe.
Explanation:
Instead they tend to occur along limited zones or belts. With the understanding of plate tectonics, scientists recognized that these belts occur along plate boundaries.
For 21-25. Refer to this Problem A A basket of fruits which is on top of a 3.5m high table has a PE of 44.1 J. What is the mass of the basket of fruits?
According to the given statement The mass of the basket of fruits is 1.2 kg.
What is the meaning of mass?A measurement of inertia, the fundamental property of all stuff. In essence, it's the resistance of a mass of matter to changing its direction or speed in reaction to the application of a force. The more mass a body possesses, the smaller the change that is brought about by an applied force.
Briefing:GPE = mgh
GPE = gravitational potential energy.
m = mass in kilograms (kg).
g = gravitational field strength in (N/kg).
h = change in height in meters (m).
GPE = 44.1 J
g = 9.8 N/kg
h = 3.5 m
Fill in the given values in the formula to find m:
44.1 = m * 9.8 * 3.5
44.1 = 34.3m
m = 44.1/34.3
m = 1.28571429
m = 1.2 kg
The mass of the basket of fruits is 1.2 kg
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If the soil can hold a lot of water, it has
Answer: Soils with smaller particles (silt and clay) have a larger surface area than those with larger sand particles, and a large surface area allows a soil to hold more water. In other words, a soil with a high percentage of silt and clay particles, which describes fine soil, has a higher water-holding capacity.
Silty clay loam: 1.80-2.00
Texture: Inches of water storage per foot of soil .
Explanation: hope this helps!!!!
What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 50 v/m ?
The magnetic field amplitude of an electromagnetic wave 1.66[tex]10^{-7}[/tex]T
Magnetic field is the portion of space near a magnetic body or a current-carrying body in which the magnetic forces due to the body or current can be detected.
The relationship between the magnetic field amplitude of the electric field and the magnetic field in an electromagnetic wave is E=cB
where
E is the electric field amplitude
B is the magnetic field amplitude
c is the speed of light
For this electromagnetic wave, we have E=50v/m
So we can solve the formula to find B:
B=E/c = [tex]\frac{50v/m}{3*10^{8}m/s }[/tex]
=1.66[tex]10^{-7}[/tex]T
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an object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function. v
Based on the calculations, the instantaneous acceleration of this object at time, t = 2 seconds is equal to 2 m/s^2.
What is velocity?Velocity can be defined as the distance covered by an object per unit of time. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction. Also, velocity can be measured as meter per seconds.
Mathematically, the velocity of any physical object can be calculated by using this formula:
Velocity = displacement/time
What is an instantaneous acceleration?An instantaneous acceleration can be defined as a continuous function of time which gives the ratio of change in velocity of a physical object. Mathematically, instantaneous acceleration can be calculated by taking the derivate of the velocity function.
Taking the derivate of the velocity function, we have:
Velocity, v = 4 + 0.5t^2
dv/dt = 0 + (0.5 × 2)×t^{2-1}
dv/dt = t
Substituting the value of time (t), we have:
Instantaneous acceleration, dv/dt = t
Instantaneous acceleration, dv/dt = 2 m/s^2.
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Complete Question:
An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function: v = 4 + 0.5t^2
The instantaneous acceleration of the object at t = 2 seconds is:
answer choices
2 m/s^2
4 m/s^2
5 m/s^2
6 m/s^2
8 m/s^2
If of work is done on a system, and of heat leave the system, what is the net change in internal energy?
W is the system's overall work product. When the system performs more work than it does for itself, W is positive. The first law of thermodynamics, U=QW, relates the change in the system's internal energy, U, to heat and work.
The internal energy of a system drops when it interacts with its environment. The internal energy of a system grows when work is done on it. Particles accelerate and pick up kinetic energy when energy is applied to increase the temperature. Potential energy is raised when a substance melts or boils because energy is expended in severing the connections holding the particles together.
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What is the term used to describe the energy of a system that is available to do work?.
The term used to describe the energy of a system that is available to do work is free energy.
What is free energy?Free energy is the energy that is available in a particular chemical system to do useful work.
The Gibbs free energy denoted by G is the enthalpy of a system minus the product of its entropy and absolute temperature.
It is referred to as free because the energy is readily available anytime. Free energy is measured in kilojoules per mole (KJ/mol).
Therefore, it can be said that the term used to describe the energy of a system that is available to do work is free energy.
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This system is now run in reverse as a refrigerator. how much heat does it extract from the cold reservoir when 900 j of work are done on the system? qc =
1500 j is extracted from the cold reservoir when 900 j of work are done on system .
We only need to think about total energy transmitted in terms of work and heat to find a solution to this issue. Essentially, the first law of thermodynamics conjugates this.
Evaluation :
The total work performed in the heat engine is if we consider the heat taken as positive and the heat released as negative.
[tex]W_{1}[/tex] = 2500 - 1000
[tex]W_{1}[/tex] = 1500 j
For the case of the engine pumps the Energy absorbed is
[tex]W_{2}[/tex] = 1500 j
In this way the ratio between the two would be
Ratio [tex]W_{1} /W_{2}[/tex] = 1
So it is reversible, because the state of efficiency of the body is totally efficient.
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the nec requires that when a suspended ceiling grid is used to support lay-in type lighting fixtures, .
The nec requires a suspended ceiling grid is used to support lay-in type lighting fixtures - the grid be securely fastened together
Does the NEC deal with spill lighting fixtures or mild pollution?
The national electrical Code does now not deal with the difficulty of "spill lights" or "light pollutants" from one belongings to some other because undesirable illumination isn't a(n) ____________________ trouble.
What have to lighting fixtures intended for set up in wet locations be marked with?
A luminaire installed in a bath, in which it's miles in near proximity to steam and water splash ought to be a humid- or wet-location luminaire and marked “suitable for Damp locations” or “appropriate for moist places.”
What article of the NEC defines outlet and receptacle?
210-21(b) Receptacles A “Receptacle,” as described in Article one hundred, is a contact device hooked up at an outlet for the connection of an attachment plug. The words “receptacle” and “receptacles” appear quite often within the country national electrical Code (NEC).
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If the initial velocity of an object is upward in the positive direction, what must the sign of the acceleration due to gravity be in a calculation?
Therefore, the direction of motion is positive for upward motion if an object is travelling vertically up. Since gravity accelerates downhill, it is assumed that this acceleration is negative.
Depending on the sign convention you desire to adhere to, the sign of the acceleration caused by gravity (g) might be either positive or negative. G will be positive if you decide to make the downward direction positive and the upward direction negative (an often-used convention). The thing is either standing still or descending. The initial velocity of an object is zero meters per second if it is dropped from a height rather than being hurled.
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If a car drives up an incline at a constant speed, what is the magnitude of its acceleration?.
If there is a hill, it will move more slowly. It will continue moving at the same speed if the surface is flat. Gravity is what causes a slope’s change in speed.
Things move more quickly when moving downhill and more slowly when moving upwards (slow down).
If an object’s speed is constant, can it accelerate?Yes, many individuals initially find this counter-intuitive because they overlook the fact that acceleration can still occur even when an object maintains a constant speed.
What forces are at work when an automobile is climbing a hill?The force that is sent up the hill is powered by the car’s engine. Because the engine makes the drive wheels rotate, the road applies this force, which is actually static friction, to the drive wheels.
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Find the wavelength of radiation that can eject 2.00-ev electrons from calcium electrode. the work function for calcium is 2.71 ev.
Radiation with a wavelength of 263.9 nm can eject a 2.00 -eV electron from a calcium electrode. Calcium has a piece function of 2.seventy one eV.
The expelled photoelectrons are E = 2.0 eV, so
⇒ [tex]2.0 eV = E_{in} -2.71 eV[/tex]
⇒ [tex]E_{in}=2.0 eV +2.71eV[/tex]
⇒ [tex]E_{in} = 4.71 eV[/tex]
in Joules, it is
⇒ [tex]E_{in} =4.71*1.6*10^{-19} J[/tex]
⇒ [tex]E_{in} =7.536*10^{-19} J[/tex]
Since [tex]E_{in}=h\nu=\frac{hc}{\lambda}[/tex], the wavelength must be
[tex]\Rightarrow \lambda = \frac{hc}{E_{in} }[/tex]
[tex]\Rightarrow \lambda=\frac{(6.64*10^{-34}Js)(3*10^{8}m/s) }{7.536*10^{-19} J}[/tex]
[tex]\Rightarrow \lambda=263.9\times10^{-9} \; m[/tex]
[tex]\Rightarrow \lambda=263.9 \;n m[/tex]
inside the photoelectric impact, the electricity of the photoelectrons chosen from metallic with work function ∅ thanks to misguided radiation of the entirety
If radiation moves a calcium electrode with the work feature ∅ = 2.seventy one eV and the power of radiation equals
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What fraction of the entire electromagnetic spectrum is spanned by visible light?.
Visible light covers a tiny fraction of the electromagnetic spectrum
Electromagnetic Spectrum is the range of all electromagnetic frequencies, including radio waves, microwaves, infrared waves, visible light, ultraviolet light, x-rays and gamma rayVisible Light is the part of the electromagnetic spectrum that consists of waves detectable by the human eyeRadio waves are longest wavelengths and lowest frequenciesMicrowaves are EM waves with higher frequncies than radio, but lower than infrared; used for radar, cell phones, cooking.gamma rays are Electromagnetic waves with the shortest wavelengths and highest frequencies.Ultraviolet are waves that are part of the electromagnetic spectrum and can't be seen by the eyes; they have a higher frequncy than visible light but a lower frequency than x-raysTo know more about electromagnetic spectrum visit : https://brainly.com/question/23727978
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a motorcyclist passing a road junction moves due west for 8 seconds at a uniform speed of 5m/s. he then moves due north for another 6 seconds with the same speed. at the end of the 6 seconds, his displacement is 50m in what direction?
Answer: N53oW
Explanation: Hope this helps :)
Education/training
What are the typical entry-level education requirements, on-the-job training, licenses,
certifications, work experience, and advancements?
What are some important qualities that are helpful in performing this work?
the questions are about being a nurse btw please help !!!!
Answer: You need your bachelor's to become a nurse at an entry level.
Explanation: Most nurses enter nursing knowing they will eventually earn their baccalaureate degree. While it’s possible to obtain an Associate Degree in Nursing (ADN), capped by earning one’s RN license by taking and passing the standardized NCLEX-RN exam, many nurses choose to further their education—and career prospects—by obtaining their baccalaureate degree. Requirements vary by state, but at the very least, the path to RN usually involves earning an Associate Degree in Nursing (ADN), qualifying a candidate to take the standardized national licensure examination known as NCLEX-RN. Only after taking this exam and passing may a nurse work as an RN. This is true of all states and the District of Columbia. Some localities may also have additional requirements.
RN - Registered Nurse
Hope this helps
:)
if you double your driving speed what happens to your stopping distance (the distance it takes to stop the car)?
If you double your driving speed, then the stopping distance will be four times the original.
What is the equation of motion?Equations of motion are equations that describe a physical system's behavior in terms of its motion as a function of time. Equations of motion, The three equations of the motion are,
v - u = atS = ut + 0.5(at²)v² - u² = 2aswhere
S is the distance,
u is the initial velocity,
v is the final velocity,
t is the time,
a is the acceleration.
Given that the car is traveling at a speed and is needed to be stopped, therefore, the car will deaccelerate. Also, the final velocity of the car will become 0. Therefore, we can write,
v² - u² = 2as
Substitute the values,
Final velocity, v = 0Initial velocity, u = uDistance covered, s = s₁Acceleration, a = -aTherefore, we can write,
v² - u² = 2as₁
(0)² - u² = 2(-a)s₁
-u² = -2as₁
u² = 2as₁
s₁ = u² / 2a
Now, if you double your driving speed. Therefore, we can write,
v² - u² = 2as
Substitute the values,
Final velocity, v = 0Initial velocity, u = 2uDistance covered, s = s₂Acceleration, a = -aTherefore, we can write,
v² - u² = 2as₂
(0)² - (2u)² = 2(-a)s₂
-4u² = -2as₂
4u² = 2as₂
s₂ = 4u² / 2a
Since u²/2a is equal to s₁, therefore, we can write,
s₂ = 4(u² / 2a)
s₂ = 4(s₁)
Hence, if you double your driving speed, then the stopping distance will be four times the original.
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Explain how emission lines and absorption lines are formed. in what sorts of cosmic objects would you expect to see each?
Absorption lines are created when electrons gain energy from photons, whereas emission lines are created when electrons lose energy (continuous spectrum). Gaseous clouds are sorts of cosmic objects in which we would expect to see each.
When an atom, element, or molecule absorbs a photon with an energy equal to the difference between two energy levels, absorption lines are created. The atom, element, or molecule is considered to be in an excited state when this happens because one electron is elevated to a higher energy level.
In a spectrum, an emission line will be seen if a source emits radiation at a particular wavelength. This emission happens when an excited atom, element, or molecule switches to a lower-energy form.
Gaseous clouds are sorts of cosmic objects in which we would expect to see each. Some of the light at specific wavelengths is scattered when it travels through the atmosphere's gas, producing darker bands. These lines were catalogued by heating common components until they created light and became known as "spectral lines."
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at highway speeds, a particular automobile is capable of an acceleration of 1.6 m/s2. at this rate, how long does it take to accelerate from 80 km/h to 110 km/h?
By using uniform motion, the time taken to accelerate is 5.21 second.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, we know that
vo = 80 km/h = 80 x 1000/3600 m/s = 22.22 m/s
vt = 110 km/h = 110 x 1000/3600 m/s = 30.56 m/s
a = 1.6 m/s²
By using first equation, we can calculate the time taken
vt = vo + a . t
30.56 = 22.22 + 1.6 . t
1.6t = 8.34
t = 5.21 second
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a key falls from a bridge that is 45 m above the water. it falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is released. what is the speed of the boat?
12 m from the point of impact when the key is released, the speed of the boat is 4.0m/s.
What do you mean by the term speed?Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path. In other words, velocity is a vector, whereas speed is a scalar value. Let’s take an example, 15km/hr shows the speed of a vehicle but 15km/hr east shows the velocity of the vehicle. Speed of an object can be calculated mathematically in a simple way. Speed of an object can be found by dividing distance traveled by the object by time taken to cover that distance.
The speed of the boat can be given by , v = d/t
Now, d = 12 m and t is the time the key takes to fall into the boat
Taking the initial time(time at which the key is dropped) to be 0 we calculate t when height(y) is 45 m.
y = ½(gt)^2
t = (2y/g)^(1/2)
t = ((2*45)/9.8)^(1/2)
t = 3.03 s
Therefore, speed of the boat = (distance covered by the boat)/(time taken)
distance = 12/(3.03)= 4.0 m/s
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