Velocity is the speed and the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
Initial velocity of first ball is given as, u₁ = 22 m/s. Initial velocity of second ball, u₂ = 15 m/s, Mass of first ball is given as, m₁ = 3.5 kg, Mass of second ball, m₂ = 1.7 kg. Let v be the velocity of combined mass after collision. The formula to find the velocity of combined mass after collision in an inelastic collision is v = (m₁u₁ + m₂u₂) / (m₁ + m₂)
Put the given values in the above equation, v = (3.5 × 22 + 1.7 × (-15)) / (3.5 + 1.7)= 5.045 m/s. Let h be the maximum height that combined two balls of putty rise above the collision point. Using the conservation of energy, the potential energy gained by combined two balls of putty is equal to the kinetic energy loss in the collision.
According to the law of conservation of energy, the initial kinetic energy of the system is equal to the potential energy gained by the system.1/2 (m₁ + m₂) v² = (m₁ + m₂)gh where g is the acceleration due to gravity and h is the maximum height that combined two balls of putty rise above the collision point. Put the given values in the above equation.1/2 (3.5 + 1.7) × (5.045)² = (3.5 + 1.7) × 9.8 × hh = 0.557 m. The combined two balls of putty will rise to a height of 0.557 m above the collision point.
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The _____________ of a lens or mirror is a point on the optic axis a distance f in front of or behind the lens or mirror.
focal plane
paraxial ray approximation
optic axis
light ray
focal point
The focal point is a critical concept in optics that helps to determine the behavior of light passing through lenses and mirrors.
The focal point of a lens or mirror is a fundamental concept in optics. It refers to a point on the optic axis, which is a line that passes through the center of the lens or mirror and is perpendicular to its surface. The distance from the lens or mirror to the focal point is known as the focal length (f). The focal point is a critical point in optics because it determines the behavior of light rays passing through the lens or mirror.
For a converging lens, the focal point is a point on the optic axis on the opposite side of the lens from the object. Light rays from an object that is parallel to the optic axis converge at the focal point after passing through the lens. For a diverging lens, the focal point is also on the opposite side of the lens, but the light rays diverge away from the focal point.
Similarly, for a concave mirror, the focal point is a point on the optic axis in front of the mirror, while for a convex mirror, the focal point is behind the mirror. The behavior of light rays reflected or refracted by a lens or mirror can be understood by considering the location of the focal point.
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which one of the four mentioned is not a plate boundary? select one: a. transform b. insurgent c. convergent d. divergent
One of the four mentioned is not a plate boundary is b. insurgent.
Plate tectonics is the theory that explains the movement of Earth's lithosphere, which is composed of large plates that glide over the mantle. The plates are separated by three types of plate boundaries: divergent, convergent, and transform. Transform boundary is where two plates slide past one another in opposite directions, either horizontally or diagonally. The San Andreas Fault is a well-known example of a transform boundary. Divergent boundaries are where two plates pull away from each other and new crust is created.
The Mid-Atlantic Ridge is an example of a divergent boundary and convergent boundary is where two plates move towards each other and one plate gets consumed or goes under the other. The Himalayas were created as a result of the collision of two convergent plates, the term insurgent is not used in plate tectonics. The correct term that describes the three main types of plate boundaries is not insurgent but instead transform, divergent, and convergent boundaries. So the correct answer is b. insurgent.
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when a platinum coil is submerged in liquid helium at temperature 4 kelvin, it is transformed into a) a semiconductor b) a superconductor c) a normal conductor d) a perfect insulator
A platinum coil turns becomes a superconductor when immersed in liquid helium at a temperature of 4 kelvin.
Energy from the outside is captured by the circulating fluid running through the coils, which then releases it through the interior coils into the building's interior. Superconductors have no electrical resistance as well as perfect diamagnetism. Cooper pairs of electrons are what cause superconductivity. The BCS theory, so named in honour of its three discoverers, describes how materials transform into "superb conductors" when their internal electrons cooperate to form Cooper pairs (or BCS pairs). When cooled to extremely low temperatures (near absolute zero, or roughly -273° Celsius), conductors completely lose all of their electrical resistance.
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Construct quantum mechanical operators for the following observables: (a) kinetic energy in one and in three dimensions, (b) the inverse separation, l/x, (c) electric dipole moment in one dimension
The quantum mechanical operators for the following observables are: (a) kinetic energy in one and in three dimensions is T = - (ħ^2 / (2m)) d^2/dx^2, and T = - (ħ^2 / (2m)) (∇^2) respectively, (b) the inverse separation is O = 1/x, (c) electric dipole moment in one dimension is μ = q x.
(a) Kinetic energy in one dimension:
The quantum mechanical operator for the kinetic energy in one dimension, T, can be written as:
T = - (ħ^2 / (2m)) d^2/dx^2,
where ħ is the reduced Planck's constant, m is the mass of the particle, and d^2/dx^2 represents the second derivative with respect to position.
Kinetic energy in three dimensions:
In three dimensions, the kinetic energy operator, T, can be expressed as:
T = - (ħ^2 / (2m)) (∇^2),
where ħ is the reduced Planck's constant, m is the mass of the particle, and ∇^2 is the Laplacian operator, which represents the sum of the second derivatives with respect to each spatial dimension.
(b) Inverse separation, l/x:
The quantum mechanical operator for the inverse separation, l/x, can be written as:
O = 1/x,
where x represents the position operator.
(c) Electric dipole moment in one dimension:
The quantum mechanical operator for the electric dipole moment in one dimension, μ, can be expressed as:
μ = q x,
where q is the charge and x represents the position operator.
Please note that the above expressions represent the quantum mechanical operators for the respective observables and should be used within the framework of quantum mechanics to analyze and calculate physical properties and behavior.
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at+waht+temperature+must+you+run+this+reaction+to+achieve+97%
Temperature is the degree of hotness or coldness of an object or substance. The SI unit of temperature is Kelvin."97%": The question suggests that a reaction must be run at a specific temperature to achieve 97% yield or completion. Yield refers to the amount of product obtained from a reaction.
To achieve 97% yield or completion, the reaction must be run at a specific temperature. Temperature plays an essential role in chemical reactions since it affects the rate of reaction, activation energy, and equilibrium. The temperature at which a reaction runs optimally, producing the most product, is known as the reaction's optimum temperature. As a result, the temperature must be controlled during a chemical reaction.To achieve 97%, the reaction must be run at a specific temperature.
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Which statement about mass is correct?
A. Mass is measured in Newtons (N).
B. Mass is the measure of the amount of matter in an object.
C. Mass is a force that attracts objects toward each other.
D. The mass in an object is variable.
Answer: B
Explanation: B
The mass of an object can be considered as the measure of the amount of matter in an object. Thus, the correct option is B.
What is Mass?Mass is a quantitative measure of inertia. It is a fundamental property of matter. Mass of an object is the resistance which a body of matter offers to change its speed or position upon the application of force. The greater the mass of an object, the smaller the change produced by an applied force on that object.
Mass is the amount of matter which is present in any object or a body. For example, a table, a chair, a glass, and even air has mass.
Therefore, the correct option is B.
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Imagine that a coffee filter is falling through the air after being released from a specific height. The filter accelerates for a time and rotates a bit so that the bottom of the filter is facing down, but then reaches a terminal velocity. Now, it is continuing to fall at a constant speed without tipping or rotating. At this moment, is the coffee cup in equilibrium?
The moment when the coffee filter fall from the upward, it is in the equilibrium.
A coffee filter is falling through the air after being released from a specific height. The filter accelerates for a time and rotates a bit so that the bottom of the filter is facing down, but then reaches a terminal velocity. Now, it is continuing to fall at a constant speed without tipping or rotating. When it is falling from the height, the gravitational force acting on it and the air resistance acting on it balances out each other. Then there is no net force on the coffee filter that is acting on it either ways. When the filter is going downwards many are the forces they are working on it, but when it is going down all the forces acting on it got cancel out and only the net forces acting on majorly cancel each other effect and it nullifies them and their effect and we got a net zero force on it. Hence, we can conclude that at the moment, when the coffee filter is falling from the height the forces are balance out and there is no net force and the coffee cup is in equilibrium.
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30 12
w
Find the total
equivalent
resistance for the
circuit.
40 12
w
9.0V
50 Ω
2012 10 12
Reg = [?] 12
Answer:
6
.40 recharge
1.0v
45.0v
In the circuit shown above, the current through the ammeter is 20 mA and the voltmeter indicates 1.0 V. What is the current through the 40 resistor?
A. 7.5mA
B. 10mA
C. 20mA
D. 40mA
Answer:
20mA
Explanation:
because it is connected in series with the ammeter
The current through the 40Ω resistor in the given circuit is 20mA, which is explained below.
Current through the resistors:The volate across resistor R is 1V, as indicated by the voltmeter.
Since the potential of the battery is 3V, according to Kirchoff's voltage law, the voltage drop across 20Ω resistors must be 1V each since they are indentical.
Let a total current I passes through 20Ω resistor as it is connected to the battery in series. From Ohm's law:
20Ω × I = 1V
I = 50mA
Now the current indicated by the ammeter is 20mA which splits according to the reistors of 15Ω and 30Ω which are connected in parallel. Then again the current adds up to 20mA when leaving the set of parallel resistors, through the 40Ω resistor.
So the current through the 40Ω resistor is 20mA
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A car engine has power than a horse because a car engine does the same amount of work in time. Yasmin and Raj each had 10 boxes of equal weight to stack next to each other on the same shelf, at the same height and in the same arrangement. Yasmin completed the task in 2 minutes, while Raj took 3 minutes to stack his boxes. Raj applied power than Yasmin because his stacking took time to do the same amount of work.
Answer:
A car engine has more power than a horse because a car engine does the same amount of work in time. Yasmin and Raj each had 10 boxes of equal weight to stack next to each other on the same shelf, at the same height and in the same arrangement. Yasmin completed the task in 2 minutes, while Raj took 3 minutes to stack his boxes. Raj applied less power than Yasmin because his stacking took more time to do the same amount of work.
Explanation:
A car engine has more power than a horse because a car engine does the same amount of work in less time. Raj applied less power than Yasmin because his stacking took more time to do the same amount of work.
What is power?The quantity of energy moved or converted per unit of time is known as power in physics. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power.
Energy divided by time represents the dimension of power. The watt (W), which equates to one joule per second, is the unit of power in the International System of Units (SI).
Another popular unit of measurement is horsepower (hp), which is equivalent to a horse's power; one mechanical horsepower is equal to around 745.7 watts.
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A box of paper is labeled 24lb paper. This means that 500 sheets (counted number) of paper size 17in x 22in weighs 24 pounds (The paper industry in the US has not switched over to metric.). On earth, 1.0lb, using the standard acceleration of gravity, corresponds to 453.6g. Calculate the mass of a single piece of paper that measures 21.59cm x 27.94cm
Answer:
The mass of a single paper is approximately 0.047 lb/paper which in SI Units is approximately 21.77 g/paper
Explanation:
The given information on the size and the weight of paper are;
The mass of a box of 500 sheets of paper = 24 lb
The number of sheets in the paper = 500 sheets
The dimensions of the paper = 17 in. × 22 in., which is equivalent to 43.18 cm × 55.88 cm
The mass of a single paper = The mass of the box of paper/(The number of sheets of paper present in the box)
The mass of a single paper = 24 lb/500 = 0.047 lb/paper
Given that 1 lb = 453.6 g, we have;
0.047 lb/paper = 0.047 lb/paper×453.6 g/(lb) = 21.77 g/paper
The mass of a single paper = 0.047 lb/paper = 21.77 g/paper.
Answer:
5.349g
Explanation:
The other post forgot about the differing answer. They wanted the answer for 21.59cm*27.94cm. when they get that 0.047=43.18cm*55.88cm we can set a ratio;
0.047/43.18*55.88=X/21.59*27.94=0.01179
then we do the same;
0.01179lb(453.6g/1lb)=5.349
(*the number is bigger but we have 4 sig figs*)
answer questions show work #3
3. Determine the value of ID and VDs for the DS following amplifier. 10 RD 10V 3KD Points 0.47μF 01 G= 0.47μF Hilt RG 1.5MO -1V N5486 VGSoff = -4V IDSS = 14mA
The given amplifier circuit is a common-source amplifier. The equivalent circuit diagram of the amplifier includes a MOSFET N5486 transistor. We can determine the drain current (ID) and drain-source voltage (VDS) using the following equations:
1. Voltage at the source terminal (VS) is calculated using Ohm's law: VS = IS x RS.2. The drain current (ID) can be calculated using the equation ID = IS (1 + GVin), where Vin is the input voltage, G is the voltage gain, and IS is the current flowing through RD.Let's calculate the values of ID and VDS:
Given:- IS = VDD / RD = 10V / 10Ω = 1A- Vin = -1V / (1.5 x 10^6Ω + 0.47μF) = -0.6666667μA (using voltage divider rule)- G = -RD / RS = -10Ω / 3kΩ = -0.003333 Calculating ID:ID = 1A (1 - 0.003333 x 0.6666667 x 10^6)≈ 0.997A = 997mACalculating VDS:VDS = VDD - IDRD= 10V - 997mA x 10Ω≈ 10V - 9.97V≈ 0.03VTherefore, the values of ID and VDS are approximately ID = 997mA and VDS ≈ 0.03V, respectively.
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Toy cars 1, 2, and 3 are launched horizontally with the trajectories shown below. Cars 1 and 2
are launched from a 15 m high cliff, while Car 3 is launched from a 30 m high cliff. We can
ignore air friction.
Initial launch speed of the cars are in order as Vcar 1 = Vcar 2< Vcar 3
Speed (often abbreviated as "s") is a scalar variable that describes how much an object's location changes over time or how much it changes per unit of time. The average speed of an item in a period of time is the distance traveled by the object divided by the duration of the period.
Time divided by distance are the speed-related metrics.. The meter per second (m/s) is the SI unit of speed, while the kilometer per hour (kph) is the most often used unit of speed in daily life.
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How is inertia responsible for removing most of the water from wet clothes in a washing machine
Answer:
Centripetal force is when everything is fixated at the center point and is accelerated inwards towards the center. This centripetal force is assisted by inertia to remove the water from the washing machine.
Explanation:
Follow instagrm at --> mvnnyvibesFollow instagrm at --> mvnnyvibesAstronauts brought back 500 lb of rock samples from the moon. how many kilograms did they bring back? 1 kg = 2.20 lb
A. 227 kg
B. 498 kg
C. 500 kg
D. 1,100 kg
Answer:
1100 kg
Explanation:
500 lb x 2.20lb (1kg) =1100kg
An air pistol fires a pellet forwards.
What is the motion of the air pistol?
A - The air pistol moves backwards with speed greater than the pellet.
B - The air pistol moves backwards with speed less than the pellet.
C - The air pistol moves forward with speed greater than the pellet.
D - The air pistol moves forward with speed less than the pellet.
The air pistol is moving backwards faster than the pellet. Subtract that stronger force's amplitude from the weaker department's magnitude to discover the centripetal acceleration.
What are a definition and an example of motion?Motion can be characterized as a shift in an object's location with regard to time. Motion can be heard in a variety of sounds, such a book falling off a table, water running from a faucet, rattling windows, etc. There is motion even in the air we breathe!
What generates motion?Motion is the result of forces You need to exert a push or a pull, which is by definition a force, in order to move something. The object will be static or continue going without accelerating in the absence of a force.
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For a flat mirror, when there’s a ray that travels parallel to the surface where the object sits and it hits the surface of the mirror, the ray will then be reflected back in the opposite direction like the following diagram. Why can’t it be the same for a concave or convex mirror when the light ray travels parallel to the principle axis?
When a light ray travels parallel to the principal axis of a curved mirror, the ray will not be reflected back in the opposite direction like in the case of a flat mirror.
What is a ray diagram?The reason why this does not occur is because the surface of a curved mirror is not a flat surface and it has a varying curvature, which causes the reflected rays to behave differently compared to the flat mirror.
In the case of a concave mirror, when a light ray travels parallel to the principal axis and strikes the mirror, it is reflected back towards the focus of the mirror. This is because the concave mirror surface curves inward, causing the reflected light rays to converge towards the focus.
In the case of a convex mirror, when a light ray travels parallel to the principal axis and strikes the mirror, it is reflected back in a direction away from the focus of the mirror. This is because the convex mirror surface curves outward, causing the reflected light rays to diverge away from the focus.
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A tennis ball "A" is released from rest down a 10.0 m long inclined ramp with a uniform acceleration of 5.0 m/s2 . Another tennis ball "B" is initially located at the same height as ball "A" right above the lower edge of the ramp. Ball "B" is thrown upward with some initial speed at the same instant as the release of ball "A". A) What was the initial velocity of ball "B" so that "A" and "B" reach the bottom of the ramp at the same time?
Answer:
4.8 m/s
Explanation:
For tennis ball "A", we are told that;
Initial velocity; u = 0 m/s
Distance; h = 10 m
Acceleration; a = 5 m/s²
Thus, using Newton's equation of motion, we can find time(t).
h = ut + ½at²
10 = 0 + ½(5)t²
10 = ½(5t²)
t² = 2 × 10/5
t² = 4
t = √4
t = 2 seconds
Now, this time would be the same for ball B since we are told that they reach the bottom at the same time.
Now, since ball B is thrown upwards, it means it is thrown against gravity. Thus;
h = -ut + ½gt²
10 = -2u + ½(9.8)(2²)
Where u is initial velocity of Ball B.
Thus;
10 = -2u + 19.6
2u = 19.6 - 10
2u = 9.6
u = 9.6/2
u = 4.8 m/s
What's the free body diagram for:
Mr. Seifert needs to push a cardboard box down the hallway for Ms. Wang. The box has a mass of 40 kg and he is pushing it with an acceleration of 2 m/s/s. Because the cardboard does not slide easily, there is a friction force of 25 Newtons acting on the box to the LEFT. How much force is Mr. Seifert applying to the box to move it forward to the RIGHT?
(a) The free body diagram for representing all the forces acting on an object.
(b) The force Mr. Seifert is applying to the box to move it forward to the RIGHT is 105 N.
What is free body diagram?
A free body diagram is a graphical illustration of all the forces acting on an object.
The force applied by Mr Seifert is calculated by applying Newton's second law of motion as follows;
F - Ff = ma
where;
F is the applied forceFf is the force of frictionm is the mass of the cardboarda is the acceleration of the cardboardThe given parameters include;
mass of the cardboard = 40 kg
force of friction = 25 N
acceleration of the cardboard = 2 m/s²
The force applied by Mr Seifert is calculated as follows;
F = Ff + ma
F = 25 N + (40 kg x 2 m/s²)
F = 105 N
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A wave travels an average distance of 6 meters in 3 seconds. What is the wave's velocity?
Answer:
2m/s
.................
An online video daredevil is filming a scene where he swings across a river on a vine. The safety crew must use a vine with enough strength so that it doesn't break while swinging. The daredevil's mass is 82.0 kg, the vine is 11.0 m long, and the speed of the daredevil at the bottom of the swing has been determined to be 8.60 m/s. What is the minimum tension force (in N) the vine must be able to support without breaking?
The minimum tension force (in N) the vine must be able to support without breaking is 3,073.1 N.
What is tension?The tension in a flexible string or rope is the force required to keep the string or rope stretched taut when pulling its end to opposing sides. Tension force formula:
F= ma
F = Tension force (N)
m= Mass (kg)
a= Acceleration (m/s²)
Here,m= 82
kgv= 8.60 m/s
L= 11.0 m
For the swinging motion of the daredevil,
Equating the sum of forces to the mass times acceleration:
F= (mv²)/L
F= (82 kg x 8.60² m/s²) / 11.0 m
F= 54,343.6 N
Therefore, the minimum tension force (in N) the vine must be able to support without breaking is 3,073.1 N.
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How is mass and weight alike?
At highway speeds a car can accelerate at 1.7 m/s2.
At this rate how long does it take to accelerate from
23.6 m/s to 27.8 m/s?
Answer: 2.5 seconds
Explanation:
We know that the acceleration is:
a(t) = 1.7 m/s^2
To get the velocity function, we must integrate over time, and we will get:
v(t) = (1.7m/s^2)*t + v0
Where v0 is the initial velocity, in this case, we assume that we start at 23.6m/s, then the initial velocity is:
v0 = 23.6 m/s
Then the velocity equation is:
v(t) = (1.7m/s^2)*t + 23.6 m/s
Now we want to find the value of t such v(t) = 27.8 m/s
Then:
v(t) = 27.8 m/s = (1.7m/s^2)*t + 23.6 m/s
27.8 m/s - 23.6 m/s = (1.7m/s^2)*t
4.2 m/s = (1.7m/s^2)*t
4.2m/s/(1.7m/s^2) = t = 2.5 s
Then at that acceleration, you need 2.5 seconds.
If you have 5 protrons and 6 neutrons how many electrons would you need to make a neutral atom
an object is placed at the position x1 = 33 cm and a second mass that is 7/3 times as large is placed at x2 = 167 cm. find the location of the center of mass of the system.
To find the location of the center of mass of the system, we can use the formula: x_cm = (m1*x1 + m2*x2) / (m1 + m2) where m1 and m2 are the masses of the objects and x1 and x2 are their respective positions.
In this case, we know that the first object is placed at x1 = 33 cm and the second object, which is 7/3 times as large, is placed at x2 = 167 cm. Let's assume the mass of the first object is m1 and the mass of the second object is 7/3*m1 (since the second object is 7/3 times as large as the first).
Substituting these values into the formula, we get:
x_cm = (m1*33 cm + (7/3)*m1*167 cm) / (m1 + (7/3)*m1)
Simplifying this expression, we get:
x_cm = (33 + 7*167/3) / (1 + 7/3)
x_cm = (33 + 391) / (10/3)
x_cm = 124.2 cm
Therefore, the location of the center of mass of the system is at x_cm = 124.2 cm.
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A rock falls from rest off a high cliff. How far has the rock fallen when its speed is 39.2 meters per second?
( plss I need help lol)
The rock fell as far as 78.4 meters.
Given the following data:
Initial speed = 0 m/s (since the rock fell from rest). Final speed = 39.2 m/sWe know that the acceleration due to gravity (a) for an object is equal to 9.8 meter per seconds square.
To find how far (distance) has the rock fallen, we would use the third equation of motion;
\(V^2 = U^2 + 2aS\)
Where:
V is the final speed. U is the initial speed. a is the acceleration. S is the distance covered.Substituting the given parameters into the formula, we have;
\(39.2^2 = 0^2 + 2(9.8)S\\\\1536.64 = 0 + 19.6S\\\\19.6S = 1536.64\\\\S = \frac{1536.64}{19.6}\)
Distance, S = 78.4 meters.
Therefore, the rock fell as far as 78.4 meters.
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A car travels at 15.0 m/s for 10.0 s. It then speeds up with a constant acceleration of 2.0 m/ 2 for 15.0 s. At the end of this time, what is its velocity?
The velocity of the car travelling at 15 m/s for 10 second speeding up with constant acceleration of 2m/s^2 for 15 second is 45 m/s.
What is velocity and how it is calculated out to be 45 m/s?Velocity as studied earlier is a quantitative quantity which describes the relation between displacement and time as velocity equals displacement per unit time.Here in this question is given the velocity with which the car is travelling for the 10 seconds and then the car speeds up.The speed up speed of the car was at a constant acceleration of 2m/s^2 for 15 seconds.That means Vo = 15 m/s , a = 2m/s^2, and t = 15 seconds, using the relation V = Vo + at .Then putting the values, V= 15 + 2x15 = 15+30 = 45 m/s , hence the velocity of the car would be 45 m/s.To know more about velocity visit:
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A student climbs to the top of the gym and drops a baseball to the ground below. A physics student standing nearby has a motion sensor and determines that the baseball hit the ground with a velocity of 17 m/s. if you ignore air resistance, how long was the baseball falling through the air?
Answer:
The baseball was falling during 1.733 seconds.
Explanation:
The baseball experimented a free fall, which is a particular case of uniformly accelerated motion, in which object is accelerated by gravity. In this case, we need to determine the time spent by the ball before hitting the ground (\(t\)), measured in seconds, which is determined by the following kinematic formula:
\(t = \frac{v-v_{o}}{g}\) (1)
Where:
\(v_{o}\), \(v\) - Initial and final speeds of the baseball, measured in meters per second.
\(g\) - Gravitational acceleration, measured in meters per square second.
If we know that \(v_{o} = 0\,\frac{m}{s}\), \(v = 17\,\frac{m}{s}\) and \(g = 9.807\,\frac{m}{s^{2}}\), then the time spent by the baseball is:
\(t = \frac{17\,\frac{m}{s}-0\,\frac{m}{s} }{9.807\,\frac{m}{s^{2}} }\)
\(t = 1.733\,s\)
The baseball was falling during 1.733 seconds.
Just like Coke is a type of soda, __________ is a type of ___________.
A.concentration,.equilibrium
B..equilibrium, concentration
C.diffusion, osmosis
D.osmosis. diffusion
Answer:
osmosis diffusionExplanation:
ok it's correct
The Hamiltonian of a spin system is given by H = (S₂ + S₂), where the constants ħ² A and B are real numbers. (a) [5pt] Find the eigenvalues of H when the spin of the system is 1/2. (b) [5pt] Find the eigenvalues of H when the spin of the system is 2. (*) Remark: You may attempt to diagonalize a 5×5 matrix. But there is a much simpler way to solve this problem.
(a) When the spin of the system is 1/2:
Eigenvalues: E₁ = (ħ²A)(3/4) - (ħ²B)(ħ/2) and E₂ = (ħ²A)(3/4) + (ħ²B)(ħ/2).
(b) When the spin of the system is 2:
Eigenvalues: E₁ = (ħ²A)2S(S + 1) - (ħ²B)ħ√(2S(S + 1)) and E₂ = (ħ²A)2S(S + 1) + (ħ²B)ħ√(2S(S + 1)).
To find the eigenvalues of the Hamiltonian H = (ħ²A)S² + (ħ²B)S₂, where A and B are real numbers, we need to consider the spin operators for the corresponding spin values.
(a) When the spin of the system is 1/2:
For a spin-1/2 system, the spin operators are given by:
S² = (3/4)ħ²,
S₂ = (ħ/2)σ₂,
Where σ₂ is the Pauli matrix for the y-component.
Substituting these values into the Hamiltonian, we have:
H = (ħ²A)(3/4) + (ħ²B)(ħ/2)σ₂.
The eigenvalues of σ₂ are ±1, so the eigenvalues of H can be found by plugging in these values:
Eigenvalues: E₁ = (ħ²A)(3/4) - (ħ²B)(ħ/2) and E₂ = (ħ²A)(3/4) + (ħ²B)(ħ/2).
(b) When the spin of the system is 2:
For a spin-2 system, the spin operators are given by:
S² = 2ħ²S(S + 1),
S₂ = ħ√(2S(S + 1))σ₂,
Where σ₂ is the Pauli matrix for the y-component.
Substituting these values into the Hamiltonian, we have:
H = (ħ²A)2S(S + 1) + (ħ²B)ħ√(2S(S + 1))σ₂.
The eigenvalues of σ₂ are ±1, so the eigenvalues of H can be found by plugging in these values:
Eigenvalues: E₁ = (ħ²A)2S(S + 1) - (ħ²B)ħ√(2S(S + 1)) and E₂ = (ħ²A)2S(S + 1) + (ħ²B)ħ√(2S(S + 1)).
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