The required distance when the relation between velocity and time is given is calculated to be at t = 0, 2 sec.
As given in the problem, v = ds/dt
ds = v dt
Taking integral on both sides, we have,
∫ ds = ∫ v dt
Replacing v by t-2 in the above equation.
∫ ds = ∫ (t - 2) dt
S = t²/2 - 2t
The minimum distance is when S = 0, t²/2 - 2t = 0
t( t/2 - 2) = 0
At t = 0, 2 sec, it is the minimum distance covered.
Thus, the required answer is t = 0, 2sec.
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much like mass and energy, the amount of electric charge in the universe is constant and cannot be created or destroyed. in physics, what law governs such a relation? if the total electric charge remains constant in a closed system, how can some objects change their charges?
The law that governs the conservation of electric charge in a closed system is known as the law of conservation of charge.
According to this law, the total amount of electric charge in a closed system remains constant and cannot be created or destroyed. As for how objects can change their charges in a closed system, it is because the distribution of electric charge can change.
For example, when two objects with different electric charges are brought into contact, electrons can flow from one object to the other until both objects have the same electric potential. This transfer of electrons results in a change in the charge of each object, but the total charge remains the same.
Another way objects can change their charges is through the process of ionization, where an atom loses or gains electrons, resulting in a change in the electric charge of the atom. Again, the total charge remains constant, as the lost or gained electrons must go somewhere.
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What is the frequency of a red light in the air where its wavelength is 6.8x10^-7?
Answer:
below
Explanation:
speed of light = wavelength X Frequency
3 x 10^8 m/s = 6.8 x 10^-7 X f
frequency = 4.41 x 10^14 hz ( or 441 TERAHERTZ)
Which would make a better reflector, a piece of metal or a piece of wood? Explain why.
A piece of metal would make a better reflector than a piece of wood because metals are good conductors of electricity.
A piece of metal is a better reflector compared to wood because it has a much higher conductivity, which results in a higher reflectivity. Metals have free electrons that are not bound to individual atoms, allowing them to respond to electromagnetic waves and reflect them back. Wood, on the other hand, is an insulator, meaning it does not conduct electricity or reflect electromagnetic waves as efficiently as metal.
Additionally, metal surfaces are usually smooth and flat, which allows them to reflect light or electromagnetic waves more efficiently, as the wave front remains more organized and less dispersed. Wood surfaces, on the other hand, tend to be rough and irregular, which can scatter the incoming light or electromagnetic waves, reducing their reflectivity.
In conclusion, metal is a better reflector than wood because of its higher conductivity, ability to respond to electromagnetic waves, and smoother surface.
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our sun's blackbody temperature is about 6000 k and its peak radiation occurs at a wavelength of about 0.5 micrometers. some stars are bluer than our sun with temperatures of 10,000 k. at what wavelength does their radiation peak?
The peak radiation of a star with a temperature of 10,000 K will occur at a wavelength of approximately 0.3 micrometers.
What is peak radiation?Generally, The peak wavelength of a blackbody's radiation is inversely proportional to its temperature.
This means that as the temperature of the blackbody increases, the wavelength of its peak radiation decreases.
In this case, the temperature of the star is higher than our sun, so its peak radiation will occur at a shorter wavelength.
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A 45 kg firefighter is working on a ladder 20 m above the ground. What will be the firefighter's gravitational potential energy decrease by when the firefighter descends to a height of 5 m above ground?
Height above Earth affects the gravitational potential energy of an item. We know the height of the ball lowers since it is rolling down a hill.
How do you calculate decrease in gravitational potential energy?Moving downward over a distance h results in an equal increase in kinetic energy and a loss of gravitational potential energy. This can be expressed mathematically as -PEg = KE.The potential energy of an object diminishes while its kinetic energy rises. The increase in kinetic energy perfectly offsets the reduction in potential energy.A doubling of the height will result in a doubling of the gravitational potential energy since the gravitational potential energy of an object is precisely proportional to its height above the zero point. The gravitational potential energy will triple for every threefold increase in height.The gravitational potential energy of the ball then reduces as a result of the height decreasing.To learn more about energy refer to:
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the frequency of the lowest standing-wave mode on a 1.0- m -long string is 40 hz . part a what is the wave speed on the string?
The wave speed on the string with frequency of the lowest standing-wave mode on a 1.0-m-long string is 40 Hz = 80 m/s
The fundamental frequency or first harmonic is the lowest possible frequency at which a string can vibrate to form a standing wave pattern. The second harmonic is the lowest frequency at which a string can vibrate; the third harmonic is the third lowest frequency; and so on.
The equation:
v = f x 2L
Where:
v = velocity/ speed of the wave (m/s)
f = frequency (Hz)
L = length of the string (m)
Hence, the wave speed of the string:
v = (40 Hz) (2 x 1.0)
= 80 m/s
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A converging lens with a diameter of 49.8 cm
forms an image of a satellite passing overhead.
The satellite has two green lights (wavelength
508 nm) spaced 1.1 m apart.
If the lights can just be resolved according
to the Rayleigh criterion, what is the altitude
of the satellite?
Answer in units of km.
The altitude of the satellite is 883.89 km
What is the altitude?Generally, The Rayleigh criterion for resolution states that the minimum angle, θ, between two point sources that can be resolved is given by:
θ = 1.22 * λ / D
where
λ is the wavelength of light and
D is the diameter of the lens.
The minimum distance, d, between two point sources that can be resolved is given by:
d = θ * L
where
L is the distance from the lens to the image.
Given the green lights have a wavelength of 508 nm, we can convert it to meters:
λ = 508 * 10^-9 m
Given the diameter of the lens is 49.8 cm, we can convert it to meters:
D = 49.8 cm * (1 m / 100 cm)
= 0.498 m
Using the Rayleigh criterion, we can find the minimum resolvable angle:
θ = 1.22 * λ / D
= 1.22 * 508 * 10^-9 / 0.498
= 1.24449799*10^{-6} radians
We know the lights on the satellite are spaced 1.1 m apart, so:
d = 1.1 m
Solving for the distance from the lens to the image, L:
L = d / θ
= 1.1 m / 1.24449799*10^{-6} radians
=883890.53 m
Finally, converting the distance to kilometers:
L = 883890.53 m * (1 km / 1000 m)
= 883.89 km
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a physician orders a diagnostic mammogram for a 42-year-old woman. which of these most likely happened before this decision was made?
A 42-year-old lady is prescribed a diagnostic mammography by a doctor. On a routine screening mammography, abnormal tissue was discovered. Values for the CBC, blood markers, or blood chemistry were abnormal.
An x-ray of a breast for diagnostic purposes is called mammogram.
As cancer cells are less specialised than healthy cells, they create abnormal proteins.
If cancer has been indicated by a suspicious lump or abnormal blood tests, then the type of body imaging which is next step is called diagnostic mammogram.
Chemotherapy functions to combat cancer because it targets characteristics of fast growing cancer cells. This means they target specific points of the cell cycle to stop cell division.
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If a car is at rest and starts traveling at 14 m/s, how long would it take to reach 28 m from the start?
Answer:
Explanation:
The cars velocity is 14m/s. That means for every second, the car moves 14m. Now, if the car wants to reach 28m, going 14m/s, it will take 2 seconds for the car to reach 28m.
why would the warmer parcel cool at a slower rate between 1.5 and 5 km?
The warmer parcel cools at a slower rate between 1.5 and 5 km because of the temperature inversion in the atmospheric boundary layer.
A temperature inversion occurs when the temperature of the air increases with height, instead of decreasing. This can create a stable layer of warm air that acts as a barrier, slowing the rate at which heat is lost from the surface.
In the case of the warmer parcel, the temperature inversion acts to slow the cooling rate, allowing it to remain warm for a longer period of time. A temperature inversion is a common phenomenon in the atmospheric boundary layer, the layer of the atmosphere closest to the Earth's surface.
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frame-by-frame analysis of news video tape shows huge waves, moving at 17 m/s, hitting the ship's bridge every 5 seconds. the ship length that is most endangered by this wave is .
The ship length that is most endangered by this wave is the bridge length. The bridge length is determined by the length of the portion of the ship that is above the waterline and is most vulnerable to incoming waves.
The frame-by-frame analysis of the news videotape shows that the waves are moving at 17 m/s and are hitting the ship's bridge every 5 seconds. This means that the wave is traveling faster than the ship can navigate and the bridge length is most endangered by the wave. The bridge length is the most vulnerable part of the ship because it is the first part to be hit by the wave, and the wave's energy can be focused on the bridge, potentially causing damage.
The wave's momentum can also cause the entire ship to be lifted up and down, which can damage the ship's structure, as well as cause instability. Additionally, the force of the wave can cause the ship to be pushed or pulled away from its intended path, which can also cause damage. Overall, the bridge length is the most endangered by the wave due to the speed, frequency, and force of the wave.
The bridge length is the part of the ship that is most vulnerable to the wave's effects and can be easily damaged or destroyed by the wave's energy. Therefore, it is important to take into account the wave's speed, frequency, and force when assessing the most endangered ship length.
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21.5 °c; volume of gas in syringe:
The values for the molar volume obtained from the two reactions are very close, and we can conclude that the molar volume of the gas produced in the reactions is approximately 5.3 × 104 L/mol at 21.5°C.
The molar volume of a gas can be calculated by dividing the volume of the gas by the number of moles of gas produced. To compare the values for the molar volume obtained from the two reactions, we need to determine the number of moles of gas produced in each reaction.
For experiment 1, the mass of zinc added was 0.100 g, and the molar mass of zinc is 65.38 g/mol, so the number of moles of zinc added is 0.100 g / 65.38 g/mol = 0.00153 mol. The volume of gas produced in the reaction is given by the volume in the gas syringe, which is 36.81 ml. At 21.5°C and 1 atm, 1 ml of a gas has a volume of 22.4 liters, so the volume of gas produced in the reaction is 36.81 ml * 22.4 L/ml = 817.24 L. Therefore, the molar volume of the gas produced in experiment 1 is 817.24 L / 0.00153 mol = 5.30 × 104 L/mol.
For experiment 2, the mass of zinc added was 0.200 g, and the molar mass of zinc is 65.38 g/mol, so the number of moles of zinc added is 0.200 g / 65.38 g/mol = 0.00306 mol. The volume of gas produced in the reaction is given by the volume in the gas syringe, which is 73.64 ml. At 21.5°C and 1 atm, 1 ml of a gas has a volume of 22.4 liters, so the volume of gas produced in the reaction is 73.64 ml * 22.4 L/ml = 1634.48 L. Therefore, the molar volume of the gas produced in experiment 2 is 1634.48 L / 0.00306 mol = 5.31 × 104 L/mol.
As we can see, the values for the molar volume obtained from the two reactions are very close, and we can conclude that the molar volume of the gas produced in the reactions is approximately 5.3 × 104 L/mol at 21.5°C.
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The complete question is:
Calculate and compare the value for the molar volume at 21.5 °C obtained based on the data for the first reaction with the value for the molar volume at 21.5 °C obtained using the second reaction. The molar mass of Zn is 65.38 g/mol. experiment 1 HCL: 45 ml Zn: 0.100 g pressure before zinc was added to HCL: 1.000 atm pressure after: 1.138 atm temp before: 21.5 C temp after: 22.3 C volume in gas syringe: 36.81 ml experiment 2 HCL: 45 ml Zn: 0.200 g pressure before zinc was added to HCL: 1.000 atm pressure after: 1.277 atm temp before: 21.5 C temp after: 23.0 C volume in gas syringe: 73.64 ml.
which of the following variables could influence the width of marine magnetic anomalies on the floor of the ocean? choose one or more: a. rate at which the plates are moving away from the mid-ocean ridge b. duration of the magnetic polarity event c. strength of the magnetic field d. frequency of sunspot activity e. latitude at which the anomaly formed
Option (A) and (B) -Duration of magnetic polarity event -rate at which the plates are moving away from mid-ocean ridge.
What determines the polarity of a magnet?
Electrons flow in the opposite direction through the wire, from negative to positive. However, the direction of the current determines the polarity of the electromagnetic field. The charge moves to the negative pole, which is the north pole of the magnet.
What is the definition of magnetic polarity?
All magnets have north pole and a south pole. The magnetic pole is strongest part of magnet. The north and south poles of a magnet attract each other. The two south poles and the two north poles repel each other. A magnetic field is area around a magnet that attracts or repels objects.
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If simultaneity is not an absolute concept, does that mean that we must discard the concept of causality? If event A is to cause event B, A must occur first. Is it possible that in some frames A appears to be the cause of B, and in others B appears to be the cause of A? Explain.
The concept of causality and simultaneity are central to our understanding of the world around us, but recent developments in physics have called their absolute nature into question. In this answer, we will explore the relationship between causality and simultaneity and whether the non-absoluteness of simultaneity implies a rejection of causality.
Causality refers to the idea that one event (A) is the cause of another event (B), meaning that event A must occur before event B. This relationship is a cornerstone of classical physics and is used to explain the behavior of physical systems. However, in the context of special and general relativity, the concept of simultaneity is not absolute, meaning that two events that appear to be simultaneous in one frame of reference may not be simultaneous in another.
In other words, the order of events can appear different in different frames of reference, which can result in A appearing to be the cause of B in one frame and B appearing to be the cause of A in another. This has led some physicists to question whether causality is an absolute concept or whether it is merely a relative concept.
In conclusion, while the non-absoluteness of simultaneity raises questions about the nature of causality, it does not necessarily imply a rejection of causality. Instead, it highlights the need for a more nuanced understanding of the relationship between causality and simultaneity in the context of modern physics.
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if a galaxy is at z =1.0, what does this mean? how is this typically measured?
The value "z = 1.0" is given to a galaxy redshift, which is a measurement of how much the galaxy's light's wavelength has been distorted as it travels through the expanding cosmos.
Redshift is expressed as a fractional value "z", where z = (λ observed - λ emitted) / λ emitted. In this case, "z = 1.0" means that the observed wavelength of light from the galaxy has been stretched by a factor of 1 (i.e., the wavelength has doubled). Redshift is typically measured using spectroscopy, which involves splitting the light from the galaxy into its individual spectral lines and comparing the observed wavelengths to the wavelengths of the same spectral lines in a laboratory or a theoretical reference spectrum. By measuring the redshift of a galaxy, astronomers can determine its distance from us and its motion relative to us. The interpretation of a redshift as a measure of distance is based on the idea that the universe is expanding, and that the farther away a galaxy is from us, the faster it will be moving away from us due to the expansion of the universe. This leads to an increase in the observed wavelength of its light (i.e., redshift), which can be used to estimate the galaxy's distance.
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A particle moves in such a way that its position z, in meters,is given as a function of t, in seconds, by the equations z=c1t^2-c2t^3
C1=2.12m/s/s C2=3.29m/s/s/s
The particle is at 0 twice. What is the time of the second occurrence of z=0 in seconds?
What is the displacement(m) of the particle between 2sec and 5 sec?
What is the velocity of the particle at t=0.657s?
The velocity is also at 0 twice. What is the time of the second occurence?
(1) The time of the second occurrence is 2.92 s (2) displacement is 29.24 m (3) velocity of the particle is 4.86 m/s (4) the time of second occurence is 2.94 s.
Given z = c1t^2 - c2t^3 and c1 = 2.12 m/s^2 and c2 = 3.29 m/s^3.
1) The particle is at z = 0 twice. To find the second occurrence, we set z = 0 and solve for t:
0 = 2.12t^2 - 3.29t^3
This is a cubic equation and can be solved using numerical methods or by using a computer algebra system.
The second solution is approximately t = 2.92 s.
2) The displacement of the particle between 2 s and 5 s can be found by finding the final position minus the initial position:
Δz = z(5s) - z(2s) = (2.12 × 5^2 - 3.29 × 5^3) - (2.12 × 2^2 - 3.29 × 2^3)
Δz = 29.24 m
3) The velocity of the particle is given by the derivative of the position function, so we can find the velocity at t = 0.657 s as:
v = dz/dt = 2c1t - 3c2t^2 = 2 × 2.12 × 0.657 - 3 × 3.29 × 0.657^2
v = 4.86 m/s
4) The velocity is at 0 twice. To find the second occurrence, we set v = 0 and solve for t:
0 = 2 × 2.12t - 3 × 3.29t^2
This is a quadratic equation and can be solved using the quadratic formula or by using a computer algebra system.
The second solution is approximately t = 2.94 s.
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Question - A particle moves in such a way that its position z, in meters, is given as a function of t, in seconds, by the equations z=c1t^2-c2t^3
1) The particle is at 0 twice. What is the time of the second occurrence of z=0 in seconds?
2) What is the displacement(m) of the particle between 2sec and 5 sec?
3) What is the velocity of the particle at t=0.657s? The velocity is also at 0 twice.
4) What is the time of the second occurence?
a cannon ball leaves a cannon traveling at 35 m/s at an angle of 45 degrees above the horizontal. determine the speed of the ball when it reaches 50 meters above the ground
The vertical speed of the ball will be 0.029 m/s, when it reaches 50 meters above the ground.
The projectile speed of the ball, v = 35 m/s
Angle of projectile motion, θ = 45°
Vertical component of velocity, u = 35sin45 = 24.75 m/s
Height of the ball, h = 50 m
Let the time taken to reach the ball is t sec, then by the second equation of motion,
h = ut - 0.5gt²
50 = 24.75×t - 0.5×9.81×t²
4.905t² - 24.75t + 50 = 0
On solving t = 2.52 & 4.905
Ignoring the t = 4.905 as it is during the freefall motion, so taking t = 2.52 sec.
Now by the first equation of motion,
v = u + at
v = u - gt
v = 24.75 - 9.81 × 2.52
v = 0.029 m/s
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an object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. the maximum displacement from equilibrium is a and the total mechanical energy of the system is e .what is the object's velocity when its potential energy is 23e ?
The velocity of the object is A√(k/3m), when its potential energy is 2/3E.
For simple harmonic motion,
kinetic energy + potential energy = total mechanical energy
When the displacement is maximum, = A, then kinetic energy will be zero, so total mechanical energy will be only potential energy = E
E = 0.5kA²
The spring constant is k, and the maximum displacement is A.
When potential energy is 2E/3, so kinetic energy would be K = E - 2E/3
K = E/3 = kA²/6
Let the velocity of the object is v.
0.5 mv² = kA²/6
v² = kA²/3m
v = A√(k/3m)
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--The given question is incomplete, the complete question is:
"An object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E.
What is the object's velocity when its potential energy is 2/3E?"--
if the ages of the earth and the moon are nearly identical, as believed, why are most rocks found on the moon so much older than rocks found on earth?
The age of the Earth and the moon are nearly identical, as believed, unlike the Earth, however most of the rock found on the moon are older than that found on the Earth. This is because, unlike the moon has no atmosphere to weather rocks or plate tectonic activity to destroy rocks.
What are tectonic plates?The movement of tectonic plates in the Earth's lithosphere and the eruption of volcanoes effectively recycles the rock on the surface, by consuming or burying the older rocks while creating the new ones. Over a period of time, some of the Earth's oldest rocks have been eroded through the action of air and water, both.
In contrast to bodies like the Moon and Mercury have remained essentially static for the time of billions of years. So, on them we see old surfaces which are heavily populated by craters that are formed from the massive meteoric impacts early in the history of the Solar System. These bodies are valuable as an enduring record of the history.
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correct answer is aaa
?
Answer:
it is in the direction of flow of elections
an electric dipole is in a uniform electric field. for which orientation is the potential energy of the dipole peast?
An electric dipole is in a uniform electric field. For The positive end of the dipole is in the direction of the electric field produces the least potential energy of the dipole.
ABOUT ELECTRIC DIPOLEThe electric dipole moment is a condition that shows the properties of a dipole in an electric field based on a vector. The existence of a moment is the result of a dipole which consists of a pair of equal electric charges. In the calculation, each charge is given a different sign. Another marker is the relatively close distance to each other.
The electric dipole moment will give information about the electric field generated by a dipole. The electric potential that arises due to the electric field is affected by the distance and the length of the dipole.
The total amount of electric potential generated can be known at each point of the charge that appears. The observation of the electric dipole moment is beyond the reach of the standard model.
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The graph shows the amount of daylight during months in Boston Ma. What best explains why the month of February has the shortest amount of daylight in the graph?
Help!!!!
The reason why the month of February has the shortest amount of daylight in the graph is most likely due to the tilt of the Earth's axis and its position in relation to the sun.
The Earth's tilt is at an angle of about 23.5 degrees, which means that different parts of the Earth receive different amounts of sunlight depending on the season.
In February, the northern hemisphere is tilted away from the sun, causing the sun's rays to hit the surface at a lower angle and for a shorter period of time each day. This results in shorter days and longer nights during the month of February, as shown in the graph.
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A cart with a mass of 120 kg collides with a stationary dumpster with a mass of 300 kg. Both the cart and the dumpster are free to roll in any direction. The cart and the dumpster stick together after the collision and move at 0.5 m/s. What other information is needed to determine the final momentum of the dumpster?
Other information needed to determine the final momentum of the dumpster is : the initial velocity of the cart.
What is collision?In physics, collision is any event in which two or more bodies exert force on each other in relatively short time. Although, most common use of the word collision refers to incidents in which two or more objects collide with great force, scientific use of the term implies nothing about the magnitude of force.
Collision is a short-duration interaction between two bodies or more than two bodies simultaneously causing change in the motion of bodies involved due to the internal forces acted between them during this.
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what is the magnitude of the resultant force (in nano-newtons) on the 9 nc charge at the origin? the coulomb constant is 8.98755 × 109 n · m2 /c 2 . answer in units of nn. answer in units of nn.
The magnitude of the resultant force (in nano-newtons) on the 9nc charge at the origin is 0nN.
The magnitude of the resultant force on the 9nC charge at the origin can be calculated using Coulomb's law. The equation is F = kQq/r2, where F is the magnitude of the force, k is the Coulomb constant (8.98755 x 10^9 N·m2/C2), Q and q are the charges of the two objects, and r is the distance between them. Since the charge at the origin is 9nC (0.000009 C) and the distance is 0, the resultant force is 0nN.
F = kQq/r2
Q = 9nC (0.000009 C)
r = 0 ; q = 0C
Coulomb constant "k" = 8.98755 x 10^9 N·m2/C2
put the value of "k", "Q", "q", "r" in F = kQq/r2
we get F = 0nN.
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which material is excellent for use as seals and diaphragm for water lubricated bearings? a. Rubber b.Titanium alloy c. Silicon d. Uranium
For seals and diaphragms in water lubricated bearings, rubber is an excellent material to use.
For seals and diaphragms in water lubricated bearings, rubber is an excellent material to use due to its properties of elasticity, flexibility, and durability. Rubber is able to withstand the pressure and wear caused by water movement, and its elasticity allows it to maintain a tight seal against the bearing surfaces.
Titanium alloys are known for their strength and corrosion resistance, but they may not have the necessary elasticity and flexibility for use as seals and diaphragms in water lubricated bearings. Silicon is commonly used in the electronics industry, but it may not have the necessary properties for use in these types of bearings. Uranium is a highly radioactive material and is not appropriate for use in seals or diaphragms in any type of machinery. Therefore, the answer is (a) rubber.
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When inspecting a roller bearing on a car for a hot box, the temperature indicator must be placed: On the lower half of the cup.
When inspecting a roller bearing on a car for a hot box, it is important to place the temperature indicator in the correct location in order to accurately detect any issues with the bearing. In this answer, we will explain why the temperature indicator must be placed on the lower half of the cup.
A hot box, also known as an overheated bearing, occurs when the temperature of a roller bearing becomes elevated due to friction or other factors. This can cause damage to the bearing, leading to reduced performance and potentially even failure. To detect hot boxes, a temperature indicator is used to measure the temperature of the bearing.
It is recommended to place the temperature indicator on the lower half of the cup for several reasons. First, the lower half of the cup typically experiences the highest temperatures due to the presence of friction in that area. By placing the temperature indicator on the lower half of the cup, it is possible to accurately measure the temperature of the bearing and detect any hot box issues.
Second, the temperature indicator will provide a more accurate reading when placed on the lower half of the cup compared to other locations, such as the outer race or the inner race. This is because the lower half of the cup is more directly exposed to the temperature of the bearing and is not affected by other factors such as temperature gradients or convection currents.
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a 1.15 kg ball (m1) moving at 5.00 m/s to the right hits a 2.15 kg ball (m2) head-on that is traveling at 3.50 m/s to the left. if this is an elastic collision, what is the velocity of each ball after the collision?
The speed of the ball having mass 1.15 kg and this 2.15 kg is 3.48m/s and 1.06m/s respectively after collision.
The ball having a mass of 1.15 kg is moving at a speed of 5m/s to the right and it hits A ball of mass 2.15 kg head on travelling with a speed of 3.5m/s to the left if the collision is elastic collision, then the speed of the balls after collision will be given by the formula,
v = 2mu/(M+m)
V = (M-m)U/(M+m)
Here,
m = 1.15 kg,
M = 2.15 kg,
u = 5m/s,
U = 3.5m/s.
v is speed of ball moving to right after collision and V is the speed of ball having mass 2.15 kg moving left after collision.
Putting values,
v = 3.48m/s and,
V = 1.06m/s.
So, the speed of the ball having a mass 1.15 kg after collision is 3.48m/s and the speed of the ball having mass 2.15 kg of the collision is 1.06m/s.
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how long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? in other words, find
The equations of motion are used to find the motion characteristics of an object with time.The time it takes the motorcycle to reach the car is approximately 5.39 seconds
Find the solution ?A) The time it takes the motorcycle to reach the car is approximately 5.39 seconds
B) The distance the motorcycle travel from the moment it starts to accelerate to the moment it catches up with the car is approximately 155 meters
The reason the above values are correct is as follows:
The given parameters are;
The initial speed of the car and the motorcycle, v₁ = 18.0 m/s
The initial distance between the motorcycle following the car = 58.0 m
The time after which the motorcycle starts to accelerate, t₁ = 5.00 secs
The acceleration of the motorcycle = 4.00 m/s²
The time at which the motorcycle catches up with the car = t₂
Required:
A) The time it takes the motorcycle to accelerate before it catches up with the car, which is to find t₂ - t₁
Method:
The distance moved by motorcycle to reach the car = The distance moved by the car in the same time + 58.0 meters
The appropriate equation of motion to use are s = u \cdot t + \dfrac{1}{2} \cdot a\cdot t^2 and d = u\cdot t
Where;
s = The distance between the motorcycle and the car = 58.0 m
u = The initial velocity of the motorcycle = 18.0 m/s
t = Δt = t₂ - t₁ = The time the motorcycle accelerates
a = The acceleration of the motorcycle = 4.00 m/s²
d = The distance moved by the car
By the method, we have;
s = d + 58.0
u \cdot t + \dfrac{1}{2} \cdot a\cdot t^2 = u \cdot t
Plugging in the values into the equation gives;
(18.0 \times t) + \dfrac{1}{2} \times 4 \times t^2 = (18.0 \times t) + 58.0
Cancelling the like term, (18.0 × t), on both sides of the equation gives;
\dfrac{1}{2} \times 4 \times t^2 = 58.0
2\cdot t^2 = 58.0
t = \Delta t = \sqrt{\dfrac{58.0}{2} } = \sqrt{29} \approx 5.39
The time it takes the motorcycle to reach the car, t ≈ 5.39 second
The time it takes the motorcycle to reach the car is approximately 5.39 seconds
B) Required:
The distance the motorcycle travels from the moment it starts to accelerate, t₁ to the time it catches up with the car, t₂
Method:
The distance travelled during the time interval t₂ - t₁ should be calculated
The distance, s, travelled during the time interval t_2 - t_1 = \Delta t = t is given as follows;
s = u \cdot t + \dfrac{1}{2} \cdot a \cdot t^2
From part (A), u = 18.0 m/s t = \sqrt{29} s, and a = 4.00 m/s², therefore;
s = 18.0 \times \sqrt{29} + \dfrac{1}{2} \times 4.00 \times (\sqrt{29} )^2 \approx 154.933
Rounded to three significant figures, the distance the motorcycle travel, s = 155 meters
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the energy of a certain charged capacitor is . what is the new energy stored in that capacitor if its charge is decreased to of its original value (imagine allowing some of the charge to move through a resistor)? remember that the capacitance, , that relates and , is unchanged.
The new energy stored in the capacitor is 1/2 of its original value.
The energy stored in a charged capacitor is given by the formula:
E = 1/2 CV^2
where C is the capacitance,
V is the voltage across the capacitor, and
E is the energy stored in the capacitor.
Let's call the original energy E1 and the new energy E2.
Then, we can write:
E1 = 1/2 CV1^2
E2 = 1/2 CV2^2
where CV1^2 is the original voltage and
CV2^2 is the new voltage.
The capacitance C is unchanged, so we can write:
C(V1^2) = C(V2^2)
Therefore, we have:
V1^2 = V2^2
Since the charge has been decreased to 1/2 of its original value, the new voltage is V2 = V1/sqrt(2).
Plugging this into the equation for the new energy, we get:
E2 = 1/2 C (V1/sqrt(2))^2
= 1/2 C (V1^2)/2
= E1/2
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a sinusoid signal gets sampled by an alaoge to digital coverter. the frequency of the analoge sine wave is 400 hz/., the sampling frequency is 340hz. what is the frequency of the sampled signal
When a sinusoidal signal with a frequency of 400 Hz is sampled by an ADC with a sampling frequency of 340 Hz, the frequency of the sampled signal is affected. In this case, the frequency of the sampled signal is not equal to the frequency of the analogue signal.
The frequency of a sinusoidal signal refers to the number of complete cycles of the waveform that occur in a certain amount of time. In signal processing, it is often necessary to convert continuous analogue signals into discrete digital signals. This is done by a process called analogue-to-digital conversion (ADC).
In this case, the maximum frequency of the analogue signal is 400 Hz, so the sampling frequency must be greater than 800 Hz. Since the sampling frequency used is only 340 Hz, the signal will be aliased, meaning that some of the higher frequency components of the signal will appear as lower frequency components in the sampled signal.
Therefore, the frequency of the sampled signal is not equal to the frequency of the analogue signal, but it is equal to the difference between the sampling frequency and the nearest multiple of the analogue signal frequency that is less than or equal to the sampling frequency.
This relationship is known as the folding frequency and can be calculated as the modulo of the sampling frequency and the analogue frequency. In this case, the frequency of the sampled signal will be 60 Hz, which is the result of 340 Hz % 400 Hz.
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