Answer:
The answer is simple….
As we know v = u + (a×t)
Where
v is the final velocity
u is the initialvelocity
a is the acceleration
t is the time taken
So according to the question:-
u=0, v=15 , a=3 and we have to find t…
So the equation is written as:-
15 = 0 + (3×t)
=> t = (15 ÷ 3) = 5
Therefore, the time required is 5 seconds..
Animals often use more than one type of clue to help them navigate. These clues include a sense of smell ('olfaction') and remembering landmarks as well as using the Sun or the Earth's magnetic field. Suggest why an animal might use more than one type of clue to find its way.
Answer pls, will give 30 points.
Finally, they rely on a variety of environmental cues such as the length of the day, the Sun's position and angle in the sky, water salinity and temperature gradients, and the Earth's magnetic field. They do this to navigate effectively.
What is animal navigation?Animal navigation refers to the ability of many animals to find their way around without the use of maps or instruments.
Birds like the Arctic tern, insects like the monarch butterfly, and fish like salmon migrate thousands of miles to and from their breeding grounds on a regular basis, and many other species navigate effectively over shorter distances.
Several animal species can use a variety of cues to help them orient and navigate effectively. Insects and birds can identify where they are and navigate by combining learned landmarks with sensed direction (from the earth's magnetic field or from the sky).
Thus, this is why an animal might use more than one type of clue to find its way.
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If it takes a planet 2.8 × 108 s to orbit a star with a mass of 6.2 × 1030 kg, what is the average distance between the planet and the star? 1.43 × 109 m 9.36 × 1011 m 5.42 × 1013 m 9.06 × 1017 m
The average distance between the planet and the star is:
R=9.36*10^11 m
Orbital velocity v=√{(G*M)/R},
G = gravitational constant =6.67*10^-11 m³ kg⁻¹ s⁻²,
M = mass of the star
R =distance from the planet to the star.
v=ωR, with ω as the angular velocity and R the radius
ωR=√{(G*M)/R},
ω=2π/T,
T = orbital period of the planet
To get R we write the formula by making R the subject of the equation
(2π/T)*R=√{(G*M)/R}
{(2π/T)*R}²=[√{(G*M)/R}]²,
(4π²/T²)*R²=(G*M)/R,
(4π²/T²)*R³=G*M,
R³=(G*M*T²)/4π²,
R=∛{(G*M*T²)/4π²},
Substitute values
R=9.36*10^11 m
As was already said, Earth is located roughly 150 million kilometres (93 million miles) from the Sun on average. It is 1 AU. Mars is on our fictitious football field's three-yard line. On average, the distance between the Sun and the red planet is around 142 million miles (228 million kilometres).
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The complete question is ''If it takes a planet 2.8 × 108 s to orbit a star with a mass of 6.2 × 10^30 kg, what is the average distance between the planet and the star? 1.43 × 10^9 m 9.36 × 10^11 m 5.42 × 10^13 m 9.06 × 10^17 m''.
A lime is thrown upward with a velocity of 5 m/s.
The maximum height reached by the lime thrown upward is 1.28 m.
What is maximum height of a projectile?The maximum height of a projectile is the highest vertical position along its trajectory.
The maximum height reached by the lime thrown upward is calculated as follows;
v² = u² - 2gh
where;
u is the initial velocity of the limeh is the maximum height reached by the limeg is acceleration due to gravityv is the final velocity of the limeAt maximum height, the final velocity of a projectile is zero.
Substitute the given parameters and solve for the maximum height reached by the lime.
0 = u² - 2gh
h = u²/2g
h = (5²)/(2 x 9.8)
h = 1.28 m
Thus, the maximum height reached by the lime thrown upward is 1.28 m.
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if an object is speeding up, . its acceleration is positive its acceleration can be positive or negative depending on the direction of motion its acceleration is negative
If an object is speeding up its acceleration can be positive or negative depending on the direction of motion.
What is positive and negative acceleration?According to mathematics, a negative acceleration indicates that the velocity will be subtracted, while a positive acceleration indicates that the velocity will be increased.
In physics,
A positive acceleration indicates a rising velocity over time.
Negative acceleration describes a speed decrease over time.
A bus or car going at an accelerating rate is said to have positive acceleration.
We may say that it is speeding up in the direction it is moving.
When we use the brake in the previous example, the speed of the car reduces.
Then it experiences a deceleration.
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If the same change in velocity occurs in less time does the magnitude of the corresponding average acceleration increase, decrease, or stay the same
The magnitude of the related average acceleration will increase if the same change in velocity occurs in less time.
The rate at which a body's distance changes in relation to time is referred to as its velocity. The SI unit is meter per second ( m/s).
Acceleration is the rate at which speed and direction of velocity vary over time. When something moves faster or slower, it is considered to be accelerating. Motion on a circle accelerates even while the speed is constant because the direction is always changing.
Acceleration can be defined as the time rate of change in velocity
a = Δv / t
Now as t is in the denominator.
The smaller value of time will result in greater acceleration values with constant velocity change.
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daniel harris has always enjoyed eating tuna fish. unfortunately, a study of the mercury content of canned tuna in 2010 found that chunk white tuna contains 0.6 ppm hg0.6 ppm hg and chunk light tuna contains 0.14 ppm.20.14 ppm.2 the u.s. environmental protection agency (epa) recommends no more than 0.1 μg hg/kg0.1 μg hg/kg body weight per day. a person weighs 69 kg69 kg . how often may the person eat a can containing 6 ounces6 ounces (16 oz
One 6 oz can of chunk light tuna is to be consumed every four days.
How to find the number of days interval?The mercury content in 2010:
White tuna chunks weigh 0.6 ppm in total.
A piece of light tuna has a mass of 0.14 ppm.
The body weighed 63 kg, and the tuna weighed 6 oz.
The maximum quantity of mercury that the body should ingest each day is advised to be no more than 0.1 micrograms.
Solution:
Let's first convert the tuna's mass to grams.
As 1 oz equals 28.3495 g
The tuna weighs 6 oz, or 28.3495 g.= 170.097 g
The maximum daily mercury (Hg) intake for a 63 kg body weight is equal to 63 0.1.
6.3 micrograms per day
But the mass of the mercury (Hg) = concentration (Hg) mass of the tuna
= 0.6 × 10⁻⁶ × 170.097 g
= 1.0206 × 10⁻⁴ g
= 102.06 μg (micrograms)
The interval needed to consume one 6 oz can of chunk white tuna = 102.06/6.3
= 16.2 days
≅ 16 days
An average of 16 days must pass between consuming one 6 oz can of chunk white tuna.
the mass of the mercury (Hg) is equal to the product of the concentration (Hg) and
the mass of the tuna (0.14 106 170.097 g = 2.4814 105 g = 23.814 g).
= 23.814/6.3
= 3.78
As a result, it takes 3.78 days plus 4 days to consume one 6 oz can of chunk white tuna.
Approximately every four days, a single 6 oz can of chunk light tuna is consumed and the total 6-ounce tuna can be consumed in 16 days.
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A Plastic fork has a mass of 5g and a volume of 5.2cm³. What is the density of the plastic fork?
Answer: 0.96153846153846 g/cm3
Explanation:
Photons are shone on a piece of metal and one electron is ejected for each absorbed photon. What happens when the wavelength of light is decreased?.
The ejected electrons would have greater kinetic energy if the wavelength of light is decreased when Photons are shone on a piece of metal and one electron is ejected for each absorbed photon.
What is Kinetic energy?This is referred to as the type of energy which is possessed by a body by virtue of its motion and it has an inverse relationship with the wavelength of light.
This therefore means that as the wavelength of light is decreased, the kinetic energy of the ejected electrons will increase and vice versa which is therefore the reason why it was chosen as the most appropriate choice.
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Tropical rainforests are being cleared at a rate of 8 million hectares per year. How many football fields per hour are being deforested? One hectare is equal to 2.47 acres, and there are 1.32 acres in a football field. (Round to the nearest acre per hour.)
The number of football fields per hour that are being deforested is 1710 football fields.
How to convert hectares to acres?According to this question, tropical rainforests are being cleared at a rate of 8 million hectares per year.
This means that 8 million hectares are being cleared every 8760 hours, since there are 365 days in a year and 24 hours in a day.
1 hectare = 2.471 acres
8 million hectares = 19.77 million acres
If 19.77 million acres is cleared every 8760 hours
Per hour, 19770000 ÷ 8760 = 2256.8 acres is cleared.
Since there are 1.32 acres in a football field, this means that approximately 1710 football fields are being deforested per hour.
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A coin lies under a glass filled with water.
Explain that you cannot see the coin
Refraction is the cause of this. We perceive an object when light reflects off of it and travels to our eyes. The penny appears to vanish because light is refracted as it passes through the glass's edges and the water, never reaching our eyes.
Refraction in physics is the change in direction that results from a wave's change in speed as it passes through a medium. The electromagnetic waves that make up light are bent due to their different speeds as they pass past the boundary of one transparent medium and into another.
When partially submerged in water and viewed from an angle other than 90° to the surface, a straight stick seems bent. When travelling from air to glass, a ray of light of a single wavelength (various wavelengths appear as different colours to the human eye) is refracted, or bent, in a way that relies on the speeds of the two mediums.
A straight stick appears bent when partially submerged in water and viewed at an angle other than 90° to the surface. A light ray of a single wavelength—different wavelengths appear as different colors to the human eye—is refracted, or bent, in a way that depends on the speeds of the two media when it travels from air to glass.
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A cheetah can maintain a constant speed of 30 m/s. At this rate, how far will it travel in 3 seconds? (Express you answer in m.)
Answer:
90m
Explanation:
it travels at 30 m/s so 30*3 is 90
J. J. Thomson used a cathode-ray tube to calculate the charge-to-mass ratio of the electron. Which of these suggested the presence of a negative particle?.
J. J. Thomson used a cathode-ray tube to calculate the charge-to-mass ratio of the electron. The deflection of cathode rays towards the positively charged surface proved that they are negatively charged particles.
In 1897, J.J Thomson performed a cathode ray tube experiment to determine the charge-to-mass ratio of electrons.
Due to high flow of voltage, a beam of particles was allowed to flow from the negatively charged end to the positively charged end of the tube.
An end of the tube was painted with phosphorous and when electrons struck that end, a green spark was observed which confirmed the presence of negatively charged particles i.e. electrons.
To put it simply, cathode rays came from the cathode tube and deflected towards a positively charged plate showing that they are negatively charged particles.
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Find the electrical energy expended by an electric lamp labelled 100 W in 8 seconds.
Here is another extremely hard question you do not want to be faced with. Is there life after death? From today till the next hundred days to come, almost every (if not all) living persons now would be dead. Death is an inescapable event which no history has survived. So, people have come to accept the inescapable fate of a living thing which is death. Now, after one’s life has ceased here on earth, does another life begin elsewhere?
The existence of an afterlife or life after this one is uncertain.
Explanation:
Wether you're reincarnated or your soul is transported to another plane of existence, such as heaven or hell for example, is uncertain. For all we know we could just cease to exist. We are born to die. And we will not know what happens once we die until we die.
Then again, there are people who die and then are resurrected. Some say there was nothing, others say there was something. We will not know until we experience death ourselves.
the 25-m crane boom ao lies in the yz plane. determine the maximum permissible tension in cable ab if the absolute value of moments about the coordinate axes of the force exerted on a by cable ab must be |mx|≤ 61.6 kn·m, |my|≤ 13.6 kn·m, |mz|≤ 9.6 kn·m.
The maximum permissible tension in cable AB is 3.11 kN
Given that,
I [tex]M_{x}[/tex] I ≤ 61.6 kN.m
I [tex]M_{y}[/tex] I ≤ 13.6 kN.m
I [tex]M_{z}[/tex] I ≤ 9.6 kN.m
OC = √ [tex]OA^{2}[/tex] - [tex]AC^{2}[/tex]
OC = √ [tex]25^{2}[/tex] - [tex]15^{2}[/tex]
OC = 20 m
[tex]r_{A}[/tex] = 15j + 20k
AB = √ [tex]2.5^{2}[/tex] + [tex]15^{2}[/tex] = 15.2069 m
P = P AB / AB = ( P ) 2.5i - 15j / 15.2069
P = 0.164399P i - 0.98639P j
[tex]M_{o}[/tex] = [tex]r_{A}[/tex] * P = [tex]\left[\begin{array}{ccc}i&j&k\\0&15&20\\0.163499P&-0.98639P&0\end{array}\right][/tex]
[tex]M_{o}[/tex] = ( 19.7828P ) i + ( 3.2700P ) j - ( 2.4525P )k
I [tex]M_{x}[/tex] I ≤ 61.6
19.7828P ≤ 61.6
P ≤ 3.11 kN
I [tex]M_{y}[/tex] I ≤ 13.6
3.2700P ≤ 13.6
P ≤ 4.16 kN
I [tex]M_{z}[/tex] I ≤ 9.6
2.4525P ≤ 9.6
P ≤ 3.91 kN
Tension is the act of stretching. It is a force transmitted through a object when pulled by forces across opposite sides.
Therefore, the maximum permissible tension in cable AB is 3.11 kN
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HELP ASAPP PLEASE!!! I know that I got one correct but i’m not sure what the other one is.
Answer:
Replace distance with "direction"
Explanation:
use the above information to answer the questions, Run 1 Distance between the intervals position (m) AB= 1,3 BC=1,3 CD 1,3 DE = 1,3 EF = 1,3 Perioel (P)=1/25×5 =0,2sec Run2 Distance between the intervals position (m) AB= 1,5 BC = 1,8 CD = 2 DE 2,2 EF=2,4 Draw a graph of position versus time for 2.1 Run 1 2.2 Run 2
Using the charter system conversation in the right angled value triangle we apply distance formula and get the G-plot value of 9.876 u.
How is position determined in velocity - time?The movement in a graph is determined through the two perpendicular axis in which the first coordinate represents the distance to be traveled in the x axis and the second coordinate shows the distance to be traveled in the y axis .
What is distance formula ?If you want to determine the distance between any two point in a graph the distance formula is used in such case the distance formula is applied like Pythagoras theorem.
Given:
A (1,3)
Period = 0.2 seconds
B (1,5)
Period = 0.5 seconds
Before applying distance formula we need to simplify the given value into charter system.
Where,
A become a substituted value for the argument of square on the basic structure.
Since A symmetrical is that of right angled triangle we can use the basic charter values.
Therefore A now become A(π,2)
Similarly B become B(e,nπ)
Using distance formula to find the graph plot we get:
AB = 5.6π - e×3.14
AB = 9.876
where AB is the distance between A and B.
Therefore using the charter system conversation in the right angled value triangle we apply distance formula and get the G- plot value of 9.876 u.
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A 28.5 g sphere is added to a graduated cylinder containing 45.50 ml of water. The water level rises to the 49.10 ml mark. What is the volume of the sphere? What is its density? Based on its density, what type of metal is it?
According to this question, a 28.5 g sphere is added to a graduated cylinder containing 45.50 ml of water. The water level rises to the 49.10 ml mark.
This means that the volume of the sphere can be calculated as follows: 49.10mL - 45.50mL = 3.6mL.
The density can be calculated by dividing the mass by its volume as follows:
Density = 28.5g ÷ 3.6mL = 7.92g/mL
Based on the density of the sphere, it is incoloy.
Therefore;
The volume of the sphere that weighs 28.5g is 3.6mLThe density of the metal sphere is 7.92g/mL.Learn more about density at: https://brainly.com/question/6107689
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From his observations of the phases of venus, galileo concluded that the ptolemaic model of planetary motion was wrong because it predicted.
Galileo’s telescopic discoveries of the moons of Jupiter are often mentioned. But they did not amount to proof that the Ptolemaic system was incorrect.
It's hard to tell you how big a shakeup this caused in astronomy at the time. Thanks to Galileo, we now knew that planets weren't perfect, ethereal lights in the sky. That things could orbit them, same as (most astronomers thought) things did around Earth, making Earth less special, and providing evidence that maybe that heliocentric theory wasn't that out there.
Basically, before Galileo, astronomers were looking at an unchanging, heavenly firmament, separate from Earth by its very heavenly nature.
After, they were studying planets - actual worlds like ours - and moons and the physical (as opposed to heavenly) reality of their place in the universe.
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When is simple observation more appropriate than experimenting in a controlled laboratory?
Simple observation more appropriate than experimenting in a controlled laboratory when the results can be gotten solely by using our sense organs.
What is Experiment?This is referred to as a part of a scientific method and it is performed by scientists to test a hypothesis so as to know whether it will be accepted or refuted.
This is usually performed by different people from all over the world so as to ascertain its authenticity before it becomes a theory or law. This doesn't involve only sense organs alone as different techniques are required to arrive at a conclusion in this process.
Observation on the other hand requires the use of sense organs such as the eyes, nose etc to determine the results and may not need the use of experiments which is therefore the reason why it was chosen as the correct choice.
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Imagine the following objects in deep space, separated by a kilometre. which pair of objects experiences the largest gravity force? a proton and an electron an apple and a brick two apples an apple and a proton
The pair of objects that experiences the largest gravity force is an apple and a brick
An object will be weightless in outer space, away from the gravitational field of Earth (or another massive planet), yet it will still have mass and consequently resistance to a given force.
When one body has a higher mass than another, it is said to be more massive. The electron, with a mass of about 9.11 10-31 kg, is one of the Universe's least massive things. Hence, the combination of a proton and electron would experience the least gravity force. The combination of an apple and a brick has the most mass hence would experience the largest gravity force. Two apples or an apple and a proton are less massive compared to an apple and a brick thus incorrect.
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When jumping, a flea accelerates at an astounding 1500 m/s2 , but over only the very short distance of 0.44 mm . if a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?
When the flea jumps straight up, and if air resistance is neglected, the height of the flea will be 0.089m.
What is air resistance?Air resistance acts as a force on objects moving through the atmosphere. This force acts in the opposite direction when a body is travelling through the air. Air resistance causes the moving body to experience frictional force. A body's speed decreases as it goes due to air resistance.
It should be noted that the equation of kinematics will be illustrated thus:
V = ✓(2 × 1500 × 0.44mm)
Therefore, h = V² / 2g
= (✓(2 × 1500 × 0.44mm)² / (2 × 9.8)
= 0.089m
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We have that the flea goes as high as
h=0.0889m
How high does the flea go?From the Question, we are told that
Acceleration =1500ms^2
Distance d=0.47mm
Generally, the equation for height is mathematically given as
h=\frac{u^2}{2 g}
Where
u^2=2 * 1500 * 0.44 * 10^{-3}
u=1.32ms
Therefore
h=\frac{1.32^2}{2 * 9.8}
h=0.0889m
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a future space explorer has been kidnapped and is held prisoner on a planet in our solar system. with nothing else to do, our prisoner amuses herself by dropping her watch from eye level (170 cm) to the floor. she observes that the watch takes 0.95 s to fall. ignore air resistance.
The acceleration due to gravity of Jupiter is found to be 24.5m/s².
What is free fall?Any motion of a body in which gravity is the sole force acting on it is referred to as free fall in Newtonian physics. A body in free fall has no force acting on it according to general relativity, where gravity is reduced to a space-time curvature.
When gravity and the resulting acceleration are the only forces acting on an object, this is referred to as freefall in physics. A body falling freely due to the earth's gravity is what the phrase "freefall" refers to. Gravitational acceleration will result from this motion.
F = (G x m1 x m2)/r2
F = (6.67 x 10-11) (1.9 x 1027) (185) / ( 7.18 x 107)2
= 4547.8 N
Since the probe is on Jupiter's surface and the force we just discovered is the force of gravity on the surface between the two, this would also be the probe's weight.
Since F = mg:
4547.8 = 185g
24.58 m/s² = g
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5. What is Deviation?
6. a) Why don't walkers usually have a problem with deviation?
b) When might deviation be a problem for a walker trying to use a compass?
7. Why can deviation be a problem in ships?
8. Describe two ways of correcting for deviation in a ship.
A gait deviation is a a physiotherapy term. It refers to change in the gait cycle that affects the trunk, hip, knee, or ankle joint. Increased age and/or certain disorders might cause gait abnormalities. These diseases can be either musculoskeletal or neurological in origin.
Why don't walkers usually have a problem with deviation?Walkers don't usually have problem with gait deviation because, walking in itself helps to correct problems with gait deviation. Walking correctly exercises the muscles and skeletons associated with gait hence preventing deviation.
When might deviation be a problem for a walker trying to use a compass?Deviation might be a problem for a walker trying to use a compass if the walker is having or experiencing a Spastic Hemiparetic Gait.
It is distinguished by unilateral leg extension and circumduction, in which the paretic limb moves laterally (circumducts) during the swing phase. This is sometimes referred to as circumductory gait.
The compass can hardly be maintained pointed in the appropriate direction with this configuration.
Why would deviation be a problem when travelling in a ships?Sea travel is known to produce gait changes or deviation.
The reason for this is not far-fetched. Ships don't travel on smooth terrain.
The open sea is characterized by complex, oscillating motion of ships in three translational dimensions (surge, sway, and heave) and three rotational dimensions (roll, pitch, and yaw).
The ship is the base of support or ground surface for passengers and crew: body control must be changed to accommodate for the ship's 6 degrees of freedom oscillatory motion.
Changes in stride that define those who have fully acclimated to living at sea are one of the most well-known characteristics of this compensation.
Anecdotal evidence focuses on a "rolling gait" that is prominent enough to be seen by casual onlookers.
What are two ways of correcting for deviation in a ship?The two ways of correcting deviation are:
In other circumstances, physical therapy may be necessary to enhance balance, strength, and flexibility. You should also undergo fall prevention training.Maintaining good foot alignment may need the use of in-shoe splints or leg braces. In circumstances of uneven leg length, a shoe raise may be useful.Learn more about physiotherapy :
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an electron is to be accelerated from a velocity of 2.50×106 m/sm/s to a velocity of 9.00×106 m/sm/s . through what potential difference must the electron pass to accomplish this?
Through -212 V potential difference must the electron pass to accomplish this
What is Potential difference?The difference in electric potential between two points, which is defined as the effort required per unit of charge to move a test charge between the two places, is known as voltage, electric potential difference, electric pressure, or electric tension.
The initial kinetic energy of the electron is,
[tex]{K_i} = \frac{1}{2}mv_i^2[/tex]
Here, m is the mass of the electron and
is the initial velocity of the electron.
[tex]\begin{array}{c}\\{K_i} = \frac{1}{2}\left( {9.11 \times {{10}^{ - 31}}\;{\rm{kg}}} \right){\left( {2.5 \times {{10}^6}\;{\rm{m/s}}} \right)^2}\\\\ = 2.88 \times {10^{ - 18}}\;{\rm{kg}}\\\end{array}[/tex]
The final kinetic energy of the electron is,
[tex]\begin{array}{c}\\{K_f} = \frac{1}{2}\left( {9.11 \times {{10}^{ - 31}}\;{\rm{kg}}} \right){\left( {9 \times {{10}^6}\;{\rm{m/s}}} \right)^2}\\\\ = 3.68 \times {10^{ - 17}}\;{\rm{kg}}\\\end{array}[/tex]
[tex]\begin{array}{c}\\{V_1} - {V_2} = \frac{{3.68 \times {{10}^{ - 17}}\;{\rm{J}} - 2.88 \times {{10}^{ - 18}}\;{\rm{J}}}}{{ - 1.6 \times {{10}^{ - 19}}\;{\rm{C}}}}\\\\ = - 212\;{\rm{V}}\\\end{array}[/tex]
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The social cognitive perspective of personality focuses on social factors such as your parents guardians and teachers and cognition what does cognition mean
The social cognitive perspective of personality focuses on social factors such as your parents guardians and teachers and cognition means how we as individuals process and store information.
What is Cognition?This is referred to as the process in which information is stored and processed through the use of our senses, experience etc and is common to all individuals.
The social cognitive perspective of personality on the other hand focuses on social factors such as parents and also in which cognition is among and it is influenced by genetic and environmental factors which therefore makes it the most appropriate choice.
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Prompt: Explain how your physical, emotional, and mental state affects your performance in your exercise. Use specific examples from your experience
Being physically, emotionally, and mentally healthy can keep you healthy and help you avoid significant health issues during exercises.
How to illustrate the information?Exercise boosts mental health by lowering anxiety, depression, and depressive symptoms, as well as by raising self-esteem and increasing cognitive abilities. Additionally, it has been discovered that exercise helps with symptoms including poor self-esteem and social withdrawal.
Exercise on a regular basis can significantly improve symptoms of sadness, anxiety, and ADHD. Additionally, it lowers stress, enhances memory, promotes sound sleep, and uplifts your mood in general. It should be noted that it's important to be in the right state of mind during exercise to prevent injuries.
Therefore, being physically, emotionally, and mentally healthy can keep you healthy and help you avoid significant health issues during exercises.
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in example 2.6, we considered a simple model for a rocket launched from the surface of the earth. a better expression for a rocket's position measured from the center of the earth is given by
The expression for velocity is [tex]v(t)=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex]
The expression for acceleration is [tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{4}{3}} \right )[/tex]
The expression for the rocket's position as measured from the center of the earth is
[tex]y(t)=[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{2}{3}[/tex]
Let
[tex]x(t)=R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t[/tex]
We have,
[tex]y(t)=[x(t)]^\frac{2}{3}[/tex]
The velocity of the rocket as a function of time is given by
[tex]v(t)=\frac{\mathrm{d} y(t)}{\mathrm{d} t}=\frac{2}{3}[x(t)]^{-\frac{1}{3}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
[tex]v(t)=\frac{\mathrm{d} y(t)}{\mathrm{d} t}=\frac{2}{3}\frac{1}{\sqrt[3]{x(t)}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
Since
[tex]x(t)=R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t[/tex]
We have,
[tex]\frac{\mathrm{d} x(t)}{\mathrm{d} t}=3\sqrt{\frac{g}{2}}R_{E}[/tex]
[tex]v(t)=\frac{2}{3}\frac{1}{\sqrt[3]{x(t)}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
[tex]v(t)=\frac{2}{3}\frac{1}{\sqrt[3]{x(t)}} X 3 \sqrt{\frac{g}{2}}R_{E}=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex]
[tex]v(t)=\frac{\sqrt{2g}}{\left ( R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t \right )^\frac{1}{3}}R_{E}[/tex]
[tex]v(t)=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex] .......(i)
The acceleration as a function of time is given by
[tex]a(t)=\frac{\mathrm{d} v(t)}{\mathrm{d} t}[/tex]
[tex]a(t)=\frac{\mathrm{d}}{\mathrm{d} t}\left (\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}\right )[/tex]
[tex]a(t)=\frac{\mathrm{d}}{\mathrm{d} t}\left ({\sqrt{2g}}R_{E}[x(t)]^{-\frac{1}{3}}\right )[/tex]
[tex]a(t)=\sqrt{2g}R_{E}\frac{\mathrm{d}}{\mathrm{d} t}[(x(t)]^{-\frac{1}{3}}[/tex]
[tex]a(t)=-\frac{1}{3}\sqrt{2g}R_{E} [(x(t)]^{-\frac{4}{3}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
[tex]a(t)=-\frac{1}{3}\sqrt{2g}R_{E} [(x(t)]^{-\frac{4}{3}}3\sqrt{\frac{g}{2}}R_{E}[/tex]
[tex]a(t)=-gR_{E}^2 [(x(t)]^{-\frac{4}{3}}[/tex]
[tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[x(t)]^\frac{4}{3}} \right )[/tex]
[tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{4}{3}} \right )[/tex] .......(ii)
Therefore, the expression for velocity is [tex]v(t)=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex]
& the expression for acceleration is [tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{4}{3}} \right )[/tex]
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In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by [tex]y(t)=[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{2}{3}[/tex]
where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2).
(a) Derive expressions for v(t) and a(t).
(Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)
An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 380 m from the crossing and its speed is 24 m/s. If the engineer’s reaction time is 0.66 s, what should be the magnitude of the minimum deceleration to avoid an accident? Answer in units of m/s 2 .
a 100 w incandescent light bulb converts approximately 2.5% of the electrical energy supplied to it into visible light. assume that the average wavelength of the emitted light is λ
The question is incomplete the right solution for this question is:
E photon = 2.39 eV, b = 6.32 * 1048 fotones/s, c = 9.87 * 1048 fotones/s.
To compute the answer, we must take into account the Plack postulate, which states that each photon's energy is given by
Ephoton is equal to h*f, where f is the frequency of light and h is the Planck universal constant.
We also know that the relationship between wavelength and frequency for waves has the following form:
velocity equals wavelength times frequency (f) Assuming that velocity in our case is the same as the speed of light, we can derive
Ephoton= h*f= h*c/ and hc= 1240 eV/nm are related terms.
Consequently, Ephoton=1240/540 nm=2.39 eV
Since power is defined as energy/time, we may calculate the power emitted by considering a number per second (n) and multiplying it by its energy.
Power in this instance: n*h*f
On the other hand, we must take into account that the light is emitted isotropically in order to compute the number of photons per second at a distance of 5 m from a light bulb using an area of 2 cm2.
the percentage of the 2 cm2 at 5 meters is 425 of the total area radiated.
0.02*0.02/25=1,6*10^-5
To perform the calculations for photons at 810 nm, we must alter the photon energy to 1.53 eV.
As 810 nm photons have lower energy, 100 W light bulbs emit more of these photons than they do.
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