Sodum has a work function of 2. 1eV and is illuminated by radiation whose wavelength the is 150mm, Calculate the maximumum energy.
Answers
The maximum energy is 6.2 eV.
Photoelectric effect: Some electrons are released from the metal surface when photons strike it. The photoelectric effect is the name given to this occurrence.
The work function (φ) of a metal is the minimal amount of energy required to remove electrons from its surface.
Maximum kinetic energy is the most energy that electrons have when they are expelled off a metal surface (KEmax).
The work function of sodium is 2.1 eV.
The wavelength of the radiation is 150 nm.
Work function, φ = 2.1 eV
Wavelength, λ = 150 nm = 150 × 10⁻⁹ = 15 × 10⁻⁸ m
Einstein's photoelectric equation is given as:
E = φ + KE(max)
KE(max) = E - φ
KE(max) = ( hc / λ ) - φ
KE(max) = ( 6.63 × 10⁻³⁴) × 3 × 10⁸ / (15 × 10⁻⁸ × 1.6 × 10⁻¹⁹) - 2.1
KE(max) = 0.8287 × 10 - 2.1
KE(max) = 8.3 eV - 2.1 eV
KE(max) = 6.2 eV
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Related Questions
What is the relationship between the sizes
of the planets and their distances from the sun?
Answers
Answer:
The inner, rocky planets are smaller than the outer, gaseous planets
Explanation:
The relationship between the sizes of the planets and their distances from the Sun is: The smaller planets are closer to the sun while the bigger planets are farther from the sun.
A solar system can be defined as a collection of both the inner and outer planetary bodies alongside the Moon in orbit (travel) around the Sun, in slightly elliptical orbits.
Basically, the nine (9) planets of the solar system orbiting (traveling) in order of their distance around the Sun are;
Mercury.Venus.Earth.Mars.Jupiter.Uranus.Neptune.Pluto.Venus.Saturn.Basically, the relationship between the sizes of the planets and their distances from the Sun is that the smaller planets are closer to the sun while the bigger planets are farther from the sun.
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A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension force of the string is: A. constant B. a sinusoidal function of time C. the square of a sinusoidal function of time D. the reciprocal of a sinusoidal function of time E. none of the above
Answers
A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension force of the string is a sinusoidal function of time. The correct option is B.
As the pendulum swings back and forth, the tension force in the string changes due to the varying angle between the string and the vertical direction. When the pendulum is at its highest point, the tension force is greatest as it must counteract both the gravitational force pulling the ball downward and the centripetal force acting towards the center of the circular path.
As the pendulum moves through its lowest point, the tension force decreases because the gravitational force and centripetal force are now acting in opposite directions. This pattern of changing tension force repeats with each swing, resulting in a sinusoidal function of time.
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The tension force of the string in a simple pendulum is not constant and it is not the square or reciprocal of a sinusoidal function of time. The correct answer is B, it is a sinusoidal function of time.
This means that as the pendulum swings back and forth, the tension force in the string will vary in a regular pattern, following the shape of a sine wave.
At the highest point of the swing, when the pendulum is momentarily at rest, the tension force will be at its maximum value. As the pendulum begins to swing back down, the tension force will decrease until it reaches its minimum value at the bottom of the swing. Then, as the pendulum swings back up again, the tension force will increase once more, following the same sinusoidal pattern.
Understanding the behavior of the tension force in a simple pendulum is important for studying its motion and behavior. By analyzing the tension force and its relationship to other factors, such as the length of the string or the mass of the ball, scientists and engineers can gain a deeper understanding of the physics behind this fundamental system.
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Help meeee
Cody is riding the Super Duper Drop at Six Flags. The ride drops him and he free falls
for 2.6 seconds.
a) What will be his final velocity at the end of the 2.6 seconds?
Answers
His final velocity at the end of the 2.6 seconds will be 25.48 m/s
given
time = 2.6 seconds
initial velocity = u = 0
acceleration = acceleration due to gravity = 9.8 \(m/s^{2}\) (since , it is a free fall )
final velocity = ?
using kinematics equation
v = u + at
v = u - g*t
v = - 9.8 * 2.6 = - 25.48 m/s
His final velocity at the end of the 2.6 seconds will be 25.48 m/s in downward direction
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Why water is not used as a thermometric liquid?
Answers
Answer:
Explanation:There are many reasons why water is not used as a thermometric liquid (or is less preferred), chief among which is its transparency. It is thus comparatively harder to make any readings with it. It also has a lower boiling and higher freezing point compared to most liquids.
what is observed when a charged perspex rod is placed close to a suspended polystyrene sphere
Answers
When a charged body is placed near the conductor, the opposite charge is appeared on the one side of the uncharged conductor body near the charged body under the effect of induction.
The opposite charge on the another body is also known as the induced charge.
The perpex rod in the given question is charged.
let the charge on the perpex is positive as shown in the figure.
Then, the polystrene sphers (insulator uncharged sphere) will not have any charge induced as the charges are not free to move inside the insulator.
Thus, when a charged perspex rod is placed close to a suspended polystyrene sphere then the induced charge on the sphere is not observed under the phenomenon of induction process and sphere remain uncharged.
2. Two people, one on Earth and the other on the Moon, try and lift 200 kg blocks. Which person
will have to exert more force to lift their block or will they need to exert the same amount of
force? Explain your reasoning(4 pts)
Answers
Answer:
The person on Earth will have to exert more force to lift their block
Explanation:
The mass of the blocks to be lifted = 200 kg
The location of the first person = On Earth
The location of the second person = On the Moon
The force a person will have to exert to lift the block = The weight of the block = The gravitational force, F, on the block which is given as follows;
\(F = \dfrac{G \times M_1}{R^2} \times m_2\)
Where;
\(\dfrac{G \times M_1}{R^2}\)= The acceleration due to gravity on the Earth or the Moon, depending on the location of the block
m₂ = The mass of the block
Therefore, given that the acceleration due to gravity on the Earth is larger than the acceleration due to gravity on the Moon, the weight of the block on the Earth is larger than the weight of the block on the Moon, and the person on Earth have to exert more force to lift the heavier weight of the block on Earth than the person on the Moon will have to exert to lift the same block as the block has a lower weight on the Moon due to lower acceleration due to gravity on the Moon.
What happens when you call someone using your cell phone?
A. Microwaves travel from your cell phone directly to the cell phone
of the person you are calling.
B. Microwaves reach a cell tower, then fiber optic cables send the
signal to a cell tower near the person you are calling.
C. A system of satellites orbiting Earth receives the microwave
signals and sends them to the person you are calling.
D. Sound waves reach a cell tower, then fiber optic cables send the
signal to a cell tower near the person you are calling.
Answers
Answer: B, Microwaves reach a cell tower, then fiber optic cables send the signal to a cell tower near the person you are calling.
Explanation:
Answer:D. Sound waves reach a cell tower, then fiber optic cables send the
signal to a cell tower near the person you are calling.
Explanation: just got it right
what is magnitude of the linear acceleration of the hoop
Answers
To determine the magnitude of the linear acceleration of a hoop, we need to consider the conditions and parameters involved. It is important to note that a hoop, by definition, is a circular object with all of its mass distributed along its circumference.
Assuming that the hoop is rolling without slipping or any other external forces acting upon it, we can determine the magnitude of its linear acceleration using the following formula:
a = R * α
where:
a is the linear acceleration of the hoop,
R is the radius of the hoop,
α is the angular acceleration of the hoop.
In the case of a hoop rolling without slipping, the relationship between linear and angular acceleration is given by α = a / R. By substituting this value back into the formula, we have:
a = R * (a / R)
a = a
From this equation, we can conclude that the magnitude of the linear acceleration (a) of the hoop is equal to the linear acceleration itself. In other words, the magnitude of the linear acceleration of a hoop rolling without slipping is simply the linear acceleration value.
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As a woman holding her breath swims deeper and deeper beneath the water'r surface, her density ____.
Answers
As a woman holding her breath swims deeper and deeper beneath the water's surface , her density increases.
The density of an object is defined as its mass per unit volume. When a woman holds her breath and dives deeper into the water, the pressure increases as the depth increases. As a result, the volume of air in her lungs decreases, which in turn decreases her overall volume. However, her mass remains constant. Since her density is defined as mass per unit volume, her density increases as her volume decreases, making it easier for her to sink to greater depths.
The density of a human body is slightly less than the density of water, which means that humans tend to float in water. However, when a person holds their breath and swims deeper, the pressure of the water increases, which compresses the person's body slightly and decreases the volume of air in the lungs. This decrease in lung volume reduces the buoyancy force acting on the person's body and makes them more dense, causing them to sink deeper in the water. Additionally, the increased pressure also compresses the body tissues and fluids, which can further increase the person's density. This is why it is important for divers to wear buoyancy compensators or carry weights to help them control their depth while diving.
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Using the letters for the seven colours and starting with R (Red), what is the correct order for the colours in a rainbow? Your answer should be in the form RXXXXXX Which of these seven colours has the shortest wavelength?
Answers
Answer:
Red
Orange
Yellow
Green
Blue
Indigo
Violet
shortest wavelength: violet (380 nanometers)
¯\(°_o)/¯
Answer:
Red Orange Yellow Green Blue Indigo Violet
violet has the shortest wavelength
happy to help :)
You ride your bike and measure how far you travel. After 10 minutes, you travel 3. 5 miles. After 30 minutes, you travel 10. 5 miles. Write an equation to model your distance. Let x represent the number of minutes and let y represent the distance traveled, in miles.
Answers
The equation to model the distance traveled is y = 0.35x, where x represents the number of minutes and y represents the distance traveled in miles.
To model the relationship between the number of minutes and the distance traveled, we can use a linear equation in the form of y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Given the data points provided, we can calculate the slope (m) by finding the change in distance (Δy) divided by the change in time (Δx). In this case, the change in distance is 10.5 - 3.5 = 7 miles, and the change in time is 30 - 10 = 20 minutes. Therefore, the slope (m) is 7/20 = 0.35 miles per minute.
Substituting the slope and one of the data points (10, 3.5) into the equation y = mx + b, we can solve for the y-intercept (b). Rearranging the equation, we have 3.5 = 0.35 * 10 + b, which gives us b = 3.5 - 3.5 = 0.
So, the equation to model the distance traveled is y = 0.35x, where x represents the number of minutes and y represents the distance traveled in miles.
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What is the cause of the aurora borealis (the northern lights)?
a. As the Earth moves through the solar magnetic field, a voltage is built up between the south and north magnetic poles. b. This voltage accelerates charged particles to collide with both poles, thus causing the atmosphere to glow.
c. The northern lights are reflections of fluorescent lights from large cities off clouds in the arctic. Electrons in the Van Allen radiation belts flip over their spin direction and emit light.
d. The Earth's magnetic field guides trapped charged particles to follow field lines toward the poles, where they collide with the atmosphere, causing a glow.
Answers
The cause of the aurora borealis (the northern lights) is the Earth's magnetic field guides trapped charged particles to follow field lines toward the poles, where they collide with the atmosphere, causing a glow. Option d.
The other options: As the Earth moves through the solar magnetic field, a voltage is built up between the south and north magnetic poles; This voltage accelerates charged particles to collide with both poles, thus causing the atmosphere to glow; The northern lights are reflections of fluorescent lights from large cities off clouds in the arctic. Electrons in the Van Allen radiation belts flip over their spin direction and emit light are all incorrect. Therefore the correct answer is option d.
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Correct statement is b. This voltage accelerates charged particles to collide with both poles, thus causing the atmosphere to glow.
How does aurora borealis occur?The cause of the aurora borealis, or the northern lights, is primarily described by option b. When the Earth moves through the solar magnetic field, it creates a voltage between the south and north magnetic poles.
This voltage accelerates charged particles, mainly electrons, in the Earth's magnetosphere. These accelerated particles then collide with atoms and molecules in the Earth's upper atmosphere, resulting in the emission of light. The glowing phenomenon of the northern lights is a direct consequence of these collisions.
The colors observed in the aurora are determined by the type of gas particles present in the atmosphere and the altitude at which the collisions occur. Hence correct statement is b. This voltage accelerates charged particles to collide with both poles, thus causing the atmosphere to glow.
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The moon completes one (circular) orbit of the earth in 23.7 days. The distance from the earth to the moon is 3.84×10^8m. Calculate the centripetal acceleration.
Answers
Given that distance of moon from the earth is, R= 3.84 x 10^8 m
Also, time taken to complete one revolution is, T= 23.7 days = 2047680 seconds
Mass of the moon is, m= 7.347 Kg
To find the centripetal acceleration,
\(a_c=\frac{m4\pi^2R}{T}\)Substituting the values, we get
\(undefined\)Please Help Me!!!.......
Answers
Answer:
D
Explanation:
Water has a high surface tension because the water molecules on the surface are pulled together by strong hydrogen bonds. That means a drop of water will "want" to have the smallest possible surface area.
Solar energy has huge potential. Theoretically, one hour of solar energy could power the world's energy needs -all 7(+billion people - for how long? Georgetown Texas is as "right-wing" politically as you can get. This need not be a partisan issue. Other than climate, it makes economic sense. The main problem (other than people's ignorance) is Big Oil, as it hurts their profits Lastly, as Gore notes earlier in the film, one can choose despair vs hope. Gore chooses hope, with the film ending with him greeting the young generation.
Answers
Solar energy has theoretical potential to power the world's energy needs. Practical implementation and challenges like political polarization and the influence of the fossil fuel industry must be overcome.
Solar energy has the potential to power the world's energy needs theoretically, but practical implementation and overcoming obstacles such as political polarization and the influence of the fossil fuel industry remain challenges. Economic viability and the need for sustainable energy solutions make solar energy an attractive option. Choosing hope and embracing renewable energy can pave the way for a brighter future, as exemplified by Al Gore in the film.
Solar energy indeed holds tremendous potential to meet the world's energy demands. The sun provides an abundant and renewable source of power that, theoretically, could generate enough energy to sustain the global population for an extended period. However, realizing this potential requires overcoming various barriers, including political and economic factors.
The mention of Georgetown, Texas being "right-wing" politically highlights that support for solar energy need not be limited to a particular partisan stance. The economic advantages of solar energy, such as job creation and reduced dependence on fossil fuels, can appeal to a wide range of political ideologies. Despite these benefits, the influence of the fossil fuel industry, often referred to as "Big Oil," can hinder the widespread adoption of solar energy as it may threaten their profits.
In the context of the film mentioned, Al Gore emphasizes the importance of choosing hope over despair. Recognizing the potential of solar energy and other sustainable solutions offers a positive outlook for addressing climate change and creating a more environmentally friendly future. The film concludes with Gore's optimistic outlook, symbolized by his interaction with the younger generation who will play a vital role in shaping our future.
the challenges and potential of solar energy, the political and economic factors influencing its adoption, and the importance of fostering hope and sustainability in combating climate change.
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What is the purpose of collecting information from clients
Answers
Answer:
to analyze and store information
Explanation:
For future references most information are collected to build a database. For future retargeting works.
8) An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 6.4 cm below the starting point. The mass is then pulled so the spring is stretched to a length of 9.6 cm. How fast will the mass be moving when it reaches the equilibrium position?
Answers
Work is accomplished by stretching or compressing a spring. Elastic potential energy is stored in the spring. It is recommended to expand the spring up to 12.8 cm.
What happens to the elastic potential energy that is stored in a spring when work is done to extend it?Elastic potential energy is stored in the spring as a result of the work required to stretch or compress it. A spring's elastic potential energy is equal to one-half the sum of its spring constant times its deformation squared.
When a spring is stretched or compressed from its initial resting position, where is the elastic potential energy stored?We'll talk about elastic potential energy as the second type of potential energy. The energy that is trapped in elastic materials as a result of their stretching or compression is known as elastic potential energy.
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as appropriate. 1. A 1,500 kg car is driving down a road. The coefficient of friction between the car's tires and the road is 0.27. a. What is the weight of the car? O b. What is the normal force acting on the car?
Answers
Hahah I look pregnant don’t I
Answers
But you see...this bobcat
Cute ain’t it?
Select the correct answer. In which situation is maximum work considered to be done by a force? A. The angle between the force and displacement is 180°. B. The angle between the force and displacement is 90°. C. The angle between the force and displacement is 60°. D. The angle between the force and displacement is 45°. E. The angle between the force and displacement is 0°.
Answers
Answer:
A. The angle between the force and displacement is 180°.
Answer:
a
Explanation:
1. Fill in the blank(s):
force mass x
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
➢ 1. force = mass × acceleration
➢ 2. Since unit of weight = kg•m/s²
Answer:
Force = Mass x Acceleration
Hope this helps.
Are the two atoms shown below in the image from the same element?
Answers
The answer is yes
They are isotopes.
Find the center of mass of the region bounded by y=9-x^2 y=5/2x , and the z-axis. Center of Mass = __?
Note: You can earn partial credit on this problem.
Answers
The centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8). Formulae used to find the centre of mass are as follows:x bar = (1/M)*∫∫∫x*dV, where M is the total mass of the system y bar = (1/M)*∫∫∫y*dVwhere M is the total mass of the system z bar = (1/M)*∫∫∫z*dV, where M is the total mass of the systemThe region bounded by y=9-x^2 and y=5/2x, and the z-axis is shown in the attached figure.
The two curves intersect at (-3, 15/2) and (3, 15/2). Thus, the total mass of the region is given by M = ∫∫ρ*dA, where ρ = density. We can assume ρ = 1 since no density is given.M = ∫[5/2x, 9-x^2]∫[0, x^2+5/2x]dAy bar = (1/M)*∫∫∫y*dVTherefore,y bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]y*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]ydA...[1].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore,y bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]y*dxdy...[2].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.Substituting the values and evaluating the integral, we get y bar = (1/M)*[(9-5/2)^2/2 - (9-(15/2))^2/2]= (1/M)*(25/2)...[3].
Also, the x coordinate of the center of mass is given by,x bar = (1/M)*∫∫∫x*dVTherefore,x bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]x*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]xdA...[4].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore, x bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]xy*dxdy...[5].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.
Substituting the values and evaluating the integral, we get x bar = (1/M)*[63/8]= (1/M)*(63/8)...[6]Thus, the centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8).
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what is the critical speed below which the rope woudl becom slack when the bucket reaches the highest point in the circle
Answers
The critical speed below which the rope would become slack when the bucket reaches the highest point in the circle is determined by the length of the rope and the radius of the circle.
When the bucket is at the highest point in the circle, it is momentarily at rest and the tension in the rope must be zero.
The formula for calculating the critical speed at which the rope becomes slack is:
v = √(gr)
where v is the critical speed, g is the acceleration due to gravity, and r is the radius of the circle.
For example, if the radius of the circle is 2 meters and the acceleration due to gravity is 9.8 m/s², the critical speed would be:
v = √(9.8 × 2) = 4.4 m/s
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Identify the three subatomic particles.
Where are each of the particles located
within the atom?
Answers
protons & neutrons are located in the nucleus
electrons are located on the rings or energy levels.
hope this can help you <3
Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. How many revolutions does the cylinder make each second, given that the minimum coefficient of static friction that is needed to keep the riders from sliding down is 0.695 and the diameter of the cylinder is 13.5 m?
Answers
Answer:
0.231 rev/s
Explanation:
\(m\) = Mass of cylinder
\(d\) = Diameter of the cylinder = \(13.5\ \text{m}\)
\(r\) = Radius = \(\dfrac{13.5}{2}=6.75\ \text{m}\)
\(\mu\) = Coefficient of static friction = \(0.695\)
\(N\) = Normal force = \(mr\omega^2\)
\(g\) = Acceleration due to gravity = \(9.81\ \text{m/s}^2\)
The force equation of the system will be
\(\mu N=mg\\\Rightarrow \mu\times mr\omega^2=mg\\\Rightarrow \omega=\sqrt{\dfrac{g}{\mu r}}\\\Rightarrow \omega=\sqrt{\dfrac{9.81}{0.695\times 6.75}}\\\Rightarrow \omega=1.45\ \text{rad/s}\)
Converting to rev/s
\(\dfrac{1.45}{2\pi}=0.231\ \text{rev/s}\)
The number of revolutions of the cylinder is 0.231 rev/s.
Light is travelling from medium A tretractive index 1.4) to medium B (retractive index 1.6. If the incident angle is 32.70 what would be retracted ankle in medium B? Express your answer in degrees
Answers
The refractive angle in medium B is 15.22°
The given values are:Medium A has a refractive index of 1.4.Medium B has a refractive index of 1.6.The incident angle is 32.70.The formula for the refractive index is:n1sin θ1 = n2sin θ2Where,n1 is the refractive index of medium A.n2 is the refractive index of medium B.θ1 is the angle of incidence in medium A.θ2 is the angle of refraction in medium B.By substituting the given values in the above formula we get:1.4sin 32.70° = 1.6sin θ2sin θ2 = (1.4sin 32.70°) / 1.6sin θ2 = 0.402 / 1.6θ2 = sin⁻¹(0.402 / 1.6)θ2 = 15.22°The refractive angle in medium B is 15.22°.Hence, the correct option is (D) 15.22°.
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An external force of 25 N acts on a system for 10 s. What is the impulse delivered to the system?
Answers
Answer:
I = 250N*s
Explanation:
I = F*t
I = impulse or momentum
F = Force
t = time
I = 25N*10s
I = 250N*s
Question 3
A stone weighing 5 newtons falls freely from a cliff 44 meters
high. The stone is accelerated at approximately
А 5 m/sec2
C 44 m/sec
B 10 m/sec2
D 220 m/sec
Answers
Based on scientific data, the stone is accelerated at approximately 10 \(m/s^2\).
Given the following data:
Weight = 5 NewtonHeight = 44 meters.What is gravity?Gravity can be defined as a force of attraction that controls the movement of the planets such as Earth around the Sun.
This ultimately implies that, gravity is a universal force of attraction that acts between all objects or matter that are having both mass and energy, and can occupy space.
Gravity on planet EarthFurthermore, the gravity near the Earth's surface generally makes it possible for all physical objects such as stones to possess weight and experience a free fall.
According to astronomical records, the acceleration due to gravity for an object experiencing a free fall near the Earth's surface is 9.8 \(m/s^2\).
In this scenario, the stone is accelerated at approximately 10 \(m/s^2\).
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The position of a point during the interval of time from t = 0 to t = 6 s is given by s = -2/3 t³ + 6t² +2t m. (a) What is the maximum velocity during this interval of time, and at what time does it occur? (b) What is the acceleration when the velocity is a maximum? {20 m/s, 0 m/s²}
Answers
The maximum velocity during this interval of time is approximately 20 m/s, and it occurs at t ≈ 3 + √10 seconds.
To find the maximum velocity and the time at which it occurs, we need to differentiate the position function with respect to time.
Given: s = -2/3 t³ + 6t² + 2t
(a) To find the maximum velocity, we differentiate the position function to get the velocity function: v = ds/dt
Taking the derivative of the position function, we have:
v = d/dt (-2/3 t³ + 6t² + 2t)
v = -2t² + 12t + 2
To find the maximum velocity, we set the derivative equal to zero and solve for t: -2t² + 12t + 2 = 0
We can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Substituting the values into the formula, we get:
t = (-12 ± √(12² - 4(-2)(2))) / (2(-2))
t = (-12 ± √(144 + 16)) / (-4)
t = (-12 ± √160) / (-4)
t = (-12 ± 4√10) / (-4)
t = 3 ± √10
Since we're looking for the time during the interval from t = 0 to t = 6 s, we discard the negative root: t = 3 + √10
So, the maximum velocity occurs at t = 3 + √10 seconds.
To find the maximum velocity, substitute the value of t into the velocity function: v = -2(3 + √10)² + 12(3 + √10) + 2
v ≈ 20 m/s
Therefore, the maximum velocity during this interval of time is approximately 20 m/s, and it occurs at t ≈ 3 + √10 seconds.
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