Answers
Average speed is total distance, not displacement. They ran 16 kilometers and back another 16 kilometers. That’s 32 kilometers. We want to change this into meters tho. That’s the si unit for speed. So multiply that by 1000 to get 32,000 meters. Now divide that by the time. Again, convert that hour and 15 minutes into seconds because the si unit for time is seconds. Do 1*3600 and then add 15*60 to get 4,500 seconds.
32,000m/4,500s = 7.1 m/s
Average velocity is displacement over time. We already went over that the displacement is 0, so therefore average velocity is 0
Related Questions
Two type of microscopes used to view cells are optical and__ microscopes
options:
laser
Electron
Answers
The mass on the spring in this diagram is in harmonic motion between x = -5
cm and x = 5 cm.
At which point does the mass have the most kinetic energy
Answers
Answer:
The mass will have the most KE at the midpoint of motion (velocity is a maximum)
Total Energy = KE + PE = constant
At zero displacement the potential energy equals zero and the kinetic energy is a maximum.
Answer:
I think it's point C but I'm not sure
What size force accelerates a 0.010 kg bullet from a rest to a speed of 1100 m/s in a distance of 1 meter?
Answers
The force that accelerates a 0.010 kg bullet from rest to a speed of 1100 m/s in a distance of 1 meter is 11 newton.
What is force?Force is the entity that changes the motion of an object. It is calculated by multiplying the mass by acceleration.
Mass is the weight of an object per unit. Acceleration is a change in the rate of velocity.
F = ma
The mass is 0.010 kga change
convert into grams = 10 grams
The acceleration is 1100 m/s
putting the value in the formula
1100 x 10 = 11, 000
convert into kg = 11
Thus, the size force accelerates is 11 N.
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Which of the following would you expect to be a strong electrolyte in solution?
Answers
The following would expect to be a strong electrolyte in solution (b) KCI is correct option.
When dissolved in water, a strong electrolyte produces a large concentration of ions in solution by totally dissociating into ions. The following compounds are typically strong electrolytes in solution according to this definition:
Al(OH)₃ (aluminum hydroxide) is a weak electrolyte. It does not dissociate significantly into ions in solution, resulting in a low electrical conductivity.KCl (potassium chloride) is a strong electrolyte. It completely dissociates into potassium ions (K⁺) and chloride ions (Cl⁻) in solution, resulting in a high concentration of ions and a high electrical conductivity.PbI₂ (lead(II) iodide) is a weak electrolyte. It does not dissociate significantly into ions in solution, resulting in a low electrical conductivity.These substances readily dissociate into ions in water and exhibit high electrical conductivity, making them strong electrolytes in solution.
Therefore, the correct option is (b).
The complete question is,
Which of the following would be a strong electrolyte in solution?
a) Al(OH)₃ b) KCI c) Pbl₂
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The depth of a pond is 1.5m. Calculate the pressure caused by the water at the bottom of the pond ??
Answers
The pressure caused by water is: P = P0 + bgh = 1.013×10^5 + 10^3×9.81 × 1.5 = 1.18 atm
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
Answers
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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What is the resistance (in Ω) of a 17.5 m long piece of 17 gauge copper wire having a 1.150 mm diameter?
Answers
In order to calculate the resistance of this wire, we can use the formula below:
\(R=\frac{\rho d}{A}\)Where p is the resistivity, d is the length and A is the cross-sectional area of the wire.
The resistivity of the copper is 1.72 * 10^-8 ohms*m, so we have:
\(\begin{gathered} R=\frac{1.72\cdot10^{-8}\cdot17.5}{\frac{\pi\cdot(1.15\cdot10^{-3})^2}{4}}\\ \\ R=\frac{30.1\cdot10^{-8}\cdot4}{\pi\cdot1.3225\cdot10^{-6}}\\ \\ R=\frac{120.4\cdot10^{-8}}{4.1547563\cdot10^{-6}}\\ \\ R=28.98\cdot10^{-2}\text{ ohms}\\ \\ R=0.2898\text{ ohms} \end{gathered}\)Can anyone please please please explain part a to me? The answer is A and E and I cannot for the life of me figure out why. Thank you :)
Answers
Answer:
A and E
Explanation:
An easy (calculation free) way to think about it is balance. The question states that the system is un-moving and therefore balanced in the picture. To keep it balanced, we want to add equal weights at equal distances on opposite sides of the pivot point. A and E are both 2 holes away from the pivot point.
The actual (physics) explanation for this is using torques. The system is balanced in the picture since the center of mass of the bar is at D and the weight is at B. They are equal distances and weights from the pivot point, and cause torques of equal magnitude in opposite directions from each other, so the net torque is 0. We want to apply the same logic when adding 2 more masses. Torque = r F sinα, where r is the distance from the pivot point and F is the weight (force of gravity). Since F is down in both cases, they will cause torques in the opposite directions. To get a net torque of 0 (balanced), we want the torques to have equal magnitude in opposite directions, so as long as r (the distance from the pivot point) is equal for each mass, the system will remain balanced.
If a body travelled a distance 's' in 't'.
What is the distance travelled in 't'
Answers
Answer: Distance traveled in time t is s
Explanation: Self Explanatory
Hi
Please help on question asap if the answer is correct I'll rate you five stars a thanks and maybe even brainliest!
When two light bulbs are connected in series, the resistance in the circuit is increase compared to that with one lightbulb. The increased resistance opposes the flow of current so far fewer electrons pass per second , transferring less energy. The lightbulbs are therefore not as bright as In a circuit with same voltage but only one bulb.
However, when Two lightbulbs are connected in parallel, each loop behaves like a separate circuit . The resistance in each branch is the same as if there were just one light bulb in the whole circuit.there is the same current in each branch of the circuit ,so the bulbs Will light up with the same brightness as a single bulb circuit. The energy stored in the battery will decrease twice as quickly and battery will run out faster than I series circuit.
6) explain the advantages and disadvantages of arranging components in series or parallel.
Answers
Advantages of Components Arranged in Series:
1. Increased resistance: Connecting components in series increases the overall resistance in the circuit. This can be advantageous in situations where you want to limit the flow of current or control the amount of power being dissipated.
2. Voltage sharing: In a series circuit, the total voltage of the power supply is divided among the components. This can be useful when you want to ensure that each component receives a specific voltage.
3. Current consistency: The current remains the same throughout the series circuit, which can be beneficial when you need to ensure a consistent current flow through multiple components.
Disadvantages of Components Arranged in Series:
1. Reduced brightness or performance: As mentioned in the question, when light bulbs are connected in series, the increased resistance reduces the flow of current, resulting in dimmer bulbs or reduced performance in other electrical devices.
2. Single point of failure: If one component in a series circuit fails, it can disrupt the entire circuit and cause all components to stop functioning.
Advantages of Components Arranged in Parallel:
1. Brightness and performance: When components such as light bulbs are connected in parallel, each component receives the full voltage, resulting in brighter bulbs and better performance in other devices.
2. Redundancy: In a parallel circuit, if one component fails, the other components can continue to function independently. This provides redundancy and ensures that the failure of one component does not affect the others.
3. Increased current capacity: Parallel arrangement allows the circuit to handle higher currents, which can be useful in situations where high power or heavy loads are required.
Disadvantages of Components Arranged in Parallel:
1. Increased complexity: Parallel circuits require more wiring and connections, which can make the circuit more complex and harder to manage.
2. Higher cost: Parallel circuits may require more components and wiring, resulting in higher costs for materials and installation.
It's important to consider the specific requirements and constraints of the application when deciding whether to arrange components in series or parallel. Each configuration has its advantages and disadvantages, and the choice depends on factors such as desired current flow, voltage distribution, and reliability.I
A bike accelerates from 0 m/s to 15 m/s over the span of 5 seconds. How fast is the bike
traveling after 2.5 seconds?
Answers
The bike is travelling at 22.5 m/s after 2.5 s
What is acceleration?This is defined as the rate of change of velocity which time. It is expressed as
a = (v – u) / t
Where
a is the acceleration v is the final velocity u is the initial velocity t is the time How to determine the acceleration Initial velocity (u) = 0 m/sFinal velocity (v) = 15 m/sTime (t) = 5 sAcceleration (a) =?a = (v – u) / t
a = (15 – 0) / 5
a = 3 m/s²
How to determine the final velocity in the first 2.5 s Initial velocity (u) = 15 m/sAcceleration (a) = 3 m/s²Time (t) = 2.5 s Final velocity (v) = ?a = (v – u) / t
3 = (v – 15) / 2.5
Cross multiply
v – 15 = 3 × 2.5
v – 15 = 7.5
Collect like terms
v = 7.5 + 15
v = 22.5 m/s
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A ball is thrown 24 m/s into the air. How high does it go?
556.4 m
0 m
29.4 m
-556.4 m
Answers
Answer:
option c is correct
Explanation:
we know that
2as=vf^2-vi^2
vf=24 m/s
vi= 0 m/s
a=g= 9.8 m/s^2
s=vf^2-vi^2/2a
s=(24)²-(0)²/2*9.8
s=576/19.6
s=29.4 m
therefore option c is correct
Look at the diagram showing the different wavelengths in sunlight.
A diagram showing the human eye and visible light. Visible light is broken down by color with wavelength in nanometers. Red is 700, orange is 600, yellow is 580, green is 550, blue is 475, indigo is 450, violet is 400.
Which has a wavelength of 350 nanometers?
red light
violet light
infrared light
ultraviolet light
Answers
Answer:
ultraviolet light
plz mark me as brainliest.
Answer:
Ultra violet
Explanation:
Describe the setup of the electromagnet. Why does the wire need to be a conductive material?
Answers
An electromagnet consists of a conductive wire wrapped around a magnetic core, creating a magnetic field when an electrical current is passed through it.
An electromagnet is a type of magnet that is created by running an electrical current through a wire. The setup of an electromagnet involves a few basic components. First, there must be a wire that is conductive, meaning that it can conduct electricity. This wire is usually wrapped around a core, which is often made of iron, steel, or another magnetic material. When an electrical current is run through the wire, it creates a magnetic field around the wire. This magnetic field then magnetizes the core, creating an even stronger magnetic field. The strength of the electromagnet can be controlled by adjusting the amount of current that is run through the wire. The wire must be a conductive material because it needs to be able to carry the electrical current that creates the magnetic field. If the wire were not conductive, then the electrical current would not be able to flow through it, and the magnetic field would not be created. In summary, the setup of an electromagnet involves a conductive wire wrapped around a magnetic core, which is magnetized by the electrical current running through the wire. The wire must be conductive to carry the electrical current and create the magnetic field.For more questions on electromagnet
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An 8.0 Kg mass is placed at = 3 where should a 10 Kg mass be placed along the − so that the center of mass will be located ay = 4.5?
Answers
Answer:
Therefore, the 10 kg mass should be placed at x = 5.7 m along the x-axis to achieve a center of mass located at y = 4.5 m.
Explanation:
To find the position along the x-axis where a 10 kg mass should be placed such that the center of mass is located at y = 4.5, we can use the formula for the center of mass:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Here, m1 and x1 represent the mass and position of the 8 kg mass, respectively. m2 is the mass of the 10 kg mass, and we need to find x2, its position.
Given:
m1 = 8 kg
x1 = 3 m
x_cm = unknown (to be found)
m2 = 10 kg
y_cm = 4.5 m
Since the center of mass is at y = 4.5, we only need to consider the y-coordinate when calculating the center of mass position along the x-axis.
To solve for x2, we can rearrange the formula as follows:
x2 = (x_cm * (m1 + m2) - m1 * x1) / m2
Substituting the given values:
x2 = (x_cm * (8 kg + 10 kg) - 8 kg * 3 m) / 10 kg
Simplifying:
x2 = (x_cm * 18 kg - 24 kg*m) / 10 kg
Now, we can set the y-coordinate of the center of mass equal to 4.5 m and solve for x_cm:
4.5 m = (8 kg * 3 m + 10 kg * x2) / (8 kg + 10 kg)
Simplifying:
4.5 m = (24 kg + 10 kg * x2) / 18 kg
Multiplying both sides by 18 kg:
81 kg*m = 24 kg + 10 kg * x2
Subtracting 24 kg from both sides:
10 kg * x2 = 81 kg*m - 24 kg
Dividing both sides by 10 kg:
x2 = (81 kg*m - 24 kg) / 10 kg
Simplifying:
x2 = 8.1 m - 2.4 m
x2 = 5.7 m
(brainlest?) ples:(
Answer:
the 10 kg mass should be placed at x = -2.4 m to achieve a center of mass at y = 4.5 m.
Explanation:
To find the position along the x-axis where the 10 kg mass should be placed so that the center of mass is located at y = 4.5, we can use the principle of the center of mass.
The center of mass of a system is given by the equation:
x_cm = (m1x1 + m2x2) / (m1 + m2),
where x_cm is the x-coordinate of the center of mass, m1 and m2 are the masses, and x1 and x2 are the positions along the x-axis.
Given:
m1 = 8 kg,
x1 = 3 m,
m2 = 10 kg,
y_cm = 4.5 m.
To solve for x2, we need to find the x-coordinate of the center of mass (x_cm) by using the y-coordinate:
y_cm = (m1y1 + m2y2) / (m1 + m2),
where y1 and y2 are the positions along the y-axis.
Rearranging the equation and substituting the given values:
4.5 = (83 + 10y2) / (8 + 10).
Simplifying the equation:
4.5 = (24 + 10*y2) / 18.
Multiplying both sides by 18:
81 = 24 + 10*y2.
Rearranging the equation:
10*y2 = 81 - 24,
10*y2 = 57.
Dividing both sides by 10:
y2 = 5.7.
Therefore, the y-coordinate of the 10 kg mass should be 5.7 m.
To find the x-coordinate of the 10 kg mass, we can use the equation for the center of mass:
x_cm = (m1x1 + m2x2) / (m1 + m2).
Substituting the given values:
x_cm = (83 + 10x2) / (8 + 10).
Since the center of mass is at x_cm = 0 (the origin), we can solve for x2:
0 = (83 + 10x2) / (8 + 10).
Rearranging the equation:
83 + 10x2 = 0.
24 + 10*x2 = 0.
10*x2 = -24.
Dividing both sides by 10:
x2 = -2.4.
A soccer ball (k = 2/3) with a radius of 0.101 meters and a mass of 0.400 kilograms rolls on a field with an angular speed of 93 radians per second. a. What is the translational kinetic energy of the ball? Include units in your answer.b. What is the rotational kinetic energy of the ball? Include units in your answer.c. The ball then rolls up a hill. What height will the ball reach before coming to rest? Include units in your answer. All answers must be in 3 significant digits.
Answers
Given,
The radius of the ball, r=0.101 m
The mass of the ball, m=0.400 kg
The angular speed of the ball, ω=93 rad/s
a.
The linear velocity of the ball is given by,
\(v=\omega r_{}\)The translational kinetic energy is given by,
\(\begin{gathered} K_t=\frac{1}{2}mv^2 \\ =\frac{1}{2}m\omega^2r^2 \end{gathered}\)On substituting the known values,
\(\begin{gathered} K_t=\frac{1}{2}\times0.400\times93^2\times0.101^2 \\ =17.6\text{ J} \end{gathered}\)hus the translational kinetic energy of the ball is 17.6 J
b.
The moment of inertia of the ball is given by,
\(I=\frac{2}{3}mr^2\)The rotational kinetic energy of the ball is given by.
\(\begin{gathered} K_r=\frac{1}{2}I\omega^2 \\ =\frac{1}{2}\times(\frac{2}{3}\times mr^2)\times\omega^2 \\ =\frac{1}{3}mr^2\omega^2 \end{gathered}\)On substituting the known values,
\(\begin{gathered} K_r=\frac{1}{3}\times0.400\times0.101^2\times93^2 \\ =11.8\text{ J} \end{gathered}\)hus the trotational kinetic energy of the ball is 11.8 J
.
From the law of conservation of energy, the energy can neither be created nor be destroyed but can be converted from one form to another.
When ball rolls up the hill the ball will lose its translational and rotational kinetic energy. But the lost kinetic energy will be converted into its gravitational potential energy.
Therefore, the gravitational potential energy of the ball when it is up the hill is equal to the sum of its translational and rotational kinetic energy.
Thus,
\(\begin{gathered} K_t+K_r=P \\ =\text{mgh} \end{gathered}\)Where g is the acceleration due to gravity and h is the height that the ball will reach before coming to rest.
On rearranging the above equation,
\(h=\frac{K_t+K_r}{mg}\)On substituting the known values,
\(\begin{gathered} h=\frac{17.6+11.8}{0.400\times9.8} \\ =7.5\text{ m} \end{gathered}\)herefore the ball will treach a height of 7.5 m before coming to rest.
Find the induced voltage in the conductor of the Figure below where B = 0.04 ay Tan
U = 2.5 sin 103t az m/s.
Answers
The induced e.m.f is -0.02sin(10^3t) (V) which is option D
What is Induced Voltage?Induced voltage refers to the electrical voltage that is generated in a conductor or coil due to a changing magnetic field.
This phenomenon is known as electromagnetic induction and is the basis for many electrical devices such as generators and transformers.
Induced voltage can be calculated using Faraday's law, which states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux.
The induced voltage can be either positive or negative depending on the direction of the changing magnetic field and the orientation of the conductor or coil.
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A horse travels 1200 meters to the right in 60 seconds. What was its velocity?
a. 72,000 m/s
b. 20 m/s
c. 0.05 m/s
d. 1260 m/s
Answers
Answer:
a
Explanation:
If its not right choose D
A lowest A on a piano has a frequency of 27.5 HZ if the tension in the 2.00m string is 308N and one half wavelength occupies the spring what is the mass of the wire
Answers
The mass of the wire of lowest A on a piano is 0.00165 kg.
The frequency of a vibrating string is given by the equation:
f = (1/2L) * sqrt(T/μ)
where f is the frequency of the string, L is the length of the string, T is the tension in the string, and μ is the linear mass density of the string (mass per unit length).
We know the frequency of the lowest A on a piano is 27.5 Hz. We also know that one half wavelength occupies the string, so the length of the string is half the wavelength:
L = (1/2) * λ
The wavelength of a sound wave is given by:
λ = 2L/n
where n is the number of nodes (points of zero displacement) in the wave. For the lowest A on a piano, n = 1, so we can write:
λ = 2L
Substituting this into the equation above for L, we obtain:
L = λ/2
Now we can substitute these values into the first equation:
27.5 = (1/2)(λ/2) * sqrt(308/μ)
Simplifying, we get:
λ = 4L
308/μ = 4(27.5)^2 (1/4)
μ = 0.000824 kg/m.
Since μ = m/L, where m is the mass of the wire and L is its length, we can find the mass of the wire by multiplying the linear mass density by the length of the string:
m = μL
The length of the string is given as 2.00 m, so we can write:
m = 0.000824 kg/m * 2.00 m = 0.00165 kg
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Two fledglings leave a nest which is 2.50 m off the ground. One drops from rest and then 0.10 s later the second charges out of the nest with a velocity with horizontal and
downward components of 1.00 and 1.50 m/s, respectively.
1. Which fledgling hits the ground first (first or second)?
2. With what speed, in m/s, does the first fledgling hit the ground?
3. With what speed, in m/s, does the second fledgling hit the ground?
4. Which fledgling travels the greater displacement?
5. How far does a parent bird have to travel on the ground between the two fledglings, in m, to make sure they are alright?
Answers
t Answer:
1) the time of the pigeon 1 is less, so it comes first
2) v = - 6,997 m / s , 3) v = 10.15 m / s ,
4) the displacement of the second point in greater
5) x = 0.883 m
Explanation:
For this exercise we will use the kinematics equations
1) ask which chick reaches the ground first
we calculate for the first chick that has zero initial velocity
y = y₀ + v₀ t - ½ g t²
0 = yo - ½ g t²
t = √ 2 y₀ / g
let's calculate
t = √ (2 2.50 / 9.8)
t = 0.714 s
We calculate the time it takes for the second chick that has velocity v = (1 i ^ - 1.5 j⁾ m / s
y = y₀ + v₀t - ½ g t²
0 = 2.5 - 1.5 t - ½ 9.8 t²
4.9 t² + 1.5 t - 2.5 = 0
t² + 0.306 t - 0.510 = 0
we solve the quadratic equation
t = [0.306 ± √ (0.306² - 4 (-0.510))] / 2
t = [0.306 ± 1.46] / 2
The results are
t₁ = -0.577 s
t₂ = 0.883 m / s
we take positive time as correct
the time of the pigeon 1 is less, so it comes first
2) the speed of the first chick is
v = v₀ - g t
we can see that
v = -gt
v = - 9.8 0.714
v = - 6,997 m / s
the negative sign indicates that the speed is down
3) the speed of the other bird is
v = -1.5 - 9.8 0.883
v = 10.15 m / s
4) which chick has the greatest displacement. The first point falls vertically and its displacement is y₀
The second point describes a parabola and its displacement is
d = √ (x² + y₀²)
therefore we see that the displacement of the second point in greater
5) calculate the horizontal displacement of the second point
x = vx t
x = 1 0.883
x = 0.883 m
Plz answer asap I need all of the answer
Answers
Answer:
Turned up side down
Explanation:
Speed of a body spinning about an axis increases from rest to 100 rpm in 5 second if a constant torque is applied. The external torque is then removed and the body comes to rest in 100sec due to friction Find the frictional torque.
Answers
All of the following are internal factors that may negatively affect an individual with dementia EXCEPT A. frustration.
What is dementia's medical condition?Dementia is a medical condition capable of altering individual skills to remember and also to reason during decision-making, which is due to irreversible degeneration of neuronal cells in the brain that lead to a complete state or a false sense of reality in the individual according to the surrounding environmental conditions.
Dementia medical conditions are often associated with aging because they may lead to different degenerative neuronal problems, which must be treated in a proper clinical setting since the person is unable to live in normal conditions on his or her own.
Therefore, with this data, we can see that dementia medical condition that must be treated in clinical medical settings and it is associated with an irreversible loss of neuronal networks in the brain.
Complete question:
All of the following are internal factors that may negatively affect an individual with dementia EXCEPT:
Frustation
Fear and confusion
False beliefs
Fatigue
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The frictional torque of the spinning body is determined as ( I × 2.1 ) N/m.
What is frictional torque?Friction torque is the force between two objects that causes one of them to rotate around an axis.
Also, friction torque is the torque caused by the frictional force that occurs when two objects in contact move.
The frictional torque is calculated by applying the following equation as shown below.
τ = Iα
where;
I is the moment of inertia of the bodyα is the angular acceleration of the bodyThe angular acceleration of the body is calculated by applying the following equation as shown below.
α = Δω / Δt
α = ( ωf - ωi ) / ( t₂ - t₁)
where;
ωf is the final angular velocity of the body = 100 rpm ωi is the initial angular acceleration of the bodyt₁ is the initial time of motion of the bodyt₂ is the final time of motion of the bodyα = ( ωf - ωi ) / ( t₂ - t₁)
ωf = 100 rev/min x 2π rad/rev x 1 min / 60s = 10.5 rad/s
α = ( 10.5 - 0 ) / ( 5 - 0 )
α = 2.1 rad/s²
The frictional torque is calculated as follows;
τ = Iα
τ = ( I × 2.1 ) N/m
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How do electrons conduct electricity?Please explain in terms of charges
Answers
The electrons are usually at a constant distance from the nucleus of an atom in precious shells. The flow of charges to the per unit of time helps the conductor to conduct electricity. The mathematic representation of the electric current is given in the terms of charges as
\(I=\frac{q}{t}\)*Here 'q' is the charge
*Here 't' is the time
The movement of electrons
The flow of charges inside the metal (conductor) is known as the electric current.
A series circuit has a 12-volt power source and two resistors of 1 ohm and 2 ohms respectively. How many amps will flow when
the circuit is closed?
Answers
Answer:
ayoooooooo
Explanation:
Which is the best description of biodiversity?
1. All animals in an ecosystem
2. The variety of the type of life within the biosphere
3. The study of life
3. The variety of plants on Earth
Answers
Answer:2
Explanation:
A motorcycle stoop is at a traffic light, when the light turns green, the motorcycle accelerates to a speed of 78 km/h over a distance of 50 m. What is the average acceleration of the motorcycle over this distance?
Answers
The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².
To calculate the average acceleration of the motorcycle, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time
First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.
Converting the final velocity:
Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s
Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:
Average acceleration = (21.67 m/s - 0 m/s) / time
To find the time taken to reach this velocity, we need to use the formula for average speed:
Average speed = total distance/time
Rearranging the formula:
time = total distance / average speed
Plugging in the values:
time = 50 m / 21.67 m/s ≈ 2.31 seconds
Now we can calculate the average acceleration:
Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²
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a bus with a maximum speed of 20m/s takes 21sec to travel 270m from stop to stop. Its acceleration is twice as great as its deceleration. Find: A, the acceleration B, the distance traveled at maximum speed
Answers
Answer:
We can use the kinematic equations to solve this problem.
Let a be the acceleration and d be the distance traveled at maximum speed.
First, we can use the equation:
d = vt + (1/2)at^2
where v is the maximum speed, t is the time traveled at maximum speed, and a is the acceleration.
We know that the bus takes 21 seconds to travel 270 meters, so the time traveled at maximum speed is:
21 - 2a = t
We also know that the acceleration is twice as great as the deceleration, so we can write:
a = 2d
Then, we can substitute these expressions into the first equation:
d = (20)(21 - 2a) + (1/2)(2d)(21 - 2a)^2
Simplifying and solving for d, we get:
d = 210 - 5.25a + 0.25a^2
To find the acceleration, we can use the fact that the maximum speed is reached at the midpoint of the trip, so the distance traveled at maximum speed is half the total distance:
d = 1/2(270)
Solving for d, we get:
d = 135
Substituting this value into the equation for d, we get:
135 = 210 - 5.25a + 0.25a^2
Simplifying and solving for a, we get:
a = 8 m/s^2
Finally, we can use the equation:
d = vt
to find the distance traveled at maximum speed:
d = (20)(21 - 2a)
Substituting the value of a, we get:
d ≈ 188.4 m
Therefore, the acceleration of the bus is 8 m/s^2 and the distance traveled at maximum speed is approximately 188.4 meters.
-0,32 m - 4.2 At the instant the marble leaves the canon, the canon starts moving backwards (recoils) at a constant velocity. 4.1 State the principle of conservation of linear momentum in words. that is stationary canon is placed 0,32 m from a fixed bare After firing, the canon takes 0,33 s to collide with a barrier at a distance of 0,32 m. Calculate the speed the: W< 1 >E S 4.2.1 Canon collides with the barrier
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The cannon will completely stop when it collides with the barrier.
To calculate the speed at which the cannon collides with the barrier, we can follow these step-by-step calculations:
Determine the initial momentum of the system.
Since the cannon is initially stationary, the initial momentum is zero.
Apply the conservation of linear momentum.
According to the principle of conservation of linear momentum, the initial momentum of the system (zero) is equal to the final momentum of the system. The final momentum is the momentum of the cannon after firing.
Calculate the final momentum of the system.
Let's assume the mass of the cannon is represented by 'm' and the final velocity of the cannon is represented by 'v'. The final momentum of the system is given by: final momentum = m × v.
Set up the equation.
Since the initial momentum is zero, we have: 0 = m × v.
Solve for the final velocity of the cannon.
Dividing both sides of the equation by 'm', we get: v = 0.
Interpret the result.
The calculation shows that the final velocity of the cannon is zero. This means that the cannon comes to a complete stop when it collides with the barrier.
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Where is the near point of an eye for which a spectacle lens of power +2 D is prescribed for reading purpose?
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The near point of a human eye is about a distance of 25 cm.
The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.
This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.
The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.
In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.
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Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answers
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.