An object travels along a straight, horizontal surface with an initial speed of 2 ms. The position of the object as a function of time is given in the table. Which of the following graphs represents the object’s velocity as a function of time?
Answers
Answer:
The options are not provided, so i will answer in a general way.
We know that:
The movement is along a straight horizontal surface, then we have one-dimensional motion.
The speed is 2m/s
We want a graph of position vs time.
Now, remember the relation:
Distance = Speed*Time
Then we can write the position as a function of time as:
P(t) = 2m/s*t + P0
Where t is our variable, that represents time in seconds, and P0 is the position at time t = 0seconds, we can assume that this is zero.
Then the equation is:
P(t) = 2m/s*t
And the graph is something like:
The velocity of the object as function of time is given as, v = u + at
The given parameters;
initial velocity of the object, u = 2 m/s
The velocity of an object is defined as the change in the displacement of the object per change in time of the object's motion.
The final velocity of the object at any time, t, is given as;
v = u + at
where;
u is the initial velocity
a is the acceleration of the object
t is the time of motion
Thus, at every time (t), the velocity of the object will be the sum of the initial velocity and the product of the acceleration and time of motion.
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Related Questions
What is the force of the block pulling forward?
Answers
When we want to move, our feet try to push the ground backwards. But it is the friction from the ground that pushes us forwards.
a car's horn is producing a sound wave having a constant frequency of 350 hertz. if the car moves toward a stationary observer at constant speed, the frequency of the car's horn detected by this observer may be
a) 320Hz
b) 330Hz
c) 350Hz
d) 380 Hz
Answers
When the car's horn is producing a sound wave having a constant frequency of 350 hertz and the car moves toward a stationary observer at constant speed, the frequency of the car's horn detected by this observer may be (b) 330 Hz.
When a car moves toward the observer, the distance between the car and the observer decreases, causing the sound waves to compress.
This results in a higher frequency and a higher pitch.
When the car is moving away from the observer, the distance between the car and the observer increases, causing the sound waves to expand.
This results in a lower frequency and a lower pitch.
So, when a car's horn is producing a sound wave having a constant frequency of 350 hertz and it moves towards a stationary observer at a constant speed, the frequency of the car's horn detected by this observer may be 330Hz.
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a roller coaster starts at rest at the top of a 51-meter-high frictionless track. at the bottom of the track, what is the approximate speed of the roller coaster?
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The approximate speed of the roller coaster is 32m/s.
Considering that the earth and the roller coaster are both parts of one system.
We can use the law of conservation of energy,
This law states that in a system, the sum of total energy is always conserved.
So we can say that the energy at the top of roller coaster will be equal to the energy at the bottom of the roller coaster.
At top, whole energy is potential energy and the bottom whole energy is kinetic energy,
So we can write,
PE = KE
Mgh = 1/2Mv²
Where M is mass of roller coaster,
v is the speed of roller coaster,
g is acceleration due to gravity and,
h is the height of the roller coaster,
Putting all the values,
gh = 1/2v²
v² = 2gh
v² = 2×9.8×51
v² = 999.6
v = 31.61 m/s.
The speed of roller coaster at the end is 32 m/s approx.
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Use coefficients to balance the following equation: (if no coefficient is needed, use "1", do not leave
any box blank!)
Answers
Answer:
P₄ + 3O₂ → 2P₂O₃
Explanation:
To balance an equation we take each element one by one on each side and balance their atoms.
Like P₄ (Tetraphosphorus) in the left side has 4 atoms of phosphorus.
While on the right side P₂O₃ (Diphosphorus Trioxide) has 2 Phosphorus atoms.
So place 2 as a coefficient in front of P₂O₃.
Now Phosphorus atoms (4 atoms) are balanced on each side.
Now number of Oxygen atoms in P₂O₃ = 2 × 3 = 6
On the left left side number of Oxygen atoms in O₂ = 2
To balance Oxygen atoms in each side, place 3 as a coefficient before O₂ on the left.
Therefore, balance equation will be,
P₄ + 3O₂ → 2P₂O₃
When you speak, your voice sounds 10 dB louder to someone standing directly in front of you than to someone at the same distance but directly behind you. What is the ratio of the intensity of your voice for someone in front of you to the intensity for someone behind you?
Answers
The ratio of the intensity of voice for someone standing in front of the person to the intensity for someone standing behind is 10:1
What is intensity ?Intensity is a physical quantity that measures the amount of energy that flows through a given area per unit of time. In the context of sound waves, intensity refers to the amount of energy carried by sound waves per unit of time and per unit of area. It is related to the amplitude (or height) of the sound waves, which determines how much the pressure varies in the medium through which the waves travel. The unit of intensity is watts per square meter (W/m^2). The intensity of sound waves is important in many applications, such as in measuring the loudness of sounds, determining safe exposure levels to noise, and designing acoustic systems.
The difference in the sound level in decibels (dB) between two positions can be calculated using the following formula:
ΔL = 10 log10(I2/I1)
where ΔL is the difference in dB, I1 is the intensity at the first position, and I2 is the intensity at the second position.
In this case, the sound level is 10 dB higher is known for someone standing directly in front than for someone at the same distance but directly behind you. Using this information to set up the following equation:
10 dB = 10 log10(I_front/I_back)
where I_front is the intensity of voice for someone standing in front and I_back is the intensity of voice for someone standing behind
We can simplify this equation by dividing both sides by 10:
1 dB = log10(I_front/I_back)
Now, raise both sides of the equation to the power of 10:
10^1 = I_front/I_back
Simplifying this expression
I_front/I_back = 10
So the ratio of the intensity of your voice for someone standing in front of you to the intensity for someone standing behind you is 10:1. In other words, your voice is 10 times louder for someone standing directly in front of you than for someone at the same distance but directly behind you.
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Consider the function e(h) = ε h h 2 6 m where m is a bound for the third derivative of a function. Show that e(h) has a minimum at p3 3ε/m
Answers
Since , e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum of function.
In mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum) or the minimum value of a function is the lowest point of a vertex
e(h) = ∈ /h +( \(h^{2}\)/6) M
e'(h) = - ∈ /\(h^{2}\) + (2h/6) M
putting , e'(h) = 0
- ∈ /\(h^{2}\) + (2h/6) M = 0
h = \((3 /M)^{1/3}\) * (∈^(1/3))
e"(h) = 2∈ / \(h^{3}\) + (2M)/6 equation 1
substituting value of h in equation 1, we get
e"(h) = 2∈M / 3∈ + M/3
e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum
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A teapot with a surface area of 700 cm2 is to be silver plated. It is attached to the negative electrode of an electrolytic cell containing silver nitrate (Ag+ NO3 −). If the cell is powered by a 12.0 V battery and has a resistance of 1.80 Ω, how long does it take for a 0.133 mm layer of silver to build up on the teapot? (The density of silver is 10.5 × 103 kg m3 ⁄ ).
Answers
Answer:
Time taken = 13095 seconds
Explanation:
Mass of silver required = density of silver * volume of silver
volume of silver = surface area of teapot * height of silver layer
volume = 700 cm² * 1 m²/ 10⁴ cm² * 0.133 * 1 m/1000 mm
volume = 9.31 * 10⁻⁶ m³
mass of silver = 10.5 * 10³ kg/m³ * 9.31 * 10⁻⁶ m³
mass of silver = 9.7755 * 10⁻² kg * 1000 g/ 1 kg = 97.755 g
1 mole of Ag⁺ will be discharged by 96500 C of charge
molar mass of silver 108 g/mol
97.755 g of silver will be discharged by = 96500 C * 97.755/108 = 87345.9 C of charge
From Q = I * t
I = V/R = 12/1.8 = 6.67 A
Therefore, t = Q/I
t = 87345.9/6.67
t = 13095 seconds
why are fuels from crude oil so widely used for transportation
Answers
Which best explains the surface tension of water? capillary action cohesion adhesion sublimation
Answers
Answer:
Cohesion
Explanation:
Surface tension of water refers to the ability of the surface of water as a liquid to resist an external force. Surface tension of a liquid like water is dependent on the force of attraction that hold its molecules to one another, which is a force called COHESIVE FORCE.
Cohesion is a property of water characterized by the ability of water molecules to be attracted to one another. This cohesive property causes its molecules to be able to resist external forces or in other words is responsible for the SURFACE TENSION. Hence, the stronger the cohesive force between molecules of a liquid, the higher the surface tension.
similar to other solar technologies, this _______ will require consistent access to sunlight to work effectively; its _______ , however, is that it has minimal to no direct emissions of carbon dioxide.
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similar to other solar technologies, this solar-powered system will require consistent access to sunlight to work effectively; its advantage, however, is that it has minimal to no direct emissions of carbon dioxide.
A solar-powered system refers to a system that utilizes solar energy to generate electricity or perform other functions. It typically includes solar panels or photovoltaic cells that convert sunlight into electrical energy. These systems harness the power of the sun to provide a sustainable and renewable source of energy. By using solar power, they reduce reliance on fossil fuels and help mitigate greenhouse gas emissions, including carbon dioxide. Solar-powered systems are used in various applications such as residential and commercial buildings, street lighting, water heating, and powering electronic devices. They offer the advantage of clean, renewable energy generation, contributing to a more sustainable and environmentally friendly energy infrastructure.
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How much work must be done to accelerate a 704.15 kg car from 15.28 m/s to 32.48 m/s?
Answers
Answer:
To calculate the amount of work required to accelerate a car from 15.28 m/s to 32.48 m/s, you can use the following formula:
Work = Force * Distance
In this case, the force is the accelerating force on the car, and the distance is the change in velocity of the car. The accelerating force can be calculated using the formula:
Force = Mass * Acceleration
To find the acceleration of the car, you can use the formula:
Acceleration = Change in Velocity / Time
The time it takes for the car to accelerate can be calculated using the formula:
Time = Distance / Velocity
Substituting these formulas into the original equation, we get:
Work = Mass * (Change in Velocity / Time) * (Time)
Plugging in the given values, we get:
Work = 704.15 kg * (32.48 m/s - 15.28 m/s) / (32.48 m/s - 15.28 m/s) * (32.48 m/s - 15.28 m/s / 32.48 m/s)
Simplifying this equation, we get:
Work = 704.15 kg * (17.2 m/s)^2
Work = 704.15 kg * 295.04 m^2/s^2
Work = 207,764.79 kg*m^2/s^2
So the total amount of work required to accelerate the car from 15.28 m/s to 32.48 m/s is 207,764.79 kg*m^2/s^2.
Explanation:
Assume a simply supported beam with span of 15m. It will be exposed to a dead load of 20kN/m (including self-weight) and a live load of 2kN/m along the full span. At the same time, it will be experiencing a concentrated dead load of 23kN + a live load of 1kN at midspan, as well as an additional dead load of 15kN located at 4m from the right support.
The beam has a rectangular cross-section with a width of 600mm and total height of 1000mm. The beam is reinforced with 10- 25M tensions bars at effective depth of 920 mm. The maximum aggregate size used is 20mm, and has the following material properties: f’c = 25MPa ,fy = 400 MPa.
Please perform the following task:
1) Draw the governing shear and bending moment diagram for the factored load.
2) Calculate the moment resistance of the cross section.
3) Comment if this cross section is adequately designed to resist the factored bending moment. (LRFD)
Answers
The values of all sub-parts have been obtained.
(1). The maximum factored load the beam can withstand is 45.2 kN/m.
(2). The moment resistance of the cross-section is 291735.65 Nm.
(3). The factored moment demand is 27939.6 Nm
1) To draw the governing shear and bending moment diagram for the factored load, we need to first calculate the maximum factored load that the beam can withstand.
The maximum factored load on the beam is given by:
Dead Load = 20 kN/m + 15 kN
= 35 kN/m.
Live Load = 2 kN/m + 1 kN
= 3 kN/m.
Total Factored Load = 1.2 x Dead Load + 1.6 x Live Load
= 1.2 x 35 kN/m + 1.6 x 3 kN/m
= 45.2 kN/m.
The maximum factored load the beam can withstand is 45.2 kN/m.
The shear force and bending moment diagrams for the given factored load can be obtained as shown below:
Shear Force Diagram:
Bending Moment Diagram:
2) To calculate the moment resistance of the cross-section, we can use the formula:
MR = σst A'(d - a/2) + 0.85f'c A''(d - a/2)
Where, σst = yield stress of tension steel [σst = fy / γst],
γst = safety factor for tension steel [γst = 1.15A']
A' = area of tension steel, [A'' = b(d - a)].
Where,
b = width of the beam [b = 600 mm],
d = total height of the beam [d= 1000 mm],
a = effective depth of tension steel [a = 920 mm]
f'c = compressive strength of concrete [f'c = 25 MPa],
MR = σst A'(d - a/2) + 0.85f'c A''(d - a/2)
MR = (400 / 1.15) x 10 x (1000 - 920/2) + 0.85 x 25 x 590 x (1000 - 920/2)
MR = 291735.65 Nm
The moment resistance of the cross-section is 291735.65 Nm.
3) To check if this cross-section is adequately designed to resist the factored bending moment (LRFD), we need to calculate the factored moment demand and compare it with the moment resistance.
The factored moment demand is given by:
MF = ϕ x Mu
Where,ϕ = resistance factor = 0.9, Mu = factored bending moment
Mu = 1.2 x Dead Load x L2 / 8 + 1.6 x Live Load x L2 / 8 + 1.2 x (Dead Load + Live Load) x L2 / 2
= 1.2 x 35 x 152 / 8 + 1.6 x 3 x 152 / 8 + 1.2 x 38 x 152 / 2
= 31044 Nm
MF = ϕ x Mu
= 0.9 x 31044
= 27939.6 Nm
The factored moment demand is 27939.6 Nm, which is less than the moment resistance of the cross-section, i.e., 291735.65 Nm.
Therefore, this cross-section is adequately designed to resist the factored bending moment.
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if the truck has a mass of 2000 kg what is the momentum (V=35 m/s) express your answer in kg Point m/s?
Answers
Answer:
70 000 kg•m/s
Explanation:
You can find the momentum multiplying the velocity by the mass:
Momentum = 2000 • 35
Momentum = 70 000
What is the size of the planets from smallest to largest?
Answers
The size of the planets from smallest to largest is: Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, and Jupiter.
The planets in our solar system range in size from the small, rocky Mercury, which has a diameter of 4,879 km, to the giant gas giant Jupiter, which has a diameter of 139,822 km. The order of the planets based on size is determined by their relative diameters, with the smallest planet, Mercury, being the first in the list and the largest planet, Jupiter, being the last.
The rocky planets, Mercury, Mars, Venus, and Earth, are all relatively close in size, with diameters ranging from 4,879 km to 12,742 km. The gas giants, Jupiter, Saturn, Uranus, and Neptune, are much larger, with diameters ranging from 49,244 km to 139,822 km.
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When do trilobites disappear from the rock sequence?
Answers
Answer:
252 million years ago
Explanation:
hope this helps :)
An electron moving at 4.10 ✕ 103 m/s in a 1.45 T magnetic field experiences a magnetic force of 1.40 ✕ 10−16 N. What angle does the velocity of the electron make with the magnetic field? There are two answers between 0° and 180°. ° (smaller value) ° (larger value)
Answers
ANSWER
\(8.46\degree;\text{ }171.54\operatorname{\degree}\)EXPLANATION
Parameters given:
Speed of electron, v = 4.10 * 10^3 m/s
Magnetic field, B = 1.45 T
Magnetic force, F = 1.40 * 10^(-16) N
To find the angle that the velocity of the electron makes with the magnetic field, apply the formula for magnetic force:
\(F=qvB\sin\theta\)where θ = angle
q = electric charge = 1.6 * 10^(-19) C
Make θ the subject of the formula:
\(\begin{gathered} \sin\theta=\frac{F}{qvB} \\ \\ \theta=\sin^{-1}(\frac{F}{qvB}) \end{gathered}\)Therefore, the angle that the velocity makes is:
\(\begin{gathered} \theta=\sin^{-1}(\frac{1.4*10^{-16}}{1.6*10^{-19}*4.1*10^3*1.45}) \\ \\ \theta=\sin^{-1}(0.1472) \\ \\ \theta=8.46\degree \end{gathered}\)To find the second angle, subtract the angle from 180 degrees:
\(\begin{gathered} 180-8.46 \\ \\ 171.54\degree \end{gathered}\)The angles are:
\(8.46\operatorname{\degree};\text{ }171.54\operatorname{\degree}\)A swimming pool of width 9.0 m and length 12.0 m is filled with water to a depth of 3.0 m. Calculate pressure on the bottom of the pool due to the water.
Hint: 1 m^3 of water has a mass of 1000 kg.
Answers
With the use of the formula, the pressure on the bottom of the pool due to the water is 29400 Pascal
Given that a swimming pool of width 9.0 m and length 12.0 m is filled with water to a depth of 3.0 m.
Volume = Length x Width x Height
Volume = 9 x 12 x 3
Volume = 324 \(m^{3}\)
Since 1 m^3 of water has a mass of 1000 kg,
Mass = 324 x 1000
mass = 324000 kg
To calculate the pressure on the bottom of the pool due to the water, let us use the pressure formula below
P = δgh
where
P = pressure
δ = density of the water = 1000 kg/\(m^{3}\)
g = Acceleration due to gravity = 9.8 m/\(s^{2}\)
h = height = 3m
Substitute all the parameters into the formula
P = 1000 x 9.8 x 3
P = 29400 Pascal
Therefore, the pressure on the bottom of the pool due to the water is 29400 Pascal
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Suppose a wire is connected between points 1 and 2. What happens to each bulb? does it get brighter, stay the same, get dimmer, or go out? Explain.
Answers
Each bulb will stay at the same brightness position as before. When a wire is connected between points 1 and 2 the circuit becomes a parallel circuit.
In a parallel circuit, the voltage across each bulb remains the same, and each bulb will remain at the same brightness position as before. The wire was connected assuming that the voltage supplied to the circuit remains constant. The overall resistance in the circuit will drop due to the added wire, so the total current supplied by the voltage source will increase.
This increased current will be divided between the bulb so each bulb will admit a slightly advanced current than earlier but not enough to create a noticeable increase in lightness. thus, each bulb will stay at the same brightness position as before.
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The value of the momentum of a system is the same at a later time earlier time if there are no as at an Select the best Answer(s), and write on your paper A. inelastic collisions between particles within the system . B. internal forces acting between particles within the system . C. collisions between particles Wlthin the system . D. changes of momentum of Individual particles within the system E. external forces acting on particles of the system,
Answers
The value of the momentum of a system is the same at a later time earlier time if there are no E. external forces acting on particles of the system.
The value of the momentum of a system remains the same over time when there are no external forces or inelastic collisions between particles within the system. This is known as the conservation of momentum. Internal forces, such as gravity, can act on particles within the system, but they do not cause changes in the overall momentum of the system. Similarly, changes in the momentum of individual particles do not affect the momentum of the entire system. Only external forces, such as a push from a wall or a pull from a rope, will change the overall momentum of the system.
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Which of the following statements about systems are correct?
i. In a closed system, matter and energy cannot escape into its surroundings.
ii. Momentum is not conserved in an open system.
iii. Kinetic energy is always conserved in a closed system.
iv. None of the above.
Answers
The correct statement about systems is i) In a closed system, matter and energy cannot escape into its surroundings.
In a closed system, matter is not exchanged with its surroundings, but energy can still be transferred between the system and its surroundings. The total energy within a closed system remains constant, although it can change from one form to another (e.g., potential energy to kinetic energy).
Momentum is conserved in both closed and open systems. In an open system, matter and energy can enter or exit, but momentum is still conserved within the system.
While energy is conserved in a closed system, kinetic energy is not always conserved. Kinetic energy can be converted into other forms of energy within the system, such as potential energy or thermal energy.
the correct statement is only i. In a closed system, matter and energy cannot escape into its surroundings.
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(a) find the far point of an eye for which a prescribed lens has an optical power of -0.65 d.
Answers
The far point of the eye is approximately 1.54 meters.
To find the far point of an eye follow these steps:
1. Determine the focal length of the lens: The optical power (P) of a lens is the inverse of its focal length (f) in meters. So, P = 1/f or f = 1/P.
2. Calculate the focal length: Given the optical power of -0.65 D, the focal length can be calculated as f = 1/-0.65 ≈ -1.54 meters. A negative sign indicates that the lens is a diverging lens, which is commonly prescribed for myopia or nearsightedness.
3. Find the far point: For a person with myopia, the far point is the distance at which they can see clearly without any corrective lenses. The far point can be found using the lens formula, which is 1/f = 1/u + 1/v, where 'f' is the focal length, 'u' is the object distance (distance of the object from the lens), and 'v' is the image distance (distance of the image formed from the lens).
Since the far point is the maximum distance at which the person can see clearly without corrective lenses, the image formed by the lens should be at infinity (v = ∞). So the formula becomes:
1/f = 1/u + 1/∞
1/f = 1/u
4. Calculate the object distance (u): Since we know the focal length (f), we can calculate the object distance (u) using the formula:
u = 1/(1/f) = 1/(1/-1.54) ≈ -1.54 meters
So, the far point of the eye is approximately 1.54 meters. Note that the negative sign indicates that the far point is a virtual point located behind the lens.
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Our solar system includes
a. galaxies
b. asteroids
c. black holes.
d. constellations
Answers
I think it's asteroids but I'm not 100% sure
On earth a bag of sugar weight 10N. on mars a bag of sugar weight 4N. suggest the weight of the sugar is different on earth and mars
Answers
Answer:
gravity
Explanation:
there eould be a different gravitational strenght on both of the planets causing it to weigh more, or less
In mars, the effect of gravity on the object is weaker compared to while on earth. This weakness is what causes the reduction in the weight of the bag of sugar while on mars.
We must understand that the mass of an object may differ depending on its location on the planet. This is due to the effect of gravity on the object.
Gravity is simply defined as any force which attracts an object towards the centre of the earth.
From the question given, we are told that the weight of sugar is 10N on the earth and 4N on Mars. This difference in their mass is attributed to the effect of gravity on the object.
In mars, the effect of gravity on the object is weaker compared to while on earth. This weakness is what causes the reduction in the weight of the bag of sugar while on mars.
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A 3000 kg truck travelling at 50km/hr strikes a stationary 1000 kg car, locking the two vehicles
together. What is the final velocity of the two vehicles?
(Please show work)
Answers
Answer:
50 x 3000 = 150000/4000 = 37.5
37.5 I think.
Explanation:
Hope this helps!
A 3000 kg truck travelling at 50km/hr strikes a stationary 1000 kg car, locking the two vehicles together, the final velocity of the two vehicles after the collision is approximately 10.43 m/s.
We may use the concept of conservation of momentum to calculate the final velocity of the two vehicles after the collision.
The total initial momentum (P_initial) is given by:
P_initial = (mass of truck) * (initial velocity of truck) + (mass of car) * (initial velocity of car)
P_initial = (3000) * (50) + (1000) * (0)
The velocity:
Vt = 50 * (1000/3600) = 13.9 m/s
Vc = 0 = 0 m/s
P_initial = (3000) * (13.9) + (1000) * (0 )
P_initial = 41700 kg·m/s
P_initial = P_final
41700 kg·m/s = (3000 kg + 1000 kg) * Vf
41700 kg·m/s = 4000 kg * Vf
Now Vf:
Vf = 41700 kg·m/s / 4000 kg
Vf ≈ 10.43 m/s
Therefore, the final velocity of the two vehicles after the collision is approximately 10.43 m/s.
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what is the wavelength of such a wave? the speed of sound in air is 340 m/s.
Answers
Answer:
wavelength is λ=fv=440340=0. 77m.
How many electrons per second flow through a wire with a 12pA current?
Answers
how does a force pumb works
Answers
Answer:
A force pump can be used to raise water by a height of more than 10m, the maximum height allowed by atmospheric pressure using a common lift pump.
In a force pump, the upstroke of the piston draws water, through an inlet valve, into the cylinder. On the downstroke, the water is discharged, through an outlet valve, into the outlet pipe.
12) Driving home from school one day, you spot a ball rolling out into the street (FIGURE 5-27). You brake for 1.20 s, slowing your 950-kg car from 16.0 m>s to 9.50 m>s. What was the average forceexerted on your car during braking and How far did you travel while braking?
Answers
We are given the following information
Mass of car = 950 kg
Initial speed of car = 16.0 m/s
Final speed of car = 9.50 m/s
Time = 1.20 s
The average force exerted on the car during braking can be found using Newton's 2nd law of motion
\(F=m\cdot a\)Where m is the mass of the car and a is the acceleration of the car.
The acceleration of the car is given by
\(\begin{gathered} a=\frac{v_f-v_i}{t} \\ a=\frac{9.50-16.0}{1.20} \\ a=-5.4167\; \; \frac{m}{s^2} \end{gathered}\)The negative sign indicates deacceleration since the car is stopping.
So, the force is
\(\begin{gathered} F=m\cdot a \\ F=950\cdot5.4167 \\ F=5145.865\; \; N \end{gathered}\)Therefore, an average force of 5145.865 N was exerted on your car during braking.
The distance traveled by the car while braking can be found as
\(s=v_i\cdot t+\frac{1}{2}\cdot a\cdot t^2\)Let us substitute the given values
\(\begin{gathered} s=16.0\cdot1.20+\frac{1}{2}\cdot(-5.4167)\cdot(1.20)^2 \\ s=19.20-3.90 \\ s=15.3\; m \end{gathered}\)Therefore, the car traveled a distance of 15.3 m while braking.
A hydraulic lift consists of two pistons acting on a common fluid. if the areas of the two pistorns are 50 cm2 and 2500 cm2, which end do you put under your 3000 lb car to lift it? how much force do you then need to lift the car? if the car is to be raised 2 m, how much must the other piston be lowered?
Answers
The other piston must be lowered by 2 m to lift the car 2 m using the equation for hydraulic pressure.
To lift a 3000 lb car with a hydraulic lift, the piston with the larger area (2500 cm^2) should be placed under the car. The force required to lift the car can be calculated using the equation for hydraulic pressure:
P = F / A
where P is the pressure, F is the force, and A is the area of the piston. Plugging in the values, we get:
P = 3000 lb / 2500 cm^2 = 1.2 lb/cm^2
The force required to lift the car is then transmitted to the other piston, which has a smaller area (50 cm^2), by the fluid. The pressure on this piston is the same, so the force required to lift the car is:
F = P * A = 1.2 lb/cm^2 * 50 cm^2 = 60 lb
To lift the car 2 m, the other piston must be lowered by an amount equal to the product of its area and the change in pressure due to the height of the lift. The change in pressure is given by the equation:
ΔP = ρgh
where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the lift. Plugging in the values, we get:
ΔP = 1000 kg/m^3 * 9.8 m/s^2 * 2 m = 19680 Pa
The change in the height of the other piston is then:
Δh = ΔP / (ρg) = 19680 Pa / (1000 kg/m^3 * 9.8 m/s^2) = 2 m
So the other piston must be lowered by 2 m to lift the car 2 m.
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what is the greatest distance (in degrees) that a star can be from polaris and still be circumpolar as seen from philadelphia pa (latitude 40.0 °)
Answers
A star is considered circumpolar if it remains above the horizon throughout the entire night. The greatest distance that a star can be from Polaris, the North Star, and still be circumpolar is 50°.
Circumpolar stars are those that do not set below the horizon but instead appear to revolve around the celestial pole. In the northern hemisphere, Polaris serves as the North Star, located very close to the celestial north pole.
For a star to be circumpolar as seen from Philadelphia (latitude 40.0°), it must remain above the horizon at all times during the night.
The distance between Polaris and the celestial pole is equivalent to the observer's latitude. In this case, since the latitude of Philadelphia is 40.0°, any star within 40.0° of Polaris will be circumpolar.
Therefore, the greatest distance a star can be from Polaris and still be circumpolar is 40.0° + 10.0° (as the North Star is approximately 10.0° away from the celestial pole), giving a total of 50.0°.
Any star within this range, up to 50.0° from Polaris, will never dip below the horizon and will remain visible throughout the entire night as a circumpolar star.
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