Each of the three choices is tasteless, exhibitionist, juvenile, and dangerous. John should do none of them.
Encountering a news crew, there's no reason for John to call attention to himself in a childish way, or interfere with their work in any way.
What he should do is:
==> Slow down
==> Pass the scene cautiously
==> Resume his normal, legal speed quietly, in case the crew happens to be recording audio at the moment.
Mysteriously, this course of action is nowhere to be found among the choices listed.
Answer:
all three options :)
Explanation:
cuz merica
A hammer is used to hit a nail into a board. Which statement is correct about the forces at play between the nail and the hammer? The nail exerts an equal force on the hammer in the same direction. The nail exerts a much smaller force on the hammer in the opposite direction. The nail exerts an equal force on the hammer in the opposite direction. The nail exerts a much smaller force on the hammer in the same direction.
Answer:
The nail exerts an equal force on the hammer in the opposite direction.
Explanation:
The Newtons third law states that there is an equal an opposite reaction for every action. When hammer pushes the nail, the nail will push the hammer back in opposite direction. When the hammer hits a nail then nail will exert the equal and opposite force to the hammer. These both objects will exert force on each other in opposite directions.
Hello, I am BrotherEye
Answer:
Answers are
1. "The nail exerts an equal force on the hammer in the opposite direction."
2. "500 N"
3. "The iron piece exerts a force of 1 N on the magnet in the opposite direction."
4. "When mass moves closer to the point of rotation, rotational inertia decreases."
5. "The skater spins slower because his rotational inertia has increased."
Explanation:
Un pez llamado PARGO ROJO vive a grandes profundidades. Si se pesca, al salir a la superficie puede tomar el aspecto de la foto porque su vejiga natatoria aumenta de volumen al disminuir la presión. La ley que lo explica es...
Answer:
Hay diversas leyes que podemos usar acá.
Acá sabemos que la vejiga aumenta su tamaño al reducir la presión, esto tiene sentido, pues al haber menos presión, hay menos fuerza que comprime la vejiga, lo que le permite aumentar su volumen.
Acá tenemos una relación inversa de la forma: V = K/P
Una relación inversa donde la presión esta en el denominador y K es un termino que no depende ni del volumen ni de la presión.
Entonces, a medida que aumenta P, el denominador aumenta, por lo que el valor del volumen decrece.
Un ejemplo de una ecuación similar es la del gas ideal, por ejemplo, para un gas ideal dentro de un globo de volumen V para una dada presión P:
V = nRT/P
donde n es el numero de moles, R es la constante termodinámica y T es la temperatura, acá podemos ver que esta ecuación tiene la misma forma fundamental que la escrita arriba.
Calculate the volume of this regular solid. A cylinder labeled B at the top, 13 centimeters high with a radius of 4 centimeters. What is the volume of the cylinder? Round your answer to the nearest hundredth.
Answer:
The volume of the cylinder is [tex]653.71\ \text{cm}^3[/tex]
Explanation:
Given that,
The height of the cylinder is 13 cm
Radius of the cylinder is 4 cm
We need to find the volume of the cylinder. The formula that is used to find the volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\V=\dfrac{22}{7} \times (4)^2 \times 13\\\\V=653.71\ \text{cm}^3[/tex]
So, the volume of the cylinder is [tex]653.71\ \text{cm}^3[/tex]
Answer:
653.45 is the answer
Explanation:
Using your own words, tell me
what is the difference between an Pure Substance and a Mixture? Make sure to give me an example of each.
Answer:
Hey there!
Mixtures are physically combined and can be separated. For example, sand and water is a mixture.
Pure substances are samples of matter with definite, and unchangeable chemical properties. For example, diamond is a pure substance.
Let me know if this helps :)
a pure substance is a substance that has not been mixed with anything, a mixture has been mixed with another substance. an example is
dirt +water=mud iron is an example of a substance
In series combination of resistors, the total electric current is equal to the current flowing through each resistor.
A. False B. True C.The statement above lacks information
WILL GIVE BRAINLIEST! :)
Answer:
The answer is B, true.
Because same current flows through each resistors in Series.
Plz Mark as Brainlist
And follow me.
[tex] \LARGE{ \underline{ \tt{ \pink{True \: or \: False}}}}[/tex]
The above statement is true.
❍ In series combination of resistors, the total electric current is equal to the current flowing through each resistor..
Explanation:-In series combination, the resistors are connected end to end.There is no branch of extra wire with resistor, Hence Current through the entire circuit remains constant.The Potential difference between the resistors changes due to variation in end points. The equivalent resistance of the total circuit is the sum of the resistors connected end to end.The total or equivalent resistance is always greater than other individual resistance.━━━━━━━━━━━━━━━━━━━━
A container contains 200g of water at initial temperature of 30°C. An iron nail of mass 200g at temperature of 50°C is immersed in the water. What is the final water temperature? State the assumptions you need to make in your calculations.
[Given the value of specific heat capacity of water is 4200 J kg^-1 °C^-1 and that of iron is
450 J kg^-1 °C^-1]
Answer:
The final temperature is 31.94°
Explanation:
The mass of the water in the container m₁ = 200 g = 0.2 kg
The initial temperature of the water, T₁₁ = 30°C
The mass of the iron, m₂ = 200 g = 0.2 kg
The temperature of the iron T₂₁= 50°C is immersed in the water,
The specific heat capacity of the water, c₁ = 4200 J/(kg·°C)
The specific heat capacity of the iron, c₂ = 450 J/(kg·°C)
Heat capacity relation is given by the formula;
Heat capacity Q = Mass, m × Specific heat capacity, c × Temperature change, (T₂ - T₁)
Given that energy can neither be created nor destroyed, and with the assumption that all the heat lost by the nail is gained by the water we have;
Heat lost by iron nail = Heat gained by the water
m₁ × c₁ × (T₂ - T₁₁) = m₂ × c₂ × (T₂₁ - T₂)
Where, T₂ is the final temperature
0.2 kg × 4200 J/(kg·°C) × (T₂ - 30) = 0.2 kg × 450 J/(kg·°C) × (50° - T₂)
840·T₂ - 25200 = 4500 - 90·T₂
4500 + 25200 = 840·T₂ + 90·T₂
29700 = 930·T₂
T₂ = 29700/930 = 31.94°.
The final temperature = 31.94°.
Please answer, it's really urgent A boy performs an experiment to measure the speed of sound. He stands 100 meters away form a large wall and claps his hands to make an echo. He claps again as soon as he was the echo, He does this ten times, each time clapping an soon as he hears the echo. The time between the first clap and the tenth echo a recorded. Why it better to time ten echoes together rather than just one echo?
Answer:
Explanation:
The speed of sound is very high . It is about 340 m /s . In one echo , it takes approximately
2 x 100 / 340
= .6 sec
In 10 simultaneous echo , it will take 6 s . It is difficult to measure .6 sec but to measure 6 s is easy and it can be made with greater precision , so we can calculate velocity of sound with great precision .
This is the reason why , instead of one echo , 10 echos are made and duration of 10 echo is measured , rather than making one echo and measuring time of one echo .
Pls help A car starts from rest and gains a velocity of 20m/s in 10 seconds calculate its acceleration and the distance covered by it in this time
Answer:
[tex] \boxed{\sf Acceleration \ (a) = 2 \ m/s^{2}} [/tex]
[tex] \boxed{\sf Distance \ covered \ (s) = 100 \ m} [/tex]
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 20 m/s
Time taken (t) = 10 sec
To Find:
(i) Acceleration (a)
(ii) Distance covered (s)
Explanation:
[tex]\sf (i) \ From \ 1^{st} \ equation \ of \ motion:[/tex]
[tex] \sf \implies v = u + at[/tex]
[tex] \sf \implies 20 = 0 + a(10)[/tex]
[tex] \sf \implies 10a = 20[/tex]
[tex] \sf \implies \frac{10a}{10} = \frac{20}{10} [/tex]
[tex] \sf \implies a = 2 \: m/ {s}^{2} [/tex]
[tex]\sf (ii) \ From \ 2^{nd} \ equation \ of \ motion:[/tex]
[tex] \sf \implies s = ut + \frac{1}{2} a {t}^{2} [/tex]
[tex]\sf \implies s = (0)(10) + \frac{1}{2} \times 2 \times {(10)}^{2} [/tex]
[tex]\sf \implies s = \frac{1}{ \cancel{2}} \times \cancel{2} \times {(10)}^{2} [/tex]
[tex]\sf \implies s = {10}^{2} [/tex]
[tex]\sf \implies s = 100 \: m[/tex]
Which example best describes a restoring force?
any force that is applied to a spring to change its length
the force applied to stretch a spring and increase its length
the force applied to restore a spring to its original length
the force applied to compress a spring and shorten its length
Answer:
the force applied to restore a spring to its original length
Explanation:
The marginal cost curve
(a) Lies below the ATC curve when the ATC curve slopes upward.
(b) Intersects the AFC and ATC curves at their respective minimum points.
(c) Lies above the AVC curve when the AVC curve slopes downward.
(d) Intersects the AFC and AVC curves at their respective minimum points.
(e) Intersects the AVC and ATC curves at their respective minimum points
Answer:
c
Explanation:
The marginal cost curve image has been attached from which we can clearly, indicate that
ATC = average total cost
AFC = average fixed cost
AVC = average variable cost.
From the graph we can indicate that the marginal cost curve
(c) Lies above the AVC curve when the AVC curve slopes downward.
a bird statue with a mass 0.2 kg hangs from a rubber band with spring constant 30 N/m.How much is the rubber band stretched when the statue hangs motionless
Answer:
Distance : 0.06533 meters or 65.33 mm
Explanation:
To solve this problem we can make the forces equal when the system is at equilibrium.
mass [tex]*[/tex] gravity ( constant ) = spring constant
where l = the length at which the rubber band is stretched
0.2 kg [tex]*[/tex] 9.8 m / s² = 30 N/m
1.96 kg [tex]*[/tex] m / s² = 30 N/m
l = 1.96 kg [tex]*[/tex] m / s² / 30 N/m = 0.06533 meters / 65.33 mm
The rubber band is stretched a distance of 0.06533 meters, or 65.33 mm.
Answer:
0.065
Explanation:
Apex i just got it right
Open the attached image to see the question.
Answer:
option A
Explanation:
STOVE RADIATE ENERGY
Dr. Bishop wants to study how small children respond to scary stimuli. She will explain the procedure to parents and ask them to sign a permission form. She will have 3-5 year old kids individually come into her lab
Each child will be given a teddy bear to cuddle with. She will then stand a couple of feet behind the child as he or she plays and make a very loud scary sound. She will observe and measure the child's responses. The
child will come back in a few days and be given the teddy bear again, she will measure any reactions the child has to the bear.
What might an ethics review committee decide about the proposal?
The proposal is approved, as it meets the ethical guidelines defined by the APA
O The proposal is approved, because there is no deception
The proposal is denied, because participants wil ikely suffer psychological harm.
O The proposal is denied, because participants are not allowed to leave the study
The proposal is denied, because it does not meet confidentiality standards
Answer:
The correct option is;
The proposal is denied, because participants will likely suffer psychological harm
Explanation:
Among the recommendations in the report on ethical research with children, it is suggested that the following should be observed by researchers;
1) Seeking consent should be a continuous process
2) Contemplate payment forms other than money to allow more discretion on child safety
3) Have two way communication with the child
4) Ask for assent of the child participating in the research
The above APA suggestions where not met by the researcher in the study.
Answer:
The proposal is denied, because participants will likely suffer psychological harm.
Explanation:
This proposal would cause psychological harm to its participents.
I also took the test and that was the correct answer.
What happens when a sound wave passes from oil into air? A. the sound wave slows down and bounces back B. the sound wave slows down and bends C. the sound wave speeds up and bounces back D. the sound wave speeds up and bends
Oil is optically denser than water. When sound/light goes from optically denser medium to optically rarer medium, their velocity increase and they moves away for normal.
Appropriate Answer:The sound wave speeds up and bends
[tex] \Large{ \underline{ \boxed{ \pink{ \bf{Option \: (D)}}}}}[/tex]
As, In optics we learnt that light undergoes refraction when travels from medium of different densities. Similarly, Sound also follows the law of refraction.
It is due to the change of speed of water in different mediums, This makes it speed up or down depending upon the medium and their densities.━━━━━━━━━━━━━━━━━━━━
Answer:
the sound wave slows down and bends
Explanation:
a p e x
A stone of 1 kg is thrown with a velocity of 40 m/s across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice? *
A)16 N
B)-4 N
C)-16 N
Answer:
C)-16 N
Explanation:
concepts used
force = mass* acceleration
equation of motion
[tex]v^2 = u^2 + 2as[/tex]
where v is the final velocity
u is the initial velocity
and s is the distance moved
______________________________________________
Given
mass = 1 kg
initial velocity (u) = 40m/s
final velocity (v) = 0 as stones comes to rest
distance moved by stone (s) = 50m
using [tex]v^2 = u^2 + 2as[/tex]
[tex]0 = 40^2 +2a*50\\=> -1600 = 100a\\=> a = -1600/100 = -16[/tex]
Thus, acceleration is -16 m/s^2
here acceleration is negative as force of friction is opposing the motion.
Force of friction = mass of stone * acceleration of stone
Force of friction = 1*-16 kgm/s^2 = -16N ( kgm/s^2 = 1 N)
Thus, option c -16N is correct choice.
explain why the density of a gas is much less than that of a solid or liquid
Answer:
A gas usually has much lower density than a solid or liquid. ... The molecules or atoms in a gas are much further apart than in a solid or a liquid. Gas molecules or atoms are usually flying around at very high speeds, occasionally bouncing off each other or the walls of the container the gas is in.
what are some factors that affect the frequency of sound
Answer:
1. direction of propagation of sound
2.medium through which sound trsnsmitted
what is the symbol of mecury
If you are talking about mecury as in a chemical element than it is: Hg
If you are talking about the planet Mercury than: The symbol for Mercury represents the head and winged cap of Mercury, god of commerce and communication, surmounting his caduceus (staff). The symbol for Venus is designated as the female symbol, thought to be the stylized representation of the hand mirror of this goddess of love.
Answer:
The symbol of mercury is....
Hydrargyrum ( Hg )
Hope this helps......
Pls mark my ans as brainliest
If an object floats, the volume of the displaced water is equal to the volume of the whole object. True or false?
Answer:
True
Explanation:
This is in fact what the Archimedes principle states, and what he used in the famous anecdote about finding if the crown of the King was really made of gold.
A fire cracker is fired and it rises to a height of 1000 m. Find the velocity by which it was
released and the time taken by it to reach the highest point (take a = 10 m/s²).
Answer:
Explanation:it is too easy
an astronaut takes a tuning fork with her to the moon she strikes it inside the cabin the cabin is normally filled with air so the humans inside the spacecraft are comfortable she also strikes it outside the spacecraft when she gets down on the surface of the moon which of the following is true about the tuning fork?
A: it does not vibrate inside the spacecraft
B: id does not vibrate on moon surface
C: it vibrations are not transmitted inside the spacecraft
D:it's vibrations are not transmitted to the moon's atmosphere
Answer:
The correct option is;
D: Its vibrations are not transmitted to the moon's atmosphere
Explanation:
A tuning fork is used to produce sound by vibration such that the tune produced is pure
The tune, sound, produced by the tuning fork is transmitted as sound wave through the air by means of the gases of the air as a transmission medium so people at a distance that have air around them can hear the tuning fork sound
On the Moon's surface, the atmosphere is very and it is referred to technically as an exosphere, so the sound of the tuning fork has no medium through which to transmit and therefore, it is not transmitted on the Moon's atmosphere.
1-A boy rolls a toy car across a floor with a velocity of 3.21 m/s. How long does it take the car to travel a distance of 4.50 m?
A-0.71s
B-1.40s
C-2.9s
D-14s
2-A girl heads out for a jog and runs at 2.95 m/s, due North, for 3600 s. How far did she run?
A-0.194 x 10^-4
B-1220m
C-5240
D-10620
3-A car is traveling South on I-85. It travels between two exits that are 5.40 km apart in 4.85 minutes. What is the average velocity of the car in m/s?
A-8.42m/s
B-12.8m/s
C-14.9m/s
D-18.6m/s
4-An airplane takes 1.30 hours to travel to an airport north of Atlanta. If the average speed of the plane is 134 m/s, what is the plane's displacement as measured from Atlanta?
A-129,324m=129,000m rounded
B-356,247m=356,000m rounded
C-498,782m=499,000m rounded
D-627,120m=627,000m rounded
5-How long does it take a sailboat traveling 18.0 m/s to go 15.7 km west?
A-15,000s
B-872s
C-594s
D-326s
A car accelerates at a rate of 3 m/s^2. If its original speed is 8 m/s, how many seconds will it take the car to reach a final speed of 25 m/s?
Answer:
[tex]\Large \boxed{\mathrm{5.67 \ seconds }}[/tex]
Explanation:
[tex]\displaystyle \mathrm{acceleration \ = \ \frac{final \ velocity - initial \ velocity }{elapsed \ time}}[/tex]
[tex]\displaystyle A \ = \ \frac{V_f - V_i }{t}[/tex]
[tex]\displaystyle 3 \ = \ \frac{25 - 8 }{t}[/tex]
[tex]\displaystyle 3 \ = \ \frac{17 }{t}[/tex]
[tex]\displaystyle t \ = \ \frac{17 }{3} \approx 5.67[/tex]
when you turn on music on your phone, what energy transformation takes place ?
Answer: A Battery contains chemical energy which transfers electrical energy into the phone, powering it and also transferring Light energy, Sound energy and Heat energy.
Explanation:
A physics student stands on a cliff overlooking a lake and decides to throw a softball to her friends in the water below. She throws the softball with a velocity of 23.5 m/s at an angle of 39.5∘ above the horizontal. When the softball leaves her hand, it is 11.5 m above the water. How far does the softball travel horizontally before it hits the water? Neglect any effects of air resistance when calculating the answer.
Answer:
66.86m
Explanation:
Velocity of ball thrown, u = 23.5 m/s
Initial height of the ball above the water, H = 11.5 m
Angle of projection, θ = 39.5°
Vertical components of veloclty = usinθ
Horizontal components of veloclty = ucosθ
The soft ball hits the water after time 't'
Considering the second equation of motion
S = ut + 1/2at^2........ 1
But since the ball went through motion under gravity ( free fall ) rather than linear motion, then equation 1 can be rewritten as:
H = ut +/- 1/2gt^2
H = - 11.5m
U = usinθ
θ = 39.5°
a = -g = -9.8m/s^2
- 11.5m = 23.5(sin39.5°)t + 1/2(-9.8)t^2
-11.5m = 23.5(0.6360)t - 4.9t^2
-11.5m = 14.946t - 4.9t^2
4.9t^2 -14.946t-11.5m = 0
Since the ball drifted horizontally
D = (Ucosθ)t
Where θ = 39.5°
U = 23.5m/s t=
Alternatively,
horizontal component of the velocity is 23.5 cos 39.5º = 18.1331 m/s
now how long does it take the ball to raise to a peak and fall to the water.
vertical component of velocity = 23.5 sin 39.5º = 14.947m/s
time to reach peak t = v/g = 11.947/9.8 = 1.5252 sec
peak reached above cliff top is
h = ½gt² = ½(9.8)(1.5252)²
= ½×22.797
= 11.3985m
now the ball has to fall 11.3985+ 11.5 = 22.8985m
time to fall from that height is
t = √(2h/g) = √(2• 22.8986/9.8) = 2.1617 sec
add up the two times to get time it is in the air, 2.1617 + 1.5252 = 3.6869
now haw far does the ball travel horizontally in that time
d = vt = 18.1331 ×3.6869= 66.856m
= 66.86m
A car travels from point A to B in 3 hours and returns back to point A in 5 hours. Points A and B are 150 miles apart along a straight highway. Which of the following statements most accurately describes the motion of the car? Choose 1 answer:(Choice A) A The average velocity is 40 miles per hour. (Choice B) B The total displacement of the trip is 300 miles. (Choice C) C The average speed is 37.5 miles per hour. (Choice D) D The car travels at 50 mph for the first half and 30 mph for the second half.
Answer: D
Explanation:
Given that a car travels from point A to B in 3 hours and returns back to point A in 5 hours. Points A and B are 150 miles apart along a straight highway.
From point A to B
The speed = distance / time
Where
Distance = 150 mile
Time = 3 hours
Substitute the values into the formula
Speed = 150/3 = 50 mile/ hours
From Point B to Point A
Distance = 150 miles
Time = 5 hours
Where speed = distance/ time
substitute all the parameters into the formula
Speed = 150/5 = 30 mph
Therefore, The car travels at 50 mph for the first half and 30 mph for the second half.
The correct answer is option D
1. A physical quantity P is related to four observables a, b and c as follows: P= (a3b 2 /c4 ) The percentage errors of measurements in a, b and c are 1%, 4% and 2% respectively. What is the percentage error in quantity P?
Answer:
The percentage error in quantity P is 19%.
Explanation:
It is given that,
A physical quantity P is related to four observables a, b and c as follows:
[tex]P=\dfrac{a^3b^2}{c^4}[/tex]
The percentage errors of measurements in a, b and c are 1%, 4% and 2% respectively.
We need to find the percentage error in quantity P. It is given by :
[tex]\dfrac{\Delta P}{P}\times 100=(3\times \dfrac{\Delta a}{a}+2\times \dfrac{\Delta b}{b}+4\times \dfrac{\Delta c}{c})\\\\=3\times 1+2\times 4+4\times 2\\\\\dfrac{\Delta P}{P}\times 100=19\%[/tex]
So, the percentage error in quantity P is 19%.
A person holds a 25 kg (250 newton) bag of cement over his head and moves it a distance of 10 m, taking 2 minutes, while another person carries it on a wheelbarrow that same distance, taking 1 minute.Who does more work ? What is the power of each person?
Explanation:
Assuming the 10 m distance is the vertical displacement, the work done by both people is the same.
Work = force × distance
W = (250 N) (10 m)
W = 2500 J
The power of the first person is:
Power = work / time
P = 2500 J / 120 s
P = 20.83 W
The power of the second person is:
P = 2500 J / 60 s
P = 41.67 W
A butterfly is flying around and its velocity(v) as a function of time(t) is given in the graph below where rightwards is the positive velocity direction. What is the butterfly's displacement x from t=2 to 4s? Answer with two significant digits.
Answer: 19 meters.
Explanation:
We want to find the total displacement between t = 2s and t = 4s.
To do it, we can integrate our function, first write our velocity equation.
for t ≤ 3s, we have a linear equation, let's write it:
A linear relationship can be written as:
y = a*t + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now we can see that our line passes through the points (1, 0) and (0, -2)
then the slope is:
a = (0 -(-2)/(1 - 0) = 2/1 = 2
and knowing that when t = 0s, v(0s) = -2m/s, then our equation is:
v(t) = (2m/s^2)*t - 2m/s for t ≤ 3s
now, for t ≥3s the equation is constant, v(t) = 4m/s.
then we have
v(t) = (2m/s^2)*t - 2m/s -------if t ≤ 3s
v(t) = 4m/s ----- if t ≥ 3s
Now we integrate over time to get the position:
for t ≤ 3s we have:
p(t) = (1/2)*(2m/s^2)*t^2 - 2m/s*t + C
where C is a constant of integration, as we are calculating the displacement this constant actually does not matter, so we can use C = 0m
p(t) = (1m/s^2)*t^2 - 2m/s*t for t ≤ 3s
and p(3s) = (1m/s^2)*3s^2 - 2m/s*3s = 9m - 6m = 3m is the initial position of the other part of the function.
for t ≥ 3s we have:
p(t) = 4m/s*t + p(3s) = 4m/s*t + 3m
then the position equation is:
p(t) = (1m/s^2)*t^2 - 2m/s*t ---- t ≤ 3s
p(t) = 4m/s*t + 3m --- if t ≥ 3s
Now the displacement will be:
p(4s) - p(2s) where for each time, you need to use the correct function:
p(4s) = 4m/s*4s + 3m = 16m + 3m = 19m
p(2s) = (1m/s^2)*2s^2 - 2m/s*2s = 4m - 4m = 0m
p(4s) - p(2s) = 19m - 0m = 19m
The butterfly displacement x from t=2 to 4s is 19 meters.
What is displacement?The spacing between two specified points is represented by the one-dimensional quantity of displacement (symbolised as d or s), commonly known as length or distance.
The total displacement between t = 2s and t = 4s.
Integrate our function, the velocity equation.
for t ≤ 3s, we have a linear equation, let's write it:
A linear relationship can be written as:
y = a x t + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
The line passes through the points (1, 0) and (0, -2)
The slope is:
a = (0 -(-2)/(1 - 0) = 2/1 = 2
When t = 0s, v(0s) = -2m/s, then our equation is:
v(t) = (2m/s²) x t - 2m/s for t ≤ 3s
now, for t ≥3s the equation is constant, v(t) = 4m/s.
v(t) = (2m/s²) x t - 2m/s -------if t ≤ 3s
v(t) = 4m/s ----- if t ≥ 3s
Now we integrate over time to get the position:
for t ≤ 3s we have:
p(t) = (1/2) x (2m/s²) x t^2 - 2m/s x t + C
where C is a constant of integration, to calculate the displacement this constant actually does not matter,
p(t) = (1m/s²)*t^2 - 2m/s x t for t ≤ 3s
and p(3s) = (1m/s^2) x 3s² - 2m/s x 3s = 9m - 6m = 3m is the initial position of the other part of the function.
for t ≥ 3s we have:
p(t) = 4m/s x t + p(3s) = 4m/s x t + 3m
then the position equation is:
p(t) = (1m/s^2) x t² - 2m/s x t ---- t ≤ 3s
p(t) = 4m/s x t + 3m --- if t ≥ 3s
Now the displacement will be:
p(4s) - p(2s) where for each time, you need to use the correct function:
p(4s) = 4m/s x 4s + 3m = 16m + 3m = 19m
p(2s) = (1m/s²) x 2s²- 2m/s x 2s = 4m - 4m = 0m
p(4s) - p(2s) = 19m - 0m = 19m
Thus, the displacement is 19 m.
To learn more about displacement, refer to the link:
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A student measures the depth of a water well with an adjustable frequency audio oscillator. 2 successive resonant frequencies are heard at 40Hz and 50Hz. What is the depth of the well?
Answer:
17.15 m
Explanation:
Assuming the well is empty (full of air instead of water), the speed of sound is v = 343 m/s.
The water well acts as a pipe closed at one end. Therefore, the depth of the water well must be an odd multiple of a quarter of the resonant wavelength.
L = (2n − 1) λ/4, n = 1, 2, 3, etc.
v = λf, so λ = v/f. Substituting:
L = (2n − 1) v/(4f)
Solving for frequency:
f = (2n − 1) v/(4L)
The difference between two successive resonant frequencies is therefore:
Δf = (2(n+1) − 1) v/(4L) − (2n − 1) v/(4L)
Δf = (2n + 1) v/(4L) − (2n − 1) v/(4L)
Δf = 2 v/(4L)
Δf = v/(2L)
Plugging in values:
50 Hz − 40 Hz = 343 m/s / (2L)
2L = 34.3 m
L = 17.15 m
