Answer:
a.) 10Hz
b.) 0.1 s
c.) 187.4 m/s
d.) -412.6 m/s^2
Explanation:
Given that an object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.
(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?
from the equation given, the angular speed w = 20π
but w = 2πf
where f = frequency.
substitute w for 20π
20π = 2πf
f = 20π/2π
f = 10 Hz
(b) What is t the first time that the object is at its farthest right?
since F = 1/T
T = 1 / f
T = 1/10
T = 0.1 s
Therefore, the t of first time that the object is at its farthest right is 0.1 s
(c) At the time found in part (b), what is the object's velocity?
The velocity can be found by differentiating the equation;
x(t) = 3sin(20πt)
dx/dt = 60πcos(20πt)
where dx/dt = velocity V
V = 60πcos(20π * 0.1)
V = 187.4 m/s
(d) At the time found in part (b), what is the object's acceleration?
to get the acceleration, differentiate equation V = 60πcos(20πt)
dv/dt = -1200πSin(20πt)
dv/dt = acceleration a
a = -1200πSin(20πt)
substitute t into the equation
a = -1200πSin(20π * 0.1)
a = - 412.6 m/s^2
The type of motion the object undergoes that consist of a back-and-forth
movement that is repetitive is a simple harmonic motion.
The correct responses are;
(a) Number of complete back-and-forth motions per second is 10(b) The first time is after 0.025 seconds(c) Velocity is 0(d) Acceleration is approximately -11843.53 m/s²Reasons:
The equation that represents the motion of the object is x(t) = 3·sin(20·π·t)
Where;
t ≥ 0
x(t) is in cm, and t is in seconds.
(a) The general sine function is y = A·sin(B·(t - C) + D
[tex]\mathrm{The \ period \ P} = \dfrac{2 \cdot \pi}{B}[/tex]
By comparison, we have;
B = 20·π
Therefore;
[tex]P = \dfrac{2 \cdot \pi}{20 \cdot \pi} = \dfrac{1}{10} = 0.1[/tex]
The period, which is the time to complete one cycle = 0.1 seconds
The number of cycle completed per second, is the frequency, f
[tex]f = \dfrac{1}{P} = \dfrac{1}{0.1} = 10[/tex]
f = 10 Hz = 10 cycles
The number of cycle completed per second is f = 10 cycles
(b) When the object is at the farthest right, we have;
sin(20·π·t) = Maximum = 1
[tex]\mathbf{sin\left(\dfrac{\pi}{2}\right)} = 1[/tex]
Therefore,
[tex]20 \cdot \pi \cdot t = \dfrac{\pi}{2}[/tex]
[tex]t = \dfrac{\pi}{20 \cdot \pi \cdot 2} = \dfrac{1}{40} = 0.025[/tex]
The first time it is at the farthest right is t = 0.025 seconds after start
(c) [tex]\mathrm{Velocity, \ v, \ is \ given \ by \ v = \dfrac{dx(t)}{dt}}[/tex]
Therefore;
[tex]v = \dfrac{dx(t)}{dt} = \dfrac{dx(t)}{dt} \left(3 \cdot sin \left(20 \cdot \pi \cdot t \right) = 60\cdot \pi \cdot cos \left(20 \cdot \pi \cdot t \right)[/tex]
At t = 0.25 seconds, we have;
[tex]v = \dfrac{dx(t)}{dt} = 60\cdot \pi \cdot cos \left(20 \times \pi \times 0.025 \right) = 0[/tex]
The velocity of the object at the t = 0.025 seconds is v(t) = 0
(d) Acceleration, a, is given by [tex]a = \dfrac{dv(t)}{dt}[/tex]
Therefore;
[tex]a = \dfrac{dv(t)}{dt} = \dfrac{d}{dt} \left( 60\cdot \pi \cdot cos \left(20 \times \pi \times t\right) \right) =-1200 \cdot \pi ^2 \cdot sin(20 \cdot t \cdot \pi)[/tex]
a = -1200·π²·sin(20·t·π)
∴ a = -1200×π²×sin(20×0.025×π)
sin(20×0.025×π) = 1
∴ a = -1200×π²×1 ≈ -11843.53
At the time found in part b the acceleration of the object, a ≈ -11843.53 m/s²
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Use the principle of superposition (Equation 1.3) to predict the electric field at the point 0.5 meters to the right and 1.5 meters above the 5 nC charge. Express your result both in terms of x and y components, and then in terms of total magnitude and direction.
Answer:
Explanation:
The x component of electric field Ex = k Q / R²
= 9 x 10⁹ x 5 x 10⁻⁹ / .5²
= 180 N .
The y component of electric field Ey = k Q / R²
The y component of electric field Ey
= 9 x 10⁹ x 5 x 10⁻⁹ / 1.5²
= 20 N
Total field = [tex]\sqrt{180^2+20^2}[/tex]
= 181.1 N .
Angle with x axis = Tanθ = Ey / Ex = 20 / 180 = .111
= 6.33⁰
a ship travels from savannah georgia to lisbon spain at a rate of 27.6 miles/hour. if the distance covered is 3982 miles how long did the trip take
Answer:3982/27.6=144.275
Explanation:The trip took 144 hours as 3982/27.6 is about 144.
A container of rocks is brought back from the Moon's surface where the acceleration due to gravity is 162 meters per second if the total mass of the container of rocks is 650 kilograms, what is its weight on
Earth's surface
Answer:
6318 N
Explanation:
From the question given above, the following data were obtained:
Acceleration due to gravity of the moon (gₘ) = 1.62 m/s²
Mass (m) of container = 650 kg
Weight (W) of container on the earth =.?
Next, we shall determine the acceleration due to gravity of the earth. This can be obtained as follow:
Acceleration due to gravity of the moon (gₘ) = 1.62 m/s²
Acceleration due to gravity of the earth (gₑ) =.?
gₘ = 1/6 × gₑ
1.62 = 1/6 × gₑ
1.62 = gₑ /6
Cross multiply
gₑ = 1.62 × 6
gₑ = 9.72 m/s²
Finally, we shall determine the weight of the container on the earth as follow:
Mass (m) of container = 650 kg
Acceleration due to gravity of the earth (gₑ) = 9.72 m/s²
Weight (W) of container on the earth =.?
W = m × gₑ
W = 650 × 9.72
W = 6318 N
Therefore, the weight of the container on earth is 6318 N
F all of the energy in a falling object's gravitational potential energy store is transferred to its kinetic energy store by the time it lands, then the relationship shown below can be used. Which of the four options below it correctly shows how this relationship can be expressed in terms of height, h?
Answer:
The options are not shown, so let's derive the relationship.
For an object that is at a height H above the ground, and is not moving, the potential energy will be:
U = m*g*H
where m is the mass of the object, and g is the gravitational acceleration.
Now, the kinetic energy of an object can be written as:
K = (1/2)*m*v^2
where v is the velocity.
Now, when we drop the object, the potential energy begins to transform into kinetic energy, and by the conservation of the energy, by the moment that H is equal to zero (So the potential energy is zero) all the initial potential energy must now be converted into kinetic energy.
Uinitial = Kfinal.
m*g*H = (1/2)*m*v^2
v^2 = 2*g*H
v = √(2*g*H)
So we expressed the final velocity (the velocity at which the object impacts the ground) in terms of the height, H.
PLEASE HELP!!!! ILL MARK BRAINLYEST!!
A change in the size or shape of a substance is a _________ change
A. chemical
B. physical
C. material
D. nuclear
Which of the following statements best describes why the mass of a bowling ball would not change if it were transported from Earth to the Moon?
Gravity is a constant force
The bowling ball wil adapt to the changes in gravity
Matter is resistant to acceleration and changes in gravity
The amount of matter in the bowling all remains the same
Answer:
D hope this helps
Explanation:
Answer:
D
Explanation:
The amount of matter in the bowling ball remains the same.
Mamie Clark was a psychologist who is known for her research on __________. A. intellectual and developmental disabilities and gifted children B. racism and its adverse effects on child development C. identity development among Asians living in the US D. academic development of children in desegregated schools
Answer:
B. racism and its adverse effects on child development
Explanation:
Dr. Mamie Clark studied the effects of segregation and racism on the self-esteem of black children.
According to Clark in O'Connell & Russo, 2001, p. 271; "To separate them from others of similar age and qualifications solely because of their race generates a feeling of inferiority as to their status in the community that may affect their hearts and minds in a way unlikely ever to be undone...."
One of her works titled "The Development of Consciousness of Self and the Emergence of Racial Identification in Negro Preschool Children" investigated the early level of conscious racial identity in black preschool children.
Answer:
B
Explanation:
cuz its B
Miguel added 150 grams of baking soda to a liter of water at 20 °C. No matter how long he keeps stirring the solution, he can’t get all of the baking soda to dissolve. Explain why.
Answer:
See the answer below
Explanation:
This is because, at 20 °C, the solution has become saturated with the baking soda.
The solubility of a substance is the maximum amount of that substance that will dissolve in a particular solvent at a given temperature. The solubility of a substance generally increases with an increase in temperature.
At 20 °C temperature, the maximum amount of baking soda that can dissolve in a liter of water has been exceeded by Miguel. Hence, no matter how hard he tries to stir the solution, the excess baking soda will not dissolve.
The reason he can’t get all of the baking soda to dissolve is; because at 20 °C, the solution has become saturated with the baking soda.
What is a saturated solution?For us to say a substance is soluble, it means that the maximum amount of that substance will dissolve in a particular solvent at a given temperature. Thus, the solubility of a substance is said increase with a corresponding increase in temperature.
From the question, at 20 °C temperature, miguel has exceeded the maximum amount of baking soda that can dissolve in a liter of water. Therefore, no matter how hard he tries to stir the solution, it will not dissolve due to the excess soda.
Read more about saturated solution at; https://brainly.com/question/4529762
what is torricellian vaccum
Answer:
a vacuum formed above the column of mercury in a mercury barometer.
Answer:
An air-free space above the free surface of a liquid in a vessel that is closed above the liquid
PLEASE HELP!!
A player punts a football at an angle of 30 degrees. The football has an initial
velocity of 20.0 m/s. Find the y-component of the ball's velocity.
17.3 m/s
O 10.0 m/s
O 30.0 m/s
0 25.1 m/s
Answer:
The y-component of the ball's velocity is 10 m/s
The second choice 10.0 m/s is correct
Explanation:
Projectile Motion
It's the type of motion that experiences an object that is projected near the Earth's surface and moves along a curved path exclusively under the action of gravity.
Being vo the magnitude of the initial velocity and θ the angle it makes with the horizontal, the components of the initial velocity are calculated as follows:
[tex]v_{ox}=v_o.\cos\theta[/tex]
[tex]v_{oy}=v_o.\sin\theta[/tex]
Since the football is kicked at vo=20 m/s and an angle of θ=30°:
[tex]v_{oy}=20.\sin 30^\circ[/tex]
[tex]v_{oy}=20*0.5=10[/tex]
The y-component of the ball's velocity is 10 m/s
The second choice 10.0 m/s is correct
PLEASE HELP!! ILL MARK BRAINLYEST!!!
A chemical change occurs when a substance changes phase.
True
False
Answer:
False
Explanation:
PLSSS HELP ITS URGENT ILL RATE YOU BRAINLIEST:) A truck whose bed is 4 m long, 2.2 m wide, and 1.0 m high is delivering sand for a sand-sculpture competition. About how many trips must the truck make to deliver 23 m^3 of sand?
Answer:
one truck load is 2.5*1.5*1 = 3.75m^3
7/3.75 = 1.86 loads,
so 2 trips must be made.
Explanation:
can the answer to density be simplified
Answer: yes because all densities can be simplifed it just depends on the number.
PLEASE HELP ME FAST!
Which of these sentences best illustrates visualization using a sequence of events? A. The earthquake sent out a shock waves in all directions. The sea surface is disturbed also. Big waves are formed. These waves travel fast across the sea. They are dangerous and can kill. B. Then, all of a sudden, a strong earthquake strikes off the coast of Alaska, deep down on the seafloor. After this, the seafloor moves up and down. Next the walls and floors of the house is suddenly start to shake. C. Both A and B. D. Neither A or B.
Answer:
Explanation:
C. Both A and B I guess
Answer:
its b
Then, all of a sudden, a strong earthquake strikes off the coast of Alaska, deep down on the sea floor. After this, the sea floor moves up and down. Next, walls and floors of the houses suddenly start to shake.
Explanation:
mark me brainleist please!
also i really hope this helps and have a really good day
-TA
Which of the following is a molecule? *
1.He
2.Be
3.NO
4.Na
!!! I NEED URGENT HELP !!!
Answer:
P = W / t where P is power and W the work done
P = F x / t = F v
Then v = P / F = 450 J/s / 350 N = 1.29 m/s
T = 46.6 m / 1.29 m/s = 36.1 sec where T is the required time
A car on flat ground accelerates at 0.785 m/s2 when a net force of 1050 N acts on it. How much normal force acts on it?
Answer:
13108.3N
Explanation:
Given parameters:
Acceleration = 0.785m/s²
Net force = 1050N
Unknown:
Normal force acting on car = ?
Solution:
The normal force on this car is the weight of the car;
Normal force = mg
where m is the mass of the car
g is the acceleration due to gravity = 9.8m/s²
Now solve for the mass;
Net force = mass x acceleration
1050 = mass x 0.785
mass = [tex]\frac{1050}{0.785}[/tex] = 1337.6kg
So,
Normal force = 1337.6kg x 9.8m/s² = 13108.3N
13108 works as well for acellus
A dictator junk gang has all the gas left in the region. They are requiring 2 kg of scrap
metal in exchange for gasoline which they are selling by the liter. Your water rig is
American made with a gallon gas tank and it can drive 30 miles per gallon. How many
liters of gasoline do you need from the junk gang in order to successfully make it the
new destination?
Explanation:
here u go..................................
The volume of the gasoline needed for the gang to successfully make it to the new destination is 340.02 liters.
"Your question is not complete, it seems to be missing to following information";
the new destination of the gang is 2695 miles
The given parameters;
the rate of gasoline consumption, v = 30 miles per gallonthe new destination of the gang = 2695 miles1 gallon = 3.785 liters
The rate of gasoline consumption in miles per liter is calculated as;
[tex]v = \frac{30 \ miles}{gallon } \times \frac{1 \ gallon}{3.785 \ liters} = 7.926 \ miles/liter[/tex]
The volume of the gasoline needed for the gang to successfully make it to the new destination is calculated as;
[tex]volume \ of \ gasoline = \frac{2695 \ miles}{7.926 \ miles/liter} = 340.02 \ liters[/tex]
Thus, the volume of the gasoline needed for the gang to successfully make it to the new destination is 340.02 liters.
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A ball is thrown vertically upward with an initial velocity of 29.4 m/s². What is the maximum height reached by the ball? How long is the ball in the air? What is the final velocity of the ball before it goes back to its original position?
Answer:
Most likely it will reach 29.4 up in the air before coming back down.
Explanation:
The force of the ball will be the same on how high it will go.
The temperature of a 5.0 kg block increases by 3 degrees C when 2,000 J of thermal energy are added to the block. What is the specific heat of the block? _____________
which force produces acceleration in falling bodies?
Answer:
Gravity produces acceleration
why does nobody love me?
Answer: I’m sure theirs people out there that like you, and if there isn’t, you should just focus on yourself.
Explanation:
Answer:
Well, There are a couple reasons it could seem like nobody loves you...
Explanation:
One reason is that people really do love you, they just were never shown love and affection so they are unsure of how to show that to you. Another reason could be that it's god telling you that you are meant for much bigger and greater things. Maybe it's him reminding you that, yeah, people really suck, but that's life, and you're better than that. If you make the right decisions in life, you will be able to stand taller than they ever did. I hope this helps.. : )
If a rock falls for 5 seconds near the surface of the earth and with no air friction, it will reach a velocity of
Answer: -49m/s.
Explanation:
As the rock only falls, we will assume that the initial vertical velocity is zero.
We neglect the air friction, so the only force acting on the rock is the gravitational force, this means that the acceleration is -g = -9.8m/s^2.
Then we can write:
a(t) = -9.8m/s^2
To write the velocity of the rock, we must ingrate over time and get:
v(t) = (-9.8m/s^2)*t + v0
where v0 is the initial vertical velocity, and as we said above, v0 = 0m/s
Then the vertical velocity as a function of time is:
v(t) = (-9.8m/s^2)*t
Now, the question is:
"...If a rock falls for 5 seconds near the surface of the earth and with no air friction, it will reach a velocity of..."
Then we need to evaluate the velocity equation in t = 5 seconds.
v(5s) = (-9.8m/s^2)*5s = -49m/s.
Answer the following:
You are going to race your friend to a tree near the back of the playground. The tree is 24 meters away from where you stand. It will take you 4 seconds to reach the tree. What will your average speed be?
Answer:
1. 6 m/s.
2. 320 miles.
Explanation:
1. Determination of the average speed.
Total distance travelled (D) = 24 m
Total time (t) = 4 s
Average speed =.?
Average speed is simply defined:
Average speed = Total distance /total time
Average speed = 24/4
Average speed = 6 m/s
2. Determination of the distance travelled by the train.
Speed = 40 mph
Time = 8 h
Distance =?
Speed is simply defined as:
Speed = Distance /time
40 = Distance / 8
Cross multiply
Distance = 40 × 8
Distance = 320 miles
Therefore, the train travels a distance of 320 miles.
plz answer this very soon
Answer:
Im gonna say it is answer A:) Hope this helps!
Explanation:
What is the momentum of a 15 kg tire rolling down a hill at 3 m/s?
5 kg • m/s
18 kg • m/s
45 kg • m/s
60 kg • m/s
Answer:
The answer is 45 kg • m/sExplanation:
The momentum of an object can be found by using the formula
momentum = mass × velocityFrom the question
mass = 15 kg
velocity = 3 m/s
We have
mass = 15 × 3
We have the final answer as
45 kg • m/sHope this helps you
Answer:
45 kg • m/s
Explanation:
Clouds in our atmosphere cause us to see the different phases of the moon.
True
False
Answer:
False
Explanation:
:)
Answer:
The answer is false
Explanation:
The clouds have nothing to do with the changes in the phases of the moon but, rather the postioning of the sun and the moon regarding revolution and the spinning of the earth on it axis.
I hope this helps you good luck and have a good day.
3 The diagram shows a model of an atom. The model has four different symbols on it. Each
symbol represents a different role for one of the particles within the atom.
Model Atom
(W
Particle
w
Charge
Negative
Positive
х
Y
Neutra!
Negative
z
w
In this model, which particle determines the identity of this atom?
A Particle w
C Particle Y
B Particle X
D Particle z
The Answer is particle Z
Answer:
answer is D
Explanation:
Digging downward through a soil profile, how deep would you have to go before you found recognizable fragments of the parent rock for the soil?
Kinetic and potential energy are forms of what kind of energy?
gravitational
chemical
electrical
mechanical
Answer:
mechanical energy
Explanation:
The key difference that exists between kinetic energy and potential energy lies in the fact that, potential energy is that form of mechanical energy which is stored within an object, ready to be released as and when needed to do some work, while, kinetic energy is that form of mechanical energy that has been released and is associated with the body in motion.