An object thrown in the air has a velocity after t seconds that can be described by v(t) = -9.8t + 24 (in meters/second) and a height h(t) = -4.9t 2 + 24t + 60 (in meters). The object has mass m = 2 kilograms. The kinetic energy of the object is given by K = __1 2mv2 , and the potential energy is given by U = 9.8mh. Find an expression for the total kinetic and potential energy K + U as a function of time. What does this expression tell you about the energy of the falling object?

Answers

Answer 1

Answer and Explanation: Kinetic energy is related to movement: it is the energy an object possesses during the movement. it is calculated as:

[tex]K=\frac{1}{2}mv^{2}[/tex]

For the object thrown in the air:

[tex]K=\frac{1}{2}.2.[v(t)]^{2}[/tex]

[tex]K=(-9.8t+24)^{2}[/tex]

[tex]K=96.04t^{2}-470.4t+576[/tex]

Kinetic energy of the object as a function of time: [tex]K=96.04t^{2}-470.4t+576[/tex]

Potential energy is the energy an object possesses due to its position in relation to other objects. It is calculated as:

[tex]U=mgh[/tex]

For the object thrown in the air:

[tex]U=9.8.2.h(t)[/tex]

[tex]U=9.8.2.(-4.9t^{2}+24t+60)[/tex]

[tex]U=-96.04t^{2}+470.4t+1176[/tex]

Potential energy as function of time: [tex]U=-96.04t^{2}+470.4t+1176[/tex]

Total kinetic and potential energy, also known as mechanical energy is

TME = [tex]96.04t^{2}-470.4t+576[/tex] + ([tex]-96.04t^{2}+470.4t+1176[/tex])

TME = 1752

The expression shows that total energy of an object thrown in the air is constant and independent of time.


Related Questions

What is applied force?

Answers

Answer:

An applied force is a force that is applied to an object by a person or another object. If a person is pushing a desk across the room, then there is an applied force acting upon the object.

Explanation:

Could someone tell me if this is right or give me the answers so i can re write them! That would be so helpful:)

Answers

Answer:

Those are all right

Explanation:

Answer:

They are right! Nice job!

Explanation:

what part of the stem cell provides instructions for building the heart

a. ribosomes
b. DNA
c. RER
d. lysosomes

Answers

It’s DNA that’s a answer

What three forms of energy are represented when a match is lit?

Answers

Answer:

Three forms of energy when a match is being lit are potential, kinetic and thermal.

hope this helps! :)

Explanation:

Answer:

Potential Energy

Kinetic Energy

Thermal Energy

Explanation:

The voltage across a 8.5-F capacitor is 2te–3t V. Find the current and the power.

Answers

Answer:

Explanation:

Given the capacitance of a capacitor = 8.5F

Voltage across the capacitor = 2te^-3tV

The current across a capacitor is expresses as shown;

I = Cdv/dt

Given V = 2te^-3tV

dv/dt = 2t(-3e^-3t) + 2(e^-3t)

dv/dt = -6te^-3t + 2e^-3t

Factor out the common term

dv/dt = -2e^-3t{3t-1}

If C = 8.5F

I = 8.5 × -2e^-3t{3t-1}

I = -17.0e^-3t{3t-1} A

Power is the product of current and voltage.

P = IV

Given I = -17.0e^-3t{3t-1} A

V = 2te^-3t V

Power = -17.0e^-3t{3t-1} × 2te^-3t

Power = (17e^-3t - 51te^-3t) × 2te^-3t

Power = 34te^{-3t-3t} - 102t²e^{-3t-3t}

Power = 34te^-6t - 102t²e^-6t

Power = 34te^-6t{1-3t} Watts

A web page designer creates an animation in which a dot on a computer screen has a position of r⃗ =[ 4.50 cm +( 2.90 cm/s2 )t2]i^+( 4.70 cm/s )tj^ . Part A Find the average velocity of the dot between t=0 and t=2.0s. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4.

Answers

Answer:

V = (5.8cm/s)i, (4.7cm/s)j

Explanation:

Given :

r⃗ =[ 4.50 cm +( 2.90 cm/s2 )t2]i^+( 4.70 cm/s )tj^

To obtain the average velocity (V)

V = (r2 - r1) / (t2 - t1)

To obtain r1 and r2, substitute t1 = 0 and t2 = 2 respectively in the equation above

r1 = [ 4.50 cm +( 2.90 cm/s2 ) 0]i^+( 4.70 cm/s )0 j

r1 = 4.50 cm + 0 + 0 = (4.50cm)i + 0j

r2 = [ 4.50 cm +( 2.90 cm/s2 )2²]i^+( 4.70 cm/s )2 j

r2 = 4.50cm + (2.90 × 4)i + (4.70 × 2)j

r2 = (16.1cm)i + (9.4cm)j

V = [(16.1 - 4.50)i - (9.4 - 0)j] / 2 - 0

V = 11.6i / 2 ; 9.4j / 2

V = (5.8cm/s)i, (4.7cm/s)j

A cheetah is running at a speed of 19.5 m/s in a direction of 69° north of west. Find the cheetahs velocity component due north and due west.

Answers

Answer:

The cheetahs velocity component due north is 6.99 m/s

The cheetahs velocity component due west is 18.21 m/s

Explanation:

Given;

speed of the cheetah, v = 19.5 m/s

direction of the cheetah's speed, θ = 69°

Find the attached document for explanation

What is a main difference between a mixture and a pure substance?
O A mixture is only a liquid, but a pure substance can be in any state.
A mixture looks the same throughout, but a pure substance does not.
A mixture can vary in composition, but a pure substance has a set composition.
A mixture can be made up of a single compound, but a pure substance cannot.
оо

Answers

Answer:

C- A mixture can vary in composition, but a pure substance has a set composition

Explanation:

The main difference between a mixture and a pure substance is: A mixture can vary in composition, but a pure substance has a set composition ( option c )

Mixture

A mixture is a substance which contains two or more constituents which can easily be separated by a physical means. It consists of two or more different substances, not chemically joined together.

Substance

A pure substance consists only of one element or one compound.

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Consider two positively charged particles, one of charge q0 (particle 0) fixed at the origin, and another of charge q1 (particle 1) fixed on the y-axis at (0,d1,0). What is the net force F⃗ on particle 0 due to particle 1? Express your answer (a vector) using any or all of k, q0, q1, d1, i^, j^, and k^.

Answers

Answer:

[tex]F_{10} = - \frac{k_{q1}* qo }{d_{1} ^{2} } j[/tex]

Explanation:

The net force ( F ) on particle 0 due to particle 1  can be expressed as

[tex]F_{10} = \frac{K_{q1}*qo }{r_{10} ^{3} } r_{10}[/tex]

k = coulomb constant

[tex]r_{10}[/tex] = distance between charge o and charge 1

to get the vector form ( attached below ) we substitute [tex]d_{1}[/tex] for [tex]r_{10}[/tex] and [tex]- d_{1} j[/tex] for [tex]r_{10}[/tex]

The net force on [tex]q_{0}[/tex]  by [tex]q_{1}[/tex] is , [tex]F=-K\frac{q_{0}*q_{1}}{r^{2} }j[/tex]

The force between two charges is given by Coulomb force law.

                 [tex]F=K\frac{q_{0}*q_{1}}{r^{2} }[/tex]

Where K is Coulomb constant, [tex]K=9*10^{9}Nm^{2}/C^{2}[/tex]

and r is the distance between both charges.

Here given that, [tex]q_{0}[/tex] is located as (0, 0, 0) and [tex]q_{1}[/tex] is located at [tex](0,d_{1}, 0)[/tex]

The force on [tex]q_{0}[/tex]  by [tex]q_{1}[/tex] in the negative y - axis.

So that , Direction of force is,  [tex]-j[/tex]

Hence, the net force on [tex]q_{0}[/tex]  by [tex]q_{1}[/tex] is , [tex]F=-K\frac{q_{0}*q_{1}}{r^{2} }j[/tex]

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Which of the following is one way creativity can help scientists? (20 points) +Brainiest

a
By ensuring they follow the scientific method

b
By increasing the amount of time it takes to complete scientific experiments

c
By making sure they only try things that have already been proven

d
By leading them to ask more questions about the natural world

Answers

your answer would be B love!

if 1 foot is 30.28 centimeters.how many cm is 130 feet

Answers

Answer:3,936.4

Explanation:

If 1 foot is 30.28 centimeters multiply 30.28 by 130

Saturn is 890,700,000 miles from the Sun. What is this distance in scientific notation? The ratio of miles to meters is 1 mile equals 1.61 x 103 meters. What is this distance in meters? If the speed of light is 3.0 x 108 meters/second, how long does it take for light from the Sun to reach Saturn? Hint: Use the distance in meters to calculate.

Answers

Answer:

13 hours, 16 minutes, 41 seconds

Explanation:

Distance of Saturn from the Sun

= 890,700,000 miles

[tex] = 8.907\times 10^8 \: miles\\

= 8.907\times 10^8 \times 1.61 \times 10^3 \:meters\\

= 14.34027\times 10^{11}\: m\\

= 1. 434027\times 10^{12}\: m\\\\

\because Time = \frac{Distance}{Speed} \\

\therefore Time = \frac{1.434027\times 10^{12}}{3\times 10^8}\\

\therefore Time = 4.78009 \times 10^{12-8}\\

\therefore Time = 4.78009 \times 10^{4} \:seconds \\

\therefore Time = 47800.9 \:seconds\\

\therefore Time = 47801 \:seconds\\

\therefore Time = 13h\: 16m\: 41s\\[/tex]

Saturn is 890,700,000 miles from the Sun. This distance in the scientific notation would be 1.434×10¹² metes.

If the speed of light is 3.0 x 108 meters/second, then it would take 4780 seconds for light from the Sun to reach Saturn.

What is Velocity?

The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object. The unit of velocity is meter/second. It can also be represented by the infinitesimal rate of change of displacement with respect to time. The generally considered unit for velocity is a meter per second.

As given in the problem Saturn is 890,700,000 miles from the Sun

1 mile = 1.61 x 10³ meters

890,700,000 miles = 890,700,000×1.61×10³ meters

                                =1.434×10¹² metes

As given  If the speed of light is 3.0 x 10⁸ meters/second

Time = distance /speed

        = 1.434×10¹² metes / 3.0 x 10⁸ meters/second

        = 4780 seconds

Thus, the distance in the scientific notation would be 1.434×10¹² metes and it would take 4780 seconds for light from the Sun to reach Saturn.

Learn more about Velocity from here,

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There are two ways that an object can get in motion. What are they?

Answers

Answer:

pull or push

Explanation:

According to Newton's first law of motion "An object will continue to stay or remain at rest or continue to be in constant motion "unless acted upon by an external force"

F= ma

Basically a force is a pull or a push

so in other words the two ways by which an object can get in motion is by

1. A pull force

2. A push force

The rifles in the figures are being fired horizontally (straight outward, off platforms). The bullets fired from the rifles are all identical, but the rifles propel the bullets are different speeds. The speed of each bullet and the height of each platform are given. All the bullets miss their targets and hit the ground. Rank the time it takes the bullets to hit the ground. Explain your reasoning.

Answers

Answer:

  t = √ 2y₀ / g

if they are at the same height, all the bullets must carry the target, since when advancing the height decreases

Explanation:

In this exercise we see that the bullets are fired horizontally so the time it takes to reach the ground is

          y = y₀ + [tex]v_{oy}[/tex]  t - ½ g t²

as they are fired horizontally their vertical velocity is zero and the height upon reaching the ground is zero y = 0

         0 = y₀ - ½ g t²

         t = √ 2y₀ / g

from here we can see that the time it takes for the bullets to hit the floor depends only on the initial height

Therefore, all the bullets that come out of the same height reach the ground at the same time, but at a different distance, so if one misses the target, everything must fail since reaching the target is below the initial height.

The horizontal distance traveled by the bullets is

        x = v₀ₓ t

        v₀ₓ =v₀

        x = v₀ √2y₀/g

For a more precise calculation we should know the height of the target and the bullets, but if they are at the same height, all the bullets must carry the target, since when advancing the height decreases

A car traveling with an initial velocity of 10 m/s accelerates at a constant rate of 2.2 m/s^2 for 2 seconds. What distance does the car travel during this process

Answers

2.5 better than the first one more game to go hard but I 46 the bucks

Answer:

hsiahdjjsdhishshdakyeacs4y9yssig

Explanation:

ntesgs7thsjv6wlubx4euc

The observation of a "wet spot" on a hot highway in the summer is caused by:_________.
a. dispersion
b. diffraction
c. refraction
d. reflection.

Answers

Answer: Refraction

Explanation:

The observation of a wet spot on a hot highway in the summer season is caused by refraction. Therefore, option (C) is correct.

What is refraction?

Refraction can be defined as the redirection of light as it passes from one medium to another medium. The redirection of light is caused by a change in the medium or by the wave's change in speed.

Refraction of light can be described as an observed phenomenon, but other waves such as sound waves and water waves also experience refraction.

Refraction of light obeys Snell's law that the ratio of the sines of the angle of incidence and refraction must be equal to the ratio of phase velocities in the two media to the refractive index of the two media.

When the sunlight makes a blacktop hot highway. The appearance of the wet spot is bright because of the refraction of light from the sky.

Learn more about refraction, here:

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The pacefic ocean has a surface area of about 166 241 700km^2 and an average depth of 3940 m. Estimate the volume of the Pacific ocean in cubic centimetres

Answers

Answer:

[tex] \lim_{(x,y) \to \(0,0)} \frac{2x {y}^{2} }{ {x}^{2} {y}^{2} } [/tex]

Explanation:

[tex]\lim_{(x,y) \to \(0,0)}[/tex]

A marathon runner runs at a steady 15 km/hr. When the runner is 7.5 km from the finish, a bird begins flying from the runner to the finish at 30 km/hr. When the bird reaches the finish line, it turns around and flies back to the runner, and then turns around again, repeating the back-andforth trips until the runner reaches the finish line. How many kilometers does the bird travel?

Answers

Answer:

The value is [tex]D =  15 \  km [/tex]

Explanation:

From the question we are told that

   The  speed of the marathon runner is  [tex]v = 15 \ km /hr[/tex]

   The distance from the distance from the finish is  [tex]d =  7.5 \  km[/tex]

   The  speed of the bird is  [tex]v_b  =  30 \ km / hr[/tex]

  Generally the time taken for the runner to reach the finish is mathematically represented as

       [tex]t =  \frac{d}{v}[/tex]

       [tex]t =  \frac{7.5}{15}[/tex]

        [tex]t =  \frac{1}{2}[/tex]

So the distance covered by the bird is  

      [tex]D =  v_b  *  t[/tex]

      [tex]D =  30  *  \frac{1}{2}[/tex]

         [tex]D =  15 \  km [/tex]

The highest speed attained by a cyclist on level ground is 105 km/h. To attain this speed, the cyclist used a streamlined recumbent bike. Starting from rest, he gradually built up his speed by pedaling furiously over a distance of 3.2 km. If his acceleration was uniform over this distance, what was the acceleration and how long did the cyclist take to build up his final speed

Answers

Answer:

The acceleration is 0.133 m/s²

The time taken to build the final speed is 219.32 s

Explanation:

Given;

final speed of the cyclist, v = 105 km/h = 29.17 m/s²

distance traveled by the cyclist, d = 3.2 km = 3,200 m

initial speed, u = 0

Apply the following kinematic equation to determine the acceleration of the cyclist;

v² = u² + 2as

(29.17 )² = 0 + (2 x 3200)a

850.89 = 6400a

a = (850.89 ) / (6400)

a = 0.133 m/s²

The time taken to build up the final speed is given by;

v = u + at

29.17 = 0 + (0.133)t

t = 29.17 / 0.133

t = 219.32 s

position (m)
80!
В
с
60
40
20
A
- 20
-40
10
20
30
40
50
time (sec)

Answers

Answer:

hola bb como estas dime bb en que te ayudo

Explanation:

if a car is traveling with a velocity of 20 m/s, how long will it take to reach 4000m

Answers

Divide 4000 by 20 which is going to equal 200
The answer is 200 if you divide 4000 by 20

A car is on a cruise control driving in a circle. Which are constant and which are changing? Speed, Velocity. Is the car accelerating?

Answers

Answer:

Only the speed is constant.

The acceleration and velocity are changing.

Explanation:

The velocity of an object refers to its speed in a specific direction. Due to the fact that the car is driving in a circle, the direction of the car is changing.  This makes the car not to have a constant velocity as this value changes each time the car makes a bend on the circular path. (which is pretty much all the time).

The acceleration is a direct derivative of the velocity of the car. As a result, if the velocity is changing, the acceleration is also changing.

Speed is a scalar quantity. This means it does not deal with the direction of the car. It only deals with how fast the car is moving. The car is on cruise control. this means that the speed of the car does not change.

During which step of the scientific method does a scientist make an educated
guess about the outcome of an experiment?
A. Collect data
B. Form a hypothesis
C. Analyze the results
O D. Design an experiment
SUBNA

Answers

B.

A hypothesis is basically an educated guess, all in all. How you form a hypothesis is like this: “If (the independent variable; What you’re changing) ____, then (dependent variable; what is being measured)...___”

A hypothesis can be wrong. Your prediction may not always be right. But you first make a hypothesis of what you think will happen in the experiment. Then you try it out.

The scientific method (typically lasting of 6 steps) is
1. Ask a question
2. Research and gather info
3. Form a hypothesis
4. Test out the hypothesis/make an experiment
4. Analyze the data you collected
6. Draw conclusions

Answer:B. Form a hypothesis

Calculate the magnitude and direction of the electric field (in N/C) 2.2 m from a long wire that is charged uniformly at λ = 3.6 ✕ 10−6 C/m. (Assume the wire goes through the origin and the point in question is located on the +z-axis. Express your answer in vector form.).

Answers

Answer:

29.5*10^3 k N/C

Explanation:

Using

E = λ/2πEor x k

So = 18*10^9 x 3.6 ✕ 10−6 / 2.2 x k

= 29.5*10^3 k N/C

1. You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is negligible and that your car brakes with constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

Answers

Answer:

-1.82m/s²

Explanation:

Given that the reaction time (t) is negligible and car brakes with constant acceleration.

Initial Velocity (u) = 20m/s

Distance(d) from Intersection when light turns red = 110m

Hence, the magnitude of braking acceleration that will bring the car to rest at exactly the intersection :

Using the motion equation:

v² = u² + 2as

Where v = final velocity at the intersection

u = initial velocity ; s = distance to intersection ; a = acceleration of the car

Exactly at the intersection ; v = 0

0 = 20² + 2×a×110

0 = 400 + 220a

-400= 220a

a = - 400 / 220

a = - 1.818

a = - 1.82 m/s²

- stands for negative acceleration (deceleration)

A single atom of an element has 11 protons, 11 electrons, and 12 neutrons. Which element is it?
Оy
O Na
OMg
O Se

Answers

The sodium atom, Na, contains 11 protons, 11 electrons, and 13 neutrons.

What is the key difference between acentralized electrical distribution grid versus a distributed electrical distribution grid? I am using the textbook provided but I can not find an answer

Answers

The electricity generated by centralized generation is distributed through the electric power grid to multiple end-users. Centralized generation facilities include fossil-fuel-fired power plants, nuclear power plants, hydroelectric dams, wind farms, and more.

The deep scattering layer (DSL):_________
a) was discovered by Charles Darwin
b) is only seen at night
c) is a biological phenomenon that can be detected with sonar
d) is not a biological phenomenon
e) is a chemical boundary in the water

Answers

Answer:

C

Explanation:

Because its a region of high biological productivity with a lot of water organism allowing for high reflectivity of sonar pulse mimicking ocean bottom

Which of the following quantities represent mass?
a. 12.0 lbs.
b. 0.34 g.
c. 120 kg.
d. 1600 kN.
e. 0.34 m.
f. 411 cm.
g. 899 MN.

Answers

Answer:

Explanation:

a ) 12.0 lbs  -  mass

b ) .34 g   - mass

c ) 120 kg    - mass  

As lbs , g and kg are units of mass , these things represent mass . lbs is FPS unit of mass and kg is  SI unit . g is CGS unit of force .

d ) 1600 kN     It represents force because kN or kilonewton is unit of  force .

e ) it represents , length or distance because m or metre  is unit of length .

f ) 411 cm It represents length or distance because cm is smaller unit of length

g ) 899 MN or million newton .  Like d ) It also represents force . Million newton is higher unit of force .

electricity is one kind of​

Answers

Answer:

I think electricity is one kind of energy

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