A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what values of t is the particle moving to the right? The particle is moving to the right only if 0

Answers

Answer 1

Answer:

The particle moves to the right when 0 ≤ t < a

Explanation:

Since at any time t≥0 its position is given by x(t) = 12(a−t)², the particle moves to the right if x(t) > 0

So,  x(t) > 0 ⇒ 12(a−t)² > 0 ⇒ (a−t)² > 0

So, (a−t)² > 0

taking square-root of both sides, we have

√(a−t)² > √0

⇒ (a−t) > 0

⇒ a > t

Since t ≥ 0 ⇒ a > t ≥ 0 ⇒ 0 ≤ t < a

So, the particle moves to the right when 0 ≤ t < a


Related Questions

A motor-cycle rider going 90km/hr around a curve with a radius of 100m must lean at an angle to the vertical. The angle at which he leans is *​

Answers

Answer:

The angle of inclination of the rider to the vertical is 32.5⁰.

Explanation:

Given;

linear speed of the motor cycle, v = 90 km/hr = 25 m/s

radius of the circle, r = 100 m

The angle of inclination of the rider to the vertical is calculated using banking angle formula;

[tex]\theta = tan^{-1}(\frac{v^2}{rg} )\\\\\theta = tan^{-1} (\frac{25^2}{100 \times 9.8} )\\\\\theta = 32.5 ^0[/tex]

Therefore, the angle of inclination of the rider to the vertical is 32.5⁰

If you wanted to learn more about ancient scientific knowledge, whose life
would you research?
O A. Ibn al-Haytham's
B. Christian Doppler's
O C. Sir Isaac Newton's
D. Galileo Galilei's

Answers

Answer:

You would want search A.Ibn al-Haytham's

If the time between the horn sounding and the people on the ship hearing the echo from the ship is 4 seconds, how far away is the ship from the cliff ? (velocity of sound in air is 331 m/s)

Question options:

A. 1324 m

B. 662 m

C. 0.012 m

D. 820 m

Answers

Answer:

D

Explanation:

How are elements similar in a group/family on the periodic table?

A. They have the same number of valence electrons

B. They are all metals

C. They have a full outer shell of electrons

D. They are all nonmetals

Answers

Answer:

A. They have the same number of valence electrons

Explanation:

A sound wave is an example of a _____ wave.

longitudinal
fluid
transverse
reverse

Answers

Answer:

longitudinal wave

OK hope this will help you

1. Which types of planets are more dense: terrestrial or
Jovian?

2. What is a light year?

Answers

Answer:

1. terrestrial

2. The distance light travels in one year

Explanation:

Which option is an example of chemical energy being transformed into
kinetic energy?
A. A ball rolling down a hill
B. A battery powering a flashlight
C. A plant storing energy from the Sun in its leaves
O D. A rocket engine igniting its fuel during liftoff
SUBMIT

Answers

D
Rocket engine igniting is chemical energy when he in turn makes it launch and move which is kinetic energy

Answer: D

Rocket engine igniting is chemical energy when he in turn makes it launch and move which is kinetic energy

Use coefficients to balance the following chemical equation. Remember a balanced chemical equation has the same number of atoms of each element on each side of the equation. Hint: create a table on scratch paper to count your atoms on each side of the equation so_(g) + ___02(g) → _so, (g)​

Answers

Answer: The given equation is balanced as  [tex]SO_{2}(g) + O_{2}(g) \rightarrow SO_{3}(g)[/tex]

Explanation:

A chemical equation that contains same number of atoms on both reactant and product side are called balanced chemical equation.

For example, [tex]SO_{2}(g) + O_{2}(g) \rightarrow SO_{3}(g)[/tex]

Here, number of atoms on reactant side are as follows.

S = 1O = 4

Number of atoms on product side are as follows.

S = 1O = 3

To balance this equation, multiply [tex]SO_{2}[/tex] by 2 on reactant side and multiply [tex]SO_{3}[/tex] also by 2 on product side.

Hence, the equation will be rewritten as follows.

[tex]2SO_{2}(g) + O_{2}(g) \rightarrow 2SO_{3}(g)[/tex]

Here, number of atoms on reactant side are as follows.

S = 2O = 6

Number of atoms on product side are as follows.

S = 2O = 6

As there are same number of atoms on both reactant and product side. So, this equation is a balanced equation.

Thus, we can conclude that the given equation is balanced as  [tex]SO_{2}(g) + O_{2}(g) \rightarrow SO_{3}(g)[/tex]

What is it that if you have, you want to share me, and if you share, you do not have?

Answers

Answer:

Secrets? Cuz if I share you the secrets then the secrets will no longer will be secrets.

In electric motors and electric generators, which part is responsible for transferring current from the power source to the commutator or from the slip rings to where the electricity is needed? armature brush axle magnet

Answers

Answer:

brush

Explanation:

its correct

Answer:

B. Brush

Explanation:

Edg 2021

All the sources of energy present on the earth are the outcomes of solar energy .Justify this statement with example​

Answers

Answer:

because all the energy is directly depend on solar .. like light energy .. wind energy.. heat energy.. etc..

Explanation:

Three bulbs are connected in series to a 4.5 V battery. The second bulb burns out. The
voltage reading on the first bulb is ____.

a) 4.5 V
b) 2.25 V
c) 0 V
d) none of the above

Answers

Answer:

0v

Explanation:

A force is acting on a 3-kg object during 5 seconds. If the object initially has a speed of 1.5m/s and after applying the force its speed is 4 m/s

Answers

Answer:

1.5 N

Explanation:

You've left us to guess what the question is. I will Assume it is what's the force?

Givens

m = 3 kg

vi = 1.5 m/s

vf = 4 m/s

t = 5 seconds

Formula

F = m * (vf - vi)/t

Solution

F = 3 * (4 - 1.5) / 5

F = 1.5 N

Which of the following regions of the electromagnetic spectrum has the highest energy
(among the 4 listed here)?
A. Visible light
B. Radio waves
C. Infared light
D. UV light

Answers

The maximum energy is found in visible light from the following areas of the electromagnetic spectrum. Option A is correct.

What is the electromagnetic spectrum?

The electromagnetic spectrum is seen as colors violet, indigo, blue, green, yellow, orange, and red.  Blue light has a very short wavelength, and so produces a higher amount of energy.

Blue light in the visible zone has a very short wavelength. So that it produces a higher amount of energy that's why the blue part of visible light transfers the most energy.

Visible light from the following regions of the electromagnetic spectrum has the highest energy.

Hence, option A is correct.

To learn more about the electromagnetic spectrum refer:

https://brainly.com/question/15576247

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Explain why the temperature of the water stays constant

Answers

Answer:

When boiling occurs, the more energetic molecules change to a gas, spread out, and form bubbles. ... In addition, gas molecules leaving the liquid remove thermal energy from the liquid. Therefore the temperature of the liquid remains constant during boiling.

Answer:

nice

Explanation:

Freeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee



(ignore pics)

Answers

Answer:

Thank you!

Explanation:

new friendssssssssss?

A germanium piece is heated, then its resistance increases or decreases​

Answers

Answer:

decreases

Explanation:

which type of motion occur in a lift in one word
Pls answer​

Answers

Answer:

Explanation:

Lift occurs when a moving flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton's Third Law of action and reaction. Because air is a gas and the molecules are free to move about, any solid surface can deflect a flow.

What is missing from the solubility graph shown on the right?

Answers

Answer:

the name and the units of the vertical axis. Explanation: As you see the horizontal axis shows that the independent variable is Temperature and that it is reported in °C.

Explanation:

Answer

The horizontal axis reveals to us that the independent variable is temperature which is reporting in C. We know that but what we dont know is the name or the untis on the vertical axis. Also a nice title and chart by it will help as well. A legend as well to explain what the colors even mean.

Explanation:

I got it right on edge.

A 57 kg ice skater moving to the right with a velocity of 1.2 m/s throws a 0.11 kg snowball to the right with a velocity of 31.5 m/s relative to the ground. What is the velocity of the ice skater after throwing the snowball? Disregard the friction between the skates and the ice.

Answers

Answer:

 v_f = 1.14 m / s

Explanation:

This is an exercise of conservation of momentum, let's define a system formed by the skater and the snowball, therefore the forces during the launch are internal and the moment is conserved.

Initial instant. Before throwing the ball

        p₀ = M v₀

Final moment. After throwing the snowball

       p_f = (M-m) v_f + m v

the moment is preserved

        p₀ = p_f

        M v₀ = (M-m) v_f + m v

        v_f = [tex]\frac{M v_o - m v}{M-m}[/tex]

let's calculate

       v_f = [tex]\frac{57 \ 1.2 - 0.11 \ 31.5}{ 57 - 0.11}[/tex]

       v_f = 64.936 / 56.89

       v_f = 1.14 m / s

I am having trouble with writing a 2 paragraph summary about this vidio can someone help me
(this si the vidio )Picture of the Big Bang (a.k.a. Oldest Light in the Universe)

Answers

Answer:

hmmm  ok

Explanation:

what effect does the earth's surface have on solar radiation?
A. The ground absorbs half the solar radiation and stored it as infrared radiation for centuries
B. Half of the solar radiation is absorbed and converted to infrared (heat)
C. Nearly all solar radiation is reflected back into space by the ground

Answers

Answer:

B.

Explanation:

Solar radiation that is not absorbed or reflected by the atmosphere (for example by clouds) reaches the surface of the Earth. The Earth absorbs most of the energy reaching its surface, a small fraction is reflected. In total approximately 70% of incoming radiation is absorbed by the atmosphere and the Earth’s surface while around 30% is reflected back to space and does not heat the surface. The Earth radiates energy at wavelengths much longer than the Sun because it is colder. Part of this longwave radiation is absorbed by greenhouse gases which then radiate energy into all directions, including downwards and thereby trapping heat in the atmosphere.

Hope this helps, sorry if it is incorrect. Have a great day/night!

Solar radiation that is not absorbed or reflected by the atmosphere (for example by clouds) reaches the surface of the Earth. The Earth absorbs most of the energy reaching its surface, a small fraction is reflected

What is solar radiation?

Solar radiation, often called the solar resource or just sunlight, is a general term for the electromagnetic radiation emitted by the sun.

Solar radiation can be captured and turned into useful forms of energy, such as heat and electricity, using a variety of technologies

Solar radiation that is not absorbed or reflected by the atmosphere (for example by clouds) reaches the surface of the Earth.

The Earth absorbs most of the energy reaching its surface, a small fraction is reflected. In total approximately 70% of incoming radiation is absorbed by the atmosphere and the Earth’s surface while around 30% is reflected back to space and does not heat the surface.

The Earth radiates energy at wavelengths much longer than the Sun because it is colder.

Part of this longwave radiation is absorbed by greenhouse gases which then radiate energy into all directions, including downwards and thereby trapping heat in the atmosphere.

To know more about solar radiation follow

https://brainly.com/question/893656

When matter changes shape, does its mass change?

Answers

Answer:

No, the mass of an object is always the same, even if a chemical reaction happens or the object becomes denser.

Explanation:


A sled slides down a hill with friction between the sled and hill but negligible alr resistance. Which of the following must be correct about the resulting change in energy of the sled Earth system?
A) The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction,
B)The gravitational potential energy decreases and the kinetic energy is constant.
C)The decrease in the gravitational potential energy is equal to the increase in kinetic energy
D)The gravitational potential energy and the kinetic energy must both decrease.

Answers

Answer:

A) The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction,

Explanation:

The kinetic energy is the energy that the object has and is defied by the work that is needed to accelerate the body. The gravitational potential is a mechanism by which an equal amount of energy is being transferred per unit mass that is needed for the object to move from the specific location.Hence when the sled moves down the hill with the force of gravity it has negligible resistance as an equal amount of energy is dissipated.

The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction.

What is principle of conservation of energy?

The principle of conservation of energy states that, the total mechanical energy of an isolated system is always conserved.

When a sled slides down a hill with friction between the sled and hill but negligible air resistance.

The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction.

Learn more about kinetic energy here: https://brainly.com/question/25959744

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Motion only occurs if someone is there to witness an object moving

Answers

Answer:

True

Explanation:

Motion is change with time of the position or orientation of a body with respect to an observer

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE

True

Motion is changed it all depends on the body .

The equation of a displacement time-curve of a particle is given as x=〖10t〗^2, the instantaneous velocity at t= 1s is *

Answers

please find ur answer in the attached image, mark as brainliest if it helps.

10. Observa la siguiente gráfica que describe un recorrido en línea recta de un caballo: a) ¿Qué tipo de movimiento presenta el caballo? Justifica la respuesta. b) Indica la distancia que ha recorrido el caballo a los tres segundos de empezar el recorrido. c) Calcula su velocidad media.

Answers

Answer:

Movimiento de translación.

Explicación:

El caballo tiene un tipo de movimiento traslacional porque todas las partes de su cuerpo se mueven de un lugar a otro. La distancia se puede encontrar usando la fórmula de distancia que es distancia = velocidad x tiempo. La velocidad promedio del caballo se puede calcular dividiendo la distancia total recorrida por el tiempo total tomado. Si los datos están disponibles, puede calcular la distancia y la velocidad promedio del caballo.

Which action would not speed up erosion in a Texas ecosystem?
A
High winds
B
Flash flooding
C
Acid rain
D
Large waves

Answers

C or D .......................

Exact Steps on how to Solve with the addition on how to properly input log10.

Answers

Answer:

Explanation:

log10 function is required to convert dB into intensity of a sound. Both are measures of loudness of a sound and the relationship can be expressed as follows:

dB = 10 log10(I/Io), where Io is 10^-12 W/m^2

Substituting, 82 = 10 log10(I/10^-12)

I = 0.0001585 W/m^2

or 1.58*10^-4 W/m^2

Answer:

Explanation:

82dB = 10log(Intensity/10^-12)

Intensity = 10^-12*10^(82/10)

=10^(-3.8)

=1.585*10^-4 W/m2

Can You Explain?
How do we obtain data about the properties of exoplanets
and objects in our solar system?
(Make sure you include tools that are used to observe them.
) We use the radial velocity method that involves watching all
the spectral

Answers

Answer:

Explanation:

The radial velocity method involves watching the spectral lines of a star as a planet orbits the star. Because of the planets gravitational pull on the star, the star will wobble. This causes Doppler shifts in the spectral lines, allowing astronomers to infer the presence of the planets.

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