You are given two converging lenses of focal lengths 3.5 cm and 2.0 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

The highest kinetic energy occurs at the points A and G. The highest potential energy occurs at point D.

We know that kinetic energy has to do with energy that is in motion. On the other hand the potential energy is the energy that is at a point. Both the kinetic energy and the potential energy are all the kinds of mechanical energy.

We have to look at the points where the object would have the highest velocity and these are the points where the kinetic energy of the body is maximum and this would occur at the points A and G. The points where the body has a maximum potential energy is the highest point and this at point  D.

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The steady-state flux and current at every location in the medium are given by Ф ≅( S(2^1/2)/π*d)* e^-a/(2)^1/2*L. Since there are isotropic sources that are equally distributed and emit s neutrons per cm3/s

According to Fick's first law, which stipulates that diffusion flow is proportional to concentration gradient, steady-state flux diffusion processes are identified by this property. Diffusion coefficient or diffusivity are other names for the proportionality constant, D. It is expressed in m2/sec. J x can be used to represent the one-dimensional case for steady-state flux. The movement of electrical charge carriers like electrons is known as current. Positive and negative locations both experience current flow. The ampere is the SI unit for calculating electrical current (A). The movement of electrical charge carriers like electrons is known as current. Positive and negative locations both experience current flow.

Ф ≅( S/4*π*d)* e^(r/l)/r

Ф ≅( S/4*π*d)* e^-a/(2)^1/2*L

Ф ≅( S(2^1/2)/π*d)* e^-a/(2)^1/2*L

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the statement is True

Oscillations cause disturbances in the medium, and these disturbances, are known as waves and, they propagate or move from one place to another.

There are several types of waves:

mechanical waves are those that propagate through a material medium.

electromagnetic waves are those waves that travel without a physical medium.

A wave moves at a certain speed based on the kind of medium it propagates through.

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The debroglie wavelength in picometers (10-12m) of an electron that is traveling at 79.1% of the speed of light is  2.8 × [tex]10^{-12}[/tex]

Mass of electron m = 9.1 × [tex]10^{-31}[/tex]kg

speed of electron v = 3 ×[tex]10^{8}[/tex] m/s * (79.1/100) = 2.37 × [tex]10^{8}[/tex] m/s

debroglie wavelength λ = h/mv

λ = 6.626 [tex]10^{-34}[/tex]/9.1 × [tex]10^{-31}[/tex] × 2.37 × [tex]10^{8}[/tex]

λ  = 2.8 × [tex]10^{-12}[/tex]

In many branches of physics, the speed of light in a vacuum, commonly abbreviated as c, plays a crucial role. Exactly 299,792,458 meters per second is the speed of light, or c. [Note 3] The speed at which common matter or energy can travel through space (and, consequently, any signal carrying information) is limited to c, according to the special theory of relativity.

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The metal that has the lowest melting point must be the metal that has the lowest density and therefore is easiest to bend. That is metal B.

The melting point of the metal depends upon the types of bonds between the metal atoms. The relationship between the melting point of a substance and the strength of the intermolecular force of that substance is directly proportional. That means that the stronger the intermolecular forces of the substance, the higher the melting point of the substance.

Tungsten has the highest melting point of any metal in the periodic table is 3422 °C.

As the strength of the intermolecular forces increases, more energy is needed to disrupt the attraction between these molecules. As a result, increasing intermolecular forces results in a concomitant increase in melting point.

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The ring will move farther than will the disk.

The torque required to achieve a desired angular acceleration about a rotational axis depends on the moment of inertia of a rigid body.

The moment of inertia of a ring is given by the following equation [tex]I=mr^{2}[/tex]

similarly, the moment of inertia of a disk is [tex]I=m\frac{r^{2} }{2}[/tex]

Where, m and r is the mass and the radii of the ring and the disc.

The body's mass distribution and the axis selected to affect the moment of inertia, with larger moments requiring more torque to change the rotation rate. The object with the lowest moment of inertia will descend to the bottom first because it is resistance to rotational motion.

Therefore the disc will reach the bottom first, but due to the higher moment of inertia than the disc the ring will move farther than the disc.

The question is incomplete. The correct question is

A ring and a disk have identical masses, radii and velocities and are not attached to each other. If they each roll without slipping up an inclined plane, how will the distances that they move up the plane before coming to rest compare?

a. The ring will move farther than the disk.

b. The disk will move farther than the ring.

c. The ring and the disk will move equal distances.

d. The relative distances depend on the angle of elevation of the plane.

e. The relative distances depend on the length of the plane.

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The diffraction-induced minimum angular spread is 633 10 9 meters.

When the hole is illuminated by a parallel ray of light of wavelength lambda, it is believed that the dispersal of the spot (gotten on the left wall of the video) equals the sum of its geometrical dispersal and the spread induced by diffraction.

Diffraction is the term used to describe the spreading out of waves when they pass through an apertures or around objects. It occurs when the aperture's or obstruction's size and the incident wave's wavelength are of same magnitude. At very small aperture diameters, the most of the wave is blocked.

Briefing : Minimum angular spread due to diffraction (θ) =  λ/b

Given.

Wavelength = 633nm = 633×10⁻⁹m

Beam diameter is 1mm.

Minimum angular spread due to diffraction (θ) =  633×10⁻⁹m/1

Minimum angular spread due to diffraction (θ) =  633×10⁻⁹m.

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Linear equation for team a; d = 6t + 2 and Linear equation for team b;

d = 6t.

To find speed, divide the distance of the journey by the time it took to travel. To calculate the time, divide distance by speed and to get the distance, multiply  speed by time.

Given that in a canoe race, team a is traveling 6 miles per hour and it is 2 miles ahead of team b.

Team b is traveling 6 miles per hour. The teams continue the traveling at their current rates for the remaining race.

We know that speed= distance/time

Linear equation for team a;

d = 6t + 2

Linear equation for team b;

d = 6t

d is distance and t is time.

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According to Moran, the evidence points to pleiotrophy and energy savings as two key factors in the cavefish eye loss.

Mexicanus was created through natural selection, pleiotropy, and genetic drift, not through human initiative. Organisms get what they need via natural selection. The fish must conserve energy to avoid going blind. Fish lose their eyes because they are unnecessary.

The Mexican tetra (Astyanax mexicanus) has been evolving in caves for the last few million years in forms that are blind. The loss of eyes is a major benefit for creatures living in the dark since maintaining eyes and the visual regions of the brain requires a lot of energy. The cavefish instead "sees" by sucking.

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The laser power is 27,69 mW.

Power= energy/sec = J/s

Photon energy= hf= hc /wavelength

# of photons/sec = power/ photon energy= rate of emission

Photon Energy= ( 6.63 × [tex]10^{-34}[/tex]) × 3×[tex]10^{8}[/tex] / 6.8×[tex]10^{16}[/tex] ≈ 3.147 ×[tex]10^{-42}[/tex] J

This should be ignored. It is part of the units and not the equation.

Power/3.147 × [tex]10^{-42}[/tex] = 8.8 × [tex]10^{26}[/tex] [tex]s^{-1}[/tex]

Power= 8.8 × [tex]10^{-26}[/tex]- 3.147 × [tex]10^{-42}[/tex] J= 0 .02769 W = 27.69 mW

How is laser power determined?

The energy levels of the electrons in the atoms of the material used to create the laser beam—often referred to as the "lasing" material—determine the intensity of the laser beam. The wavelength of the light generated by the lasing material has an inverse relationship with the energy level of the photons that are created by it.

Can a laser's power be increased?

The intensity of the light increases with the amount of energy used to excite those atoms in the laser. It almost resembles dialing up the sound system's volume control. However, if you turn that level up too loud, you run the danger of harming your hearing or the sound system itself.

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The central angle relating to an object's position on a circle changes as it moves along a circular path.The rate at which this angle changes with respect to time is known as the angular velocity, denoted by the symbol w.

A Ferris wheel, for instance, might rotate pi / 6 radians every minute.

If a disk of indefinite radius is rotated at an angular velocity $w$ in a large volume of liquid, the liquid will experience a force known as the centrifugal force.

This force is directed radially outward from the axis of rotation and is given by the equation $F = mrw^2$, where $m$ is the mass of the liquid, $r$ is the distance from the axis of rotation, and $w$ is the angular velocity.

The magnitude of the force increases with the mass of the liquid, the distance from the axis of rotation, and the angular velocity of the disk.

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The theoretical Coefficient of Performance (COP) to cool the room A is 33.52.

Temperature in room A = T₁ = 18.6 oc

Temperature in room B = T₂ = 27.3 oc

To convert temperatures in Kelvin,

= T₁ = 18.6 + 273 =

= T₁ = 291.6 K

and,

=  T₂ = 27.3 + 273

=  T₂ = 300.3 K

The COP value to cool room A =

= COP = T₁ / (T₂ - T₁)

= COP = 291.6  / (300.3 - 291.6 )

= COP = 291.6 / 8.7

= COP = 33.52

The theoretical coefficient of performance to cool room A is 33.52 when the temperature of room A is 18.6 oc and that of room B is 27.3 oc.

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It's crucial to understand that when a diver leaps off a springboard, their angular momentum stays constant until they touch the water's surface.

Despite acting on the diver, gravity does not exert a net positive or negative torque on the diver since it passes through the diver's center of mass. The diver can make two to three rotations when in the tuck position, but only one or two rotations when in the pike position. The moment of inertia of the two places is the cause. The moment of inertia of the diver in the tuck position can be lower. Given that the diver's angular speed is inversely proportional to the moment of inertia, she will make more rotations for the constant angular momentum.

I1w1 =I2w2

w1/w2 = I1/I2

I1 = mr1^2

I2 = mr2^2

r2<r1

then I2<I1

w1/w2<1

w1<w2

From the above analysis we can say that the angular velocity is less in the first case than in the later case which means the number of rotations made in the tuck position is more than number of rotations made than that in pike position.

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James braid, a physician, is credited with coining the term hypnosis after becoming mesmerized while traveling. Hence, the relevant option is option (b).

James Braid was born on June 19, 1795, and passed away on March 25, 1860. He was a well-known Scottish surgeon who was also a gentleman scientist and natural philosopher. According to Braid, hypnotic suggestion can be an effective treatment for nervous system functioning problems. Comparative anatomy has been defined as the study of similar body features in various animal species in order to suggest or comprehend modifications that have to occur underground during the course of evolution from very similar predecessors.

The research that compares the structural differences between various animal species in order to comprehend the changes that each species went through during the stage of evolution from their common ancestors. James braid, a physician, is credited with coining the term hypnosis after being mesmerized while traveling.

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The ball is seen to be speeding up as the distance increases with time.

We know that speed is the ratio of the distance to the time that is taken by the object. We know that when an object is speeding up, the distance of the object is going to increase linearly with the time taken.

If we look at the graph that has been shown in the image that is attached to this answer, we would notice that the distance that is covered is increasing with time.

The speed can then we obtained from;

Speed = [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex]

= 80 - 0/6.5 - 0

= 12.3 m/s

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Never does a free body revolve around its center of mass ( the instantaneous axis of rotation never passes through the center of mass).

Being a hypothetical object, the axis of rotation might be a challenging notion to understand. An imaginary line that extends through the joint's pivot or rotation point is referred to as the axis of rotation in terms of human anatomy (for example, the axis of rotation for flexing and extending the arm projects through the elbow joint).

The intersection of these three axes, which are the longitudinal, lateral, and vertical ones, each of which is perpendicular to the others, occurs at the center of gravity of the aero plane.

Position, momentum, and angular momentum make up an object's motion when it is rigid. Therefore, the "axis of rotation" is the unit vector, which is the object's angular momentum vector divided by the angular momentum magnitude (and therefore undefinable in the absence of angular momentum).

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It will take 4.24 hours for a sample of titanium-45 to decay from 65. 0 grams to 25. 0 grams.

Half life of first order reaction is given by: [tex]t_{1/2}[/tex] = 0.693/k

Given half life is 3.08 hours.

So k = 0.225

Rate of first order reaction is given by: [tex]kt = 2.303 * log(R'/R)[/tex]

Where k = rate of reaction = 0.225

t= time taken

R' = final amount = 25g

R = initial amount =65g

Putting these values we get t=4.24 hours.

So it will take 4.24 hours for a sample of titanium-45 to decay from 65. 0 grams to 25. 0 grams.

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A) The energy in electron volts for a particle with this wavelength if the particle is a photon is; .E = 4969.5 eV or 4.9695 Kev

B) B) If a particle with this wavelength is an electron, its energy in electron volts is E = 23.58 eV.

C) E = 0.003306 eV

A) The formula for the energy here is;

E = hc/λ

where;

h is Planck's constant

= 6.626 × 10⁻³⁴ J.s

c is speed of light

= 3 × 10⁸ m/s

wavelength is equal to 0.25 nm (0.25 x 109 m).

Thus;

E = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(0.25 x 10⁻⁹)

79.512 × 10⁻¹⁷ J

converting to eV gives;

E = (79.512 × 10⁻¹⁷)/(1.6 × 10⁻¹⁹)

E = 4969.5 eV or 4.9695 keV

B) Formula for the energy if the particle is an electron is;

E = h²/(2mλ²)

where m = 9.31 × 10⁻³¹ kg

E = (6.626 × 10⁻³⁴)²/(2 × 9.31 × 10⁻³¹ × (0.25 x 10⁻⁹)²)

E = 37.726 × 10⁻¹⁹ J

Converting to eV gives;

E = (37.726 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹)

E = 23.58 eV

C) Mass of alpha particle is; m = 6.64 × 10⁻²⁷ kg

E = h²/(2mλ²)

where m = 6.64 × 10⁻²⁷ kg

E = (6.626 × 10⁻³⁴)²/(2 × 6.64 × 10⁻²⁷ × (0.25 x 10⁻⁹)²)

E = 52.896 × 10⁻²³ J

Converting to eV gives;

E = (52.896 × 10⁻²³)/(1.6 × 10⁻¹⁹)

E = 0.003306 eV

The complete question is : For crystal diffraction experiments, wavelengths on the order of 0.25 nm are often appropriate.

A) Find the energy in electron volts for a particle with this wavelength if the particle is a photon.

B) Find the energy in electron volts for a particle with this wavelength if the particle is an electron.

C) Find the energy in electron volts for a particle with this wavelength if the particle is an alpha particle (m=6.64×10−27kg).

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The potential energy of the object when it is at the surface of the Earth is -3.53 x 10^14 J

What is potential energy?
Potential energy in physics is the energy that an object retains as a result of its position in relation to other objects, internal stresses, electric charge, or even other elements. The gravitational potential of an object, this same elastic potential energy of a stretched spring, as well as the electric potential power of the an electric charge inside an electric field are examples of common types of potential energy. The joule, denoted by the letter J, is the energy unit inside the International System of Units (SI). Although it has connections to the Greek philosopher Aristotle's idea of potentiality, the term "potential energy" was coined by the Scottish engineer as well as physicist William Rankine in the 19th century.

(a) The potential energy of the object when it is at the surface of the Earth is equal to the gravitational potential energy, which is calculated by the equation:
PE = -GmM/r
Where G is the gravitational constant (6.67 x 10^-11 m^3 kg^-1 s^-2), m is the mass of the object (100 kg), M is the mass of the Earth (5.98 x 10^24 kg) and r is the distance between the object and the center of the Earth (6.37 x 10^6 m).
Therefore, the potential energy of the object when it is at the surface of the Earth is:
PE = -GmM/r = -6.67 x 10^-11 x 100 x 5.98 x 10^24 / 6.37 x 10^6 = -3.53 x 10^14 J

(b) The potential energy of the object when it is at a height above the Earth's surface equal to the Earth's radius is calculated by the same equation as above, but with a different value for r. Since the height is equal to the Earth's radius, the distance between the object and the Earth's center is doubled and the potential energy is equal to:
PE = -GmM/r = -6.67 x 10^-11 x 100 x 5.98 x 10^24 / (2 x 6.37 x 10^6) = -1.76 x 10^14 J

(c) The escape speed for a body projected from this height is calculated by the equation:
v_esc = sqrt(2GM/r)
Where G is the gravitational constant (6.67 x 10^-11 m^3 kg^-1 s^-2), M is the mass of the Earth (5.98 x 10^24 kg) and r is the distance between the object and the Earth's center (2 x 6.37 x 10^6 m).
Therefore, the escape speed for a body projected from this height is:
v_esc = sqrt(2GM/r) = sqrt(2 x 6.67 x 10^-11 x 5.98 x 10^24 / (2 x 6.37 x 10^6)) = 11.2 km/s

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The angular distance should be the angular distance that the pie plate has moved through in revolutions, radians, and degrees are 5.59 revolution and  2012.4° respectively.

In revolution, θ = 8.24 revolution.

In radian = θ = 57.78 rad.

In degree θ = 2966.4°.

Calculation of the angular distance:

Since

Pie diameter = 9 in

So,  the circumference of the pie should be

P = πd = 9π in

And, rim of the pie rotates 158 in,

So,

1 Revolution of the pie is 9π in,

So, for 158 it should be

= 158 in / 9π in revolution

= 5.59 revolution

Now in the case when

1 revolution is 2πrad

So,

5.59 revolution = 5.59 × 2π = 87.79 rad.

And also, 1 revolution is 360°

5.59 revolution = 5.59 × 360 = 2012.4°

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The method used by engineers to pierce rock at angles other than just a straight line is known as directional drilling.

What is method?
A procedure connected to a message and an object is referred to as a method throughout object-oriented programming (OOP). An object is made up of state information and behaviour, which together make up the interface that outlines how any of the object's various consumers may use it. A method is indeed a consumer-parametrized behaviour of an object. Behaviors have been represented as methods, while data is represented as an object's properties. For instance, a Window object may have properties like open and close as well as methods like open and close, and its state (whether it is opened or closed at any given time) would be a method.

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The work done by friction on the ball before it transitions to rolling without slipping is 7.04 J.

The final velocity of the bowling ball is calculated by applying the principle of conservation of angular momentum as follows;

Li = Lf

mv₁r = mv₂r + Iω

where;

mv₁r = mv₂r + (²/₅mr²)ω

mv₁r = mv₂r + (²/₅mr²)(v₂/r)

mv₁r = mv₂r + (²/₅mr)(v₂)

r(mv₁) = r(mv₂ + ²/₅mv₂)

mv₁ = mv₂ + ²/₅mv₂

v₁ = v₂ + ²/₅v₂

v₁ = 7v₂/5

7v₂ = 5v₁

v₂ = 5v₁/7

v₂ = (5 x 2.35 m/s)/7

v₂ = 1.678 m/s

The work done by friction on the ball before it transitions to rolling without slipping is calculated as follows;

work done by friction = change in kinetic energy of ball

ΔK.E = ¹/₂m(v₂² - v₁²)

ΔK.E = ¹/₂ x 5.2(1.678² - 2.35²)

ΔK.E = -7.04 J

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Answer:

-7.03266 N

Explanation:

Work = Final kinetic energy - initial kinetic energy

[tex]W_{nc} = K_{f} - K_{i}[/tex]

Finding initial kinetic energy:

[tex]K_{i}=\frac{1}{2}mv^{2}= \frac{1}{2}(5.2)(2.35)^{2}=14.3585\\[/tex]

Finding final kinetic energy:

We have mass, but don't have final velocity. Have to find [tex]v_{f}[/tex] next.

We can use the kinematics equation combined with the fωorce equation. The force that slow the ball down is friction force. [tex]v_{f}=v_{0}+at=v_{0}+\frac{F}{m}t=v_{0}-\frac{f}{m}t[/tex]

Finding f/m

f=μmg ⇒ (f/m)=μg=0.211(9.81)=2.06991

Plug that back into the equation

[tex]v_{f}=2.35-2.06991t[/tex]

Now to find time, we can use angular velocity

τ=fR and α=τ/I and [tex]I=\frac{2}{5}MR^{2}[/tex], so [tex]\alpha =\frac{fR}{\frac{2}{5} MR^{2}}=\frac{5ug}{2R}[/tex]

ω=αt=(5μg)(t)/(2R)=5.174775(t/R)

v=rω=5.174775t

Therefore, [tex]v_{f}=2.35-2.06991t=5.174775t[/tex]

t=0.32437

Plug time back into the v_f equation.

[tex]v_{f}=2.35-2.06991(0.32437)=1.67858[/tex]

Plug v_f back into the K_f equation

[tex]K_{f}=\frac{1}{2}mv^{2}= \frac{1}{2}(5.2)(1.67858)^{2}=7.32584[/tex]

Work done by friction

[tex]W_{nc} = K_{f} - K_{i}=7.32584-14.3585=-7.03266[/tex]

Movement that will result in the largest increase in potential energy : All the movements will result in the same change in potential energy because they each move a roller coaster car for the same distance.

Since they move in the same direction, therefore share the same magnetic qualities and move one unit identically.

The potential energy increases because train moves against the magnetic force and potential energy does not change because the magnets in the system do not change. Engineer is experimenting with two identical magnetic roller coaster cars on the different sides of a center magnet that cannot move.

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The item moves halfway around a circle of radius r. an inward radial pressure of magnitude f is exerted on it. the paintings done on the item through the radial force being exerted on it is zero.

In physics, paintings is the power transferred to or from an object via the software of pressure along a displacement. In its most effective form, for a consistent strain aligned with the direction of motion, it equals the fabricated from the force strength and the gap traveled.

The work modifications the quantity of mechanical and internal electricity possessed with the aid of devices. whole paintings is carried out on a gadget or object, power is added to it.

The individual of labor accomplished can be categorised in three instructions. they're +ve paintings, -ve paintings and 0 work. The character of work is based upon at the attitude amongst stress and displacement..

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The loop's induced current flows counterclockwise because a long, straight wire carries current in that direction (to the right). There is a square wire loop above the wire. if the loop departs from the lengthy.

The loop's magnetic flux will decrease as the current in wire AB in the wire drops. Therefore, to counteract the drop in magnetic flux, the current introduced into the loop must be counterclockwise. Induced current definition The current that results from electromagnetic induction is known as the induced current. The production of electric power relies heavily on electromagnetic induction. Typically, metal is drawn through a hole in a die or draw plate to create wire. There are numerous standard sizes for wire gauges.

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Wave passing through a single slit  it becomes twice as width of the central maximum of its diffraction pattern as the slit is made half as wide.

The central maximum lies between the first-order minima defined by the relation sinθ dark =mλ/a=λ/a. Because the angle is small, sinθ dark  ≈tanθ dark  =y dark/L, so the width of the central maximum is proportional to Lλ/a. Thus, the central maximum becomes twice as wide if the slit width a becomes half as wide.

In order to enter the region of geometric shadow cast by the obstruction or aperture, waves must interact with one another or bend around its edges, which is referred to as diffraction. A secondary source of the wave that is propagating is in fact created by the diffracting item or aperture. The term "diffraction" was originally used in 1660 by the Italian scientist Francesco Maria Grimaldi, who was also the first to make precise observations of the phenomena.

On the registration plate, an infinite number of spots (three are illustrated) along length d project phase contributions from the wave front, resulting in a constantly changing intensity.

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When a rigid item rotates along a fixed axis, the following occurs:

They are all moving at the same angular speed.

They are all moving at the same angular velocity.

When a rigid item rotates along a fixed axis, the following occurs:

They are all moving at the same angular speed.

They are all moving at the same angular velocity.

When a rigid item rotates along a fixed axis, all of its angular speeds are the same.

All of the particles in the rotating object have the same angular speed.

They are all moving at the same angular velocity.

All of the particles in the rotating object have the same angular acceleration.

All of this stems from the following relationships:

v=wR

a = alpha*R

where w is the angular velocity and alpha is the angular acceleration.

tangential velocity and acceleration depend on the distance from the axis, whereas angular velocity and acceleration are the same for all the points on the rotating body.

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Diffraction is defined as the bending of waves through an aperture or around the edges of an obstruction into the vicinity of the barrier and The wavelength's length directly affects the angle of diffraction.

When electromagnetic radiation such as radio waves, light waves, or infrared (heat) waves travel through space, they leave behind distinctive patterns. The wave has a distinct size and shape. Wavelength is the separation between peaks (high points).

A wavelength's frequency plus energy (E) drop as it gets longer. You may conclude from these formulas that the length gets shorter as the frequency rises. The wavelength lengthens as the frequency drops.

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The moment of inertia of wheel a will be twice the moment of inertia of wheel b. This is because the moment of inertia is proportional to the mass of an object.

What is inertia?

The concept of inertia states that an object will maintain its current motion until a force changes its speed or direction. The phrase should be understood as a shortened form of Newton's first law of motion's description of "the principle of inertia." Newton's Latin is directly translated into the word "perseveres" in this sentence. In contemporary textbooks, other, softer words like "to continue" as well as "to remain" are frequently used. The modern application results from some modifications made by Euler, d'Alembert, as well as other Cartesians to Newton's original mechanics (as noted in the Principia).

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