A charge of 18 nC is uniformly distributed along a straight rod of length 3. 1 m that is bent into a circular arc with a radius of 1. 9 m. What is the magnitude of the electric field at the center of curvature of the arc?

The electric flux through the surface A1 which envelopes the three objects is 1.6 x 10⁵ Nm²/C.

According to Gauss's law, the electric flux through a closed surface is given by:

                       Φ = q/ε₀

q is the charge on a closed surface

ε₀ is the electrical permit of free space and has a value of 8.854 × 10⁻¹² square coulombs per newton per square meter.

q₁ =+4.0 µC

q₂ = –2.5 µC

q₃ = 0

Compared to,

Φ = q/ε0

Φ = (q₁ + q₂ + q₃)/ε₀

Φ = (4 -2.5 + 0) x 10⁻⁶/8.854 × 10⁻¹²

Φ = 1.6 x 10⁵ Nm²/C

Your question is incomplete but most probably your full question was:

Two objects, O1 and O2, have charges of +4.0 µC and –2.5 µC, respectively, and a third object 0, is electrically neutral. What is the electric flux through surface A1 that encloses all three objects?

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False. The equation ||au + v1|2 = 0 + ||u||2 + ||v||2 is the Parallelogram Law, which states that the magnitude of the sum of two vectors is equal to the sum of the magnitudes of the vectors.

The equation states that the length of the diagonal of a parallelogram, given by the sum of two vectors u and v, is equal to the sum of the lengths of u and v. This equation does not relate the scalar a to the vectors u and v.

The Parallelogram Law states that the magnitude of the sum of two vectors u and v, denoted by ||au + v||, is equal to the sum of the magnitudes of the individual vectors, ||u|| and ||v||. This law is often written as:

||au + v|| = ||u|| + ||v||

where a is a scalar, u and v are vectors, and ||.|| denotes the Euclidean norm, or the length of a vector.

The equation represents the fact that the length of the diagonal of a parallelogram, formed by vectors u and v, is equal to the sum of the lengths of u and v. In other words, the magnitude of the vector sum of two vectors is equal to the sum of the magnitudes of the individual vectors.

This law is useful in physics and engineering, where vectors are often used to represent physical quantities, such as forces, velocities, and accelerations, and the sum of these quantities must be calculated to understand their combined effect.

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Let the time, T is proportional to [tex]c^{x} g^{y}h^{z}[/tex]

=> T = k     [tex]c^{x} g^{y}h^{z}[/tex]

Taking dimensions on both the sides,

[[tex]M^{0} L^{0}T^{1}[/tex]] = [tex][L^{1}T^{-1}]^x[/tex] [tex][M^{-1} L^{3}T^{-2}]^y[/tex] [tex][M^{1} L^{2}T^{-1}]^z[/tex]

i.e.,

[[tex]M^{0} L^{0}T^{1}[/tex]] = [tex][M^{-y+z} L^{x+3y+2z}T^{-x-2y-z}][/tex]

Equating power of M,L,T on both sides, we get

-y + z= 0...….. (1)

x+3y+2z= 0...….(2)

-x-2y-z= 1........(3)

From (1) => y=z

Adding (2) and (3)=> y+z=1

or 2y=1 (from (1)) i.e., y= [tex]\frac{1}{2}[/tex]

Therefore, z=y= [tex]\frac{1}{2}[/tex]

Putting these values in (2) we get,

[tex]x+\frac{3}{2} +1 = 0[/tex] or [tex]x =- \frac{5}{2}[/tex]

Hence , [T]= [tex][g^{\frac{1}{2} }h^{\frac{1}{2} }c^{\frac{-5}{2} } ][/tex]

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In this case, the rock has dimensions of 1 x 1 x 1 meter, meaning it is a cube with sides of equal length. This means that the volume of the rock, which is a measure of the amount of space it takes up, is equal to 1 x 1 x 1 = 1 cubic meter.

In order to answer the question about which one would weigh the least, it is important to understand the concept of weight and how it is related to the dimensions of a rock. The weight of a rock is determined by the density of the material it is made of, as well as its size or volume. When we talk about the dimensions of a rock, we are referring to its length, width, and height.

If we know the density of the material the rock is made of, we can calculate its weight using the formula weight = density x volume. So, when it comes to which rock would weigh the least, it all depends on the density of the material the rock is made of. For example, if the rock is made of a low-density material like pumice, it would weigh less than if it was made of a high-density material like iron. The lower the density of the material, the less weight it will have for the same volume.

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Explanation:

Estimate the number of times the earth will rotate on its axis during a human's lifetime. The answer is 3x10^4.

There are several possible hypotheses for changing the pitch of sound:

Changing the frequency of the sound wave: The pitch of a sound wave is directly proportional to its frequency. Therefore, changing the frequency of the sound wave will change its pitch.

Changing the length of the vibrating object: The length of the vibrating object has an effect on the pitch of the sound wave it produces. If the length is shortened, the pitch of the sound will increase. Conversely, if the length is lengthened, the pitch of the sound will decrease.

Changing the tension in the vibrating object: The tension in the vibrating object affects the pitch of the sound wave it produces. Increasing the tension will raise the pitch of the sound, while decreasing the tension will lower the pitch.

Changing the density of the medium: The density of the medium through which the sound wave travels can also affect the pitch of the sound. If the medium is denser, the pitch of the sound will be higher, and if the medium is less dense, the pitch of the sound will be lower.

Modifying the sound wave through electronic means: The pitch of sound can be changed electronically by using devices such as equalizers, filters, and pitch shifters. These devices modify the frequency of the sound wave, which changes its pitch.

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Regarding friction and the brake system in the preceding sentence, Techs A and B are correct.

The heat produced by friction between brake drum linings and drums also reduces the mechanical energy required to move the brake drums and wheels. In conclusion, both experts are accurate because the brake-by-wire system is known to frequently use the electric motor as a type of generator, which helps to reduce the vehicle The following expression can be used to determine the car's kinetic energy (Ek). Ek = 1/2 m/v2 = 1/2 (1450 kg)/(36 m/s)2 = 9.4 105 J. where, m: mass, speed v. As soon as the car comes to a halt, this energy is transformed into heat (Q), which is then utilized to increase the temperature of the iron brake drums. Q = c × m × ΔT where c: particular heat, m: mass. T: Alteration in temperature

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Answer:

Elastic collision

Explanation:

Two billiard balls colliding is an example of an elastic collision. An elastic collision is a type of collision in which the total kinetic energy of the objects involved is conserved before and after the collision.

In other words, the objects bounce back after the collision with the same amount of energy that they had before the collision.

Answer: The collision is elastic.

Explanation: This is because they depend on the seperation between the centres of the billiard balls.

For the function g(x)=(√x−4x) / (x-11), its range is all real numbers less than or equal to 0, expressed as the interval [tex]$(-\infty, 0]$[/tex].

The function formula for f is [tex]$C = 2 \pi r$[/tex].

This implies that f(15) addresses the circumference (in cm) of a circle whose range is 15 cm.

On the off chance that f(a)=15, addresses the range (in cm) of a circle whose circumference is 15 cm.

The qualities that r can accept in this setting are genuine numbers more noteworthy than or equivalent to 0, communicated as the span [tex]$[0,\infty)$[/tex]. The values that f(r) can assume in this context are all real numbers greater than or equal to 0, expressed as the interval [tex]$[0,\infty)$[/tex].

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The question is -

Consider a circle whose size can shift. Allow r to address the sweep of the circle (in cm) and allow C to address the periphery of the circle (in cm). Assume the capability f decides the boundary of the circle in cm, C, given its sweep length in cm, r.

Compose a capability equation for f.

What does f ( 15 ) address in this unique circumstance? Select all that apply.

A circle with a range of 15 cm.

The periphery (in cm) of a circle whose span is 15 cm.

A circle with a periphery of 15 cm.

The range (in cm) of a circle whose outline is 15 cm.

If f ( a ) = 15, what does an address in this specific circumstance? Select all that apply.

The sweep (in cm) of a circle whose periphery is 15 cm.

A circle with a periphery of 15 cm. A circle with a range of 15 cm.

The periphery (in cm) of a circle whose span is 15 cm.

What values could r at any point expect in this unique situation? Express your response as a span.

What values can f ( r ) expect in this specific circumstance? Express your response as a stretch.

Suppose g(x)=√x−4x/x-11.

Find the range of g.

Answer: [tex]E = \frac{p^{2} }{2m}[/tex]

What is Kinetic Energy?

Kinetic energy is the energy of motion observable as the motion of a body or subatomic particle. All moving objects and particles have kinetic energy. A person walking, a baseball flying high, crumbs falling from a table, and charged particles in an electric field are all examples of how kinetic energy works.

The kinetic energy of the body mass m and momentum p is given by:

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

[tex]E = \frac{1}{2m} m^{2} v^{2}[/tex]

[tex]E = \frac{p^{2} }{2m}[/tex]

Hence, [tex]E = \frac{p^{2} }{2m}[/tex]

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A  ball of mass m and momentum p has kinetic energy equal to p2/m.

What is kinetic energy?

Kinetic energy is the energy of motion. It is the energy that an object possesses due to its motion. Kinetic energy is directly proportional to the mass of the object and to the square of its velocity. It is calculated by the equation K = 1/2mv2, where m is the mass of the object and v is its velocity. Kinetic energy is a form of energy which can be converted into other forms of energy. It can be used to power machines and to generate electricity.

The kinetic energy of a ball of mass m and momentum p is given by the equation KE = p2/2m, where KE is the kinetic energy and m is the mass of the ball. Thus, the kinetic energy of the ball is equal to p2/m.

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It would take 0.717 seconds to reach the ground if it is thrown straight down with the same speed.

What is speed?

Speed is the rate of motion or movement of an object. It is calculated by dividing the distance the object travels by the time it takes to travel that distance. It can be calculated in different ways, such as miles per hour, kilometers per hour, meters per second, and feet per second. Speed is essential for activities such as driving, running, and biking. Speed can also be used to measure the velocity of an object in a given direction. It is an important concept in physics, with speed being a vector quantity that is the magnitude of a velocity.

[tex]$$The known values are: $t=2.35 \mathrm{~s} ; y=0 \mathrm{~m} ; v_0=+8.00 \mathrm{~m} / \mathrm{s} ;$ and $a=-9.8 \mathrm{~m} / \mathrm{s}^2$Based on the given values, the formula that we shall use is$$y=y_0+v_0 t+\frac{1}{2} a t^2$$Substituting the values, we have$$[/tex]

[tex]$$\begin{aligned}y & =y_0+v_0 t+\frac{1}{2} a t^2 \\0 & =y_0+(8.00 \mathrm{~m} / \mathrm{s})(2.35 \mathrm{~s})+\frac{1}{2}\left(-9.80 \mathrm{~m} / \mathrm{s}^2\right)(2.35 \mathrm{~s})^2 \\y_0 & =8.26 \mathrm{~m} \quad \text { }\end{aligned}$$[/tex]

Therefore, the cliff is 8.26 meters high.

[tex]$\begin{aligned}y & =y_0+v_0 t+\frac{1}{2} a t^2 \\0 \mathrm{~m} & =8.26 \mathrm{~m}+(-8.00 \mathrm{~m} / \mathrm{s}) t+\frac{1}{2}\left(-9.80 \mathrm{~m} / \mathrm{s}^2\right) t^2 \\4.9 t^2+8 t-8.26 & =0\end{aligned}$$ \text {Using the quadratic formula to solve for the value of t we have}$$\begin{aligned}& t=\frac{-8 \pm \sqrt{(8)^2-4(4.9)(-8.26)}}{2(4.9)} \\& t=0.717 \mathrm{~s} \quad \text { }\end{aligned}$$[/tex]

Thus, It would take 0.717 seconds to reach the ground if it is thrown straight down with the same speed.

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Complete question:

(a) Calculate the height of a cliff if it takes 2.35 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.00 m/s.

(b) How long would it take to reach the ground if it is thrown straight down with the same speed?

The distance of a spacecraft from the Earth when it is launched toward the Sun depends on its trajectory. Generally, a spacecraft will travel from Earth to the Sun at an average distance of over 150 million kilometers.

Trajectory is the path of a moving object or particle as it travels through space. It is defined as the path taken by a projectile, such as a missile, rocket, bullet, or thrown object, as it moves under the action of given forces, such as gravity, air resistance, lift, and thrust. Trajectory is usually graphed as a curve in three-dimensional space. Trajectory may also refer to the path of a spacecraft or satellite as it orbits a planet, or the path of an airplane as it flies through the air. Trajectory is an important part of the study of mechanics and physics. It is used to calculate the speed, distance, and time needed to reach a destination. It is also used to determine the stability of a given system, such as a space shuttle or a rocket. Trajectory plays an important role in the field of aeronautics, as it is used to determine the optimal flight path for an aircraft.

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Let V = {(a1, a2) : a1, a2 ∈ R}. Define addition of elements of V coordinate wise, and for (a1, a2) in V and c ∈ R, define

c(a1, a2) =      [tex]\left \{ {{(0, 0) if c = 0 } \atop {ca1,a2cif c 6= 0.}} \right.[/tex]

Is V a vector space over R with these operations? Justify your answer.

Solution:

No-V a not a vector space over R with these operations because VS(8) fails: Let c, d ∈ R and (a1, a2) ∈ V . Then

(c + d) = (c + d)(a1, a2) = ( (c +d)a₁,a₂/c+d)

                                   ≠  ( (c +d)a₁,a₂/c + a₂/d)

                                     = (ca₁ + da₁, a₂/c + a₂/d)

                                      = c(a₁, a₂) + d (a₁, a₂)

The set v = {(a1, a2) : a1, a2 ∈ R} is not a vector space over R with the given operations because the set does not satisfy the axioms of a vector space. Specifically, the axiom of associativity for vector addition is violated.

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The dimensionless parameters values can be found by dividing the physical quantities with characteristic scales.

Dimensionless parameters are numbers that represent ratios of physical quantities and are independent of the units in which they are expressed. They play a crucial role in many areas of science and engineering, including fluid dynamics, heat transfer, and mechanics.

To find the dimensionless parameters values, one needs to divide the physical quantities by their characteristic scales, which are selected based on the specific problem being studied. The characteristic scales serve as reference points, allowing for a non-dimensional comparison of physical quantities.

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Answer:

the force acting on it will be zero

The option C) a satellite in geosynchronous orbit is an example of an object with a non-zero kinetic energy., is correct amongst the given options of the question.

The energy which is acquired by an object due to its motion is called kinetic energy. An object with nonzero kinetic energy is an object that is in motion, meaning its velocity is not equal to zero. The amount of kinetic energy an object has depends on its mass and velocity and is given by the equation KE = 0.5 × m × v², where v is its velocity and m is the mass of the object.

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The next time the maximum will be at x = 0 is at time t = (2π) / ω, and the correct answer is C: 2π / ω.

The next time we will see the maximum again at x = 0 is given by:

t = (2π) / ω

This is because the maximum will repeat after one full wavelength has been completed, and the wavelength of the wave is given by λ = 2π / k. The angular frequency, ω, is related to the wavelength and the velocity of the wave, v, by the relationship:

ω = 2πf = 2π(v / λ)

So, one complete cycle of the wave takes time (2π) / ω to complete. The maximum will occur at x = 0 after this amount of time has passed.

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Titration refers to the act of adding a known solution to an unknown solution in order to complete the reaction.A standard solution is a a solution of accurately known concentration.

A biological endpoint is a term used to describe a health impact (or the likelihood of that effect) brought on by exposure to a chemical. Examples of biological endpoints include disease symptoms or death.

What is an illustration of a common solution?

Primary standard answers include the following examples: The typical standard solution for processes involving silver nitrate is sodium chloride, or table salt. Zinc powder - Zinc powder is frequently used to standardise ethylene diaminetetra acetic acid, also known as EDTA, a stabilising agent used in many medicinal products.

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"The net number of electrons per second that pass through the cross-section of a wire is 3.125 × 10¹⁹."

Current is the flow of electrical charge carriers, known as electrons. Current flows from negative to positive points.

The SI measurement unit for electric current is the ampere (A). One coulomb of electric charges travelling through a single point in one second is referred to as one ampere of current. Appliances in the home and in business frequently use electricity.

There is a 5 Ampere current carrying wire.

The charge carried by each electron is 1.60 × 10⁻¹⁹ C.

The formula of current is,

Current = total charge/time

Total charge = current × time

Total charge in 1 sec = 5 × 1 = 5 C.

No. of electrons crossing per second

= (total charge crossing/sec)/(charge of each electron)

Substituting the values,

No. of electrons crossing per second = 5/(1.60 × 10⁻¹⁹)

On simplifying,

No. of electrons crossing per second = 3.125 × 10¹⁹.

Therefore, 3.125 × 10¹⁹ electrons cross the cable in total every second.

The given question is incomplete. The complete question is 'what is the net number of electrons per second that pass through the cross-section of a wire carrying 5 a of dc current?'

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Any measurement that includes both magnitude and direction is vector.

A vector is a quantity that has both magnitude and direction.

Force, acceleration, and displacement, for instance

A "vector" is a quantity that possesses both magnitude and direction.

A vector is a quantity with magnitude and direction in physics.It is sometimes shown as an arrow with a length proportional to the size of the quantity, pointing in the same general direction as the amount. A vector has magnitude and direction but not position. As long as a vector's length remains constant, it is therefore unaffected by displacement that occurs parallel to it.

Scalars are regular quantities that have a magnitude but no direction, in contrast to vectors. In contrast to speed (the amount of velocity), time, and mass, which are scalar values, displacement, velocity, and acceleration are vector quantities.

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a)1.037 x 10⁻⁵ N The direction of the force is toward the other sphere.

b)The force each sphere exerts on the other will then be zero.

The equation for the electrical force acting between two charged objects was ?

the equation for the calculation was given by Coulomb's law:

F = k * q₁ * q₂ / r²

where F is the force, k is the Coulomb constant (9 x 10⁹ N * m² / C²), q1 and q2 are the charges on the two objects, and r is the distance between their centers.

(a) Using this equation, the electric force exerted by one sphere on the other can be calculated as follows:

F = k * 12.0 nC * (-15.0 nC) / (0.275 m)²

= 9 x 10⁹N * m² / C² * 12.0 x 10⁻⁹C * -15.0 x 10⁺⁹ C / (0.275 m)²

= 1.037 x 10⁻⁵ N

The direction of the force is toward the other sphere.

(b) After the spheres are connected by a conducting wire, they will come to equilibrium, meaning that the total charge on the two spheres will be equal and opposite. The force each sphere exerts on the other will then be zero.

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Ans;[tex]-22.655 m/s^2[/tex]. The acceleration of a particle can be found by taking the derivative of velocity with respect to time.Since we're given the velocity equation in terms of position (s).

v = [tex]22 - 0.05s^2[/tex]

[tex]∫v ds = ∫(22 - 0.05s^2) ds = 22s - 0.05s^3 + C[/tex]

Where C is an arbitrary constant of integration. To determine C, we'll need to know the position of the particle at some time t0:

[tex]s = 22t - 0.05t^3 + C[/tex]

Now, to find the acceleration at s = 17m, we'll take the derivative of velocity with respect to time:

[tex]a = dv/dt = d/dt (22 - 0.05s^2) \\= -0.1(22t - 0.05t^3 + C)(22 - 0.05(22t - 0.05t^3 + C))[/tex]

Since we're looking for the acceleration at s = 17m, we can substitute s = 17 into the velocity equation to find the corresponding time t:[tex]17 = 22t - 0.05t^3 + Ct = (17 + 0.05t^3 - C)/22[/tex]

We can then substitute this expression for t into the equation for acceleration to find the acceleration at s = 17m:

[tex]a = -0.1(22t - 0.05t^3 + C)(22 - 0.05(22t - 0.05t^3 + C))\\= -0.1(22(17/22) - 0.05(17/22)^2)(22 - 0.05(22(17/22) - 0.05(17/22)^2))\\= -0.1(17)(22 - 0.05(17))\\= -0.1(17)(22 - 0.85)\\= -0.1(17)(13.15)\\= -22.655 m/s^2[/tex]

So the acceleration of the particle at s = 17 m is approximately [tex]-22.655 m/s^2.[/tex]

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A. The longest strip of paper is required for the planet Jupiter.

B. The shortest strip of paper is required for Mercury.

What are the solar system planets?

The planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, listed in order of their distance from the Sun. All planets, with the exception of Mercury and Venus, have at least one moon. Four planets—Jupiter through Neptune—have ring systems.

a.

The longest strip of paper is required for the planet JUPITER, because in our solar system Jupiter is by far the largest planet-more than twice massive as all the others planet combined.

b.

The shortest strip of paper is required for MERCURY, because mercury is very smaller  planet than other planets in our solar system. (Mercury is the closest to sun)

Hence , planet needs the longest paper strip possible and the world needs the tiniest paper strip possible.

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Complete question:

The given statement is true.

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The required new volume of the balloon when initial pressure, temperature and volume are specified is 5/6 L.

From ideal gas law, we know,

PV/T = constant

When we have to compare the pressures, volumes and temperatures of two different gasses, we can write the formula as,

P₁V₁/T₁ = P₂V₂/T₂ ----(1)

It is given that volume of ideal gas V₁ = 5 L ----(2)

Pressure of the ideal gas P₂ = 3 P₁

P₁/P₂ = 1/3 -----(3)

It is given that temperature is halved T₂ = 1/2 T₁

T₂/T₁ = 1/2 ----(4)

The new volume of the balloon V₂ = ?

Making V₂ as subject in (1) and substituting (2), (3) and (4), we have,

P₁V₁/T₁ = P₂V₂/T₂

V₂ = P₁V₁ T₂/P₂ T₁ = (P₁/P₂)(T₂/T₁)V₁ = 1/3 × 1/2 × 5 = 5/6 L

Thus, the new volume of the balloon is 5/6 L.

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The angle of inclination of the plane is 59.36 degrees. A package that weighs 200 lb and a force of 80 lb is just sufficient to keep the package from sliding, the angle of inclination of the plane is 59.36.

The power of 80 lb is the power of gravity following up on the bundle toward the path inverse to the heading of the incline. The power of gravity can be addressed by the situation:

F_gravity = m * g

where m is the mass of the bundle and g is the speed increase because of gravity (9.8 m/s^2). To find the mass of the bundle, we want to switch the load from pounds over completely to kilograms:

m = 200 lb * 0.45359237 kg/lb = 90.718474 kg

Then, we can involve the condition for power of gravity to track down the point of tendency of the plane:

F_gravity = m * g

80 lb = 90.718474 kg * 9.8 m/s^2

80 lb = 886.697 N

The ordinary power following up on the bundle is equivalent and inverse to the power of gravity. This ordinary power is given by:

F_normal = m * g * sin(θ)

where θ is the point of tendency of the plane. Setting F_normal equivalent to 80 lb, we can track down the point of tendency:

80 lb = 90.718474 kg * 9.8 m/s^2 * sin(θ)

80 lb/(90.718474 kg * 9.8 m/s^2) = sin(θ)

0.86603 = sin(θ)

θ = sin^-1(0.86603) = 59.36 degrees

In this way, the point of tendency of the plane is 59.36 degrees

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Δv / Δt. is average acceleration formula .

What is acceleration ?

Acceleration is a measure of how quickly an  object changes its velocity, or speed and direction. It is a vector quantity and is expressed in units such as meters per second squared (m/s^2), feet per second squared (ft/s^2), or g (where g = 9.8 m/s^2 is the acceleration due to gravity at the surface of the Earth). Acceleration is a result of a force acting on an object and can be calculated using Newton's second law of motion as follows: acceleration = force / mass. Positive acceleration means that the object is speeding up, while negative acceleration means that the object is slowing down. Acceleration is an important physical quantity that is used to describe the motion of objects and to calculate the velocity and position of an object over time. It plays a crucial role in many areas of science and engineering, including mechanics, rocket science, and vehicle design.

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The claim that nitrogen and oxygen make up the majority of the atmosphere is untrue.

Plants flourish thanks to nitrogen. But having excessive amounts of a wonderful thing can be harmful. Fast-growing plants outcompete and suffocate slower-growing beneficial plants when too much nitrogen gets into our bays. Oxygen is depleted by decaying plants, that destroys fishes.

Although producing ammonia, which is needed for fertiliser, explosives, as well as other materials, is the primary industrial use of nitrogen, there are many other uses for it. Nitrogen can be discovered and used in fewer places and for more things than you might have anticipated, from medications to food packaging.

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Answer:

the final velocities are V1 = 4 m/s and V2 = 0 m/s.

Explanation:

The velocity after a perfect inelastic collision can be calculated using the conservation of momentum equation. In this type of collision, the total momentum of the system is conserved, but the kinetic energy is not.

Let's call the velocity of m1 after the collision V1 and the velocity of m2 after the collision V2.

The conservation of momentum equation can be written as follows:

m1 * v1 + m2 * v2 = m1 * V1 + m2 * V2

Substituting the given values:

80 * 6 + 40 * 0 = 80 * V1 + 40 * V2

Simplifying:

480 = 80 * V1 + 40 * V2

Dividing both sides by 80 + 40:

480 / (80 + 40) = V1 = 4 m/s

And since m2 is at rest before and after the collision, its velocity is 0 m/s:

V2 = 0 m/s

So the final velocities are V1 = 4 m/s and V2 = 0 m/s.