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The angular momentum of a system is conserved when there is no external torque acting on the system.

This is known as the law of conservation of angular momentum. Mathematically, it can be expressed as:

L = Iω

where L is the angular momentum of the system, I is the moment of inertia, and ω is the angular velocity. If the net external torque acting on the system is zero, then the angular momentum of the system remains constant.

This law has many applications in physics, including in rotational motion, celestial mechanics, and quantum mechanics. For example, the conservation of angular momentum explains why a spinning ice skater speeds up when they bring their arms inwards, and why the Earth's rotation remains constant over long periods of time.

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Answer:  D, Edit each test document and write down the number of errors

Explanation: I did the test and got 5/5 gl! :D

Explanation:

speed = wavelength * frequency

          = 2 m * .0025/s = .005 m/s

The air pressure that will produce a force of the given magnitude is 135 times the pressure transmitted by the liquid. The value of P2, the pressure transmitted by the liquid, is not given in the problem, so we cannot determine the exact value of P1.

The planet's gravitational pull on the gases above its surface produces atmospheric pressure, which depends on the planet's mass, the radius of its surface, the quantity, makeup, and vertical distribution of the gases in the atmosphere.

The following equations describe the force that compressed air exerts on a tiny piston:

F1 = P1 * A1

The larger piston, which has a larger area A2, receives the power via the liquid. The larger piston's power is determined by:

F2 = P2 * A2

Pascal's rule states that the larger piston receives the same amount of pressure P1 as the smaller piston, so we have:

P1 = P2

Since the forces F1 and F2 are equal, we have:

F1 = F2

Therefore:

P1 * A1 = P2 * A2

P1 * (pi * (5.00 cm)²) = P2 * (pi * (15.0 cm)²)

Simplifying and solving for P1, we get:

P1 = (P2 * A2 * (5.00 cm)²)/ (A1 * (15.0 cm)²)

Substituting A1 = pi * (5.00 cm)² and A2 = pi * (15.0 cm)², we get:

P1 = (P2 * 15.0²) / 5.00²

P1 = 135 * P2.

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Using the formula given, the Schwarzschild radius are calculated below;

Problem 1:

Given: R = 2GM/c² and R = 1.48 × 10⁻²⁷M

Using c = 3x10^8 m/s and G = 6.67x10^-11 Nm^2/kg^2

G = gravitational constant, c = speed of light

Substituting the values, we get:

1.48 × 10⁻²⁷M = 2GM/c²

R = 2GM/c² = (2 x 6.67x10^-11 x M)/(9x10^16)

R = 1.48 x 10^-27 M

The radius is 1.48 * 10^-27M

Problem 2:

To calculate the Schwarzschild radius, we simply need to substitute the values into the equation

Given: M = 5.7 x 10^24 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x M)/(9x10^16)

R = 8.45 * 10^-3m

Problem 3:

Given: M = 1.9 x 10^30 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x M)/(9x10^16)

R = 2816.2 kilometers

Problem 4:

Given: M = 250 billion suns = 250 x 10^9 x 1.9 x 10^30 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x 2.5 x 10^11 x 1.9 x 10^30)/(9x10^16)

R = 7.04 x 10^14 kilometers

Problem 5:

Given: M = 60 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x 60)/(9x10^16)

R = 8.9 x 10^-26 meters

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The temperature of the air would be 6.3 °C.

The speed of sound in air depends on the temperature of the air according to the equation:

v = 331.5 m/s * sqrt(T/273.15 K)

where v is the speed of sound, T is the temperature of the air in Kelvin, and 273.15 K is the temperature at which the speed of sound is 331.5 m/s.

We know the frequency and wavelength of the sound wave, which are:

f = 668 Hz

λ = 0.5 m

The speed of sound can be calculated from the formula:

Substituting this value for v and the given value for the speed of sound at 0°C into the equation above and solving for T gives:

The temperature of the air is 279.4 K, which is equivalent to 6.3 °C, rounded to 1 decimal place.

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If Cv reduces by 2%, calculate the percentage gain in efficiency of the a diesel cycle with a bit rate of 16 and a cut-off ratio of 10% of a swept volume. Taking Cv = 0.717 & 1.4; the answer is 1.23%.

In cubic units, the volume answer is displayed. Volume is determined by multiplying the length, breadth, and height.

The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called a cubic meter (m3) serves as the SI volume measurement unit.

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Observations of a Milky Way have brought out that stars close to the galaxy's edge rotate rather quickly, which implies that there is more solar masses that we are unable to perceive.

The Sun-like star is known as a 1-solar mass star. At the rightmost to the bottom left in the stars, the primary structure region is where this type of star begins. Nearing the end its main-sequence existence, the star transforms into a red giant as it keeps burning its fuel.

As far as I'm aware, "massive stars" are defined as having masses equal or greater than to eight solar masses.

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the coefficient of kinetic friction is approximately 0.689, the mechanical advantage is 4/3, and the velocity ratio is 1.22.

the coefficient of kinetic friction, mechanical advantage, and velocity at the bottom of the ramp, we need to use the conservation of energy principle. At the top of the ramp, the block has potential energy given by mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the ramp. At the bottom of the ramp, the block has kinetic energy given by (1/2)m[tex]v^2[/tex], where v is its velocity. Assuming there is no energy loss due to friction, we can equate the potential energy at the top of the ramp to the kinetic energy at the bottom of the ramp.

1-Ep = Ek + Wf

mgh = 1/2 * m[tex]v^2[/tex]+ μk * mg * d

Solving for the coefficient of kinetic friction, we get:

μk = (mgh - 1/2 * m[tex]v^2[/tex]) / (mgd)

μk = (2gh - [tex]v^2[/tex]) / (2gd)

μk = (2 * 9.81 m/[tex]s^2[/tex] * 3 m - [tex]v^2[/tex]) / (2 * 4 m)

μk = 0.689

2-The mechanical advantage of the ramp is given by the ratio of the length of the ramp to the height from which the block falls:

MA = d / h = 4 m / 3 m = 4/3

3-VR = v / sqrt(2gh)

Ep = Ek + Wf

mgh = 1/2 * m[tex]v^2[/tex] + μk * mg * d

Solving for v, we get:

v = sqrt(2gh - 2μkgd) = 5.77 m/s

So the velocity ratio is:

VR = 5.77 m/s / sqrt(2 * 9.81 m/[tex]s^2[/tex] * 3 m) = 1.22

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Answer: The mass of the remaining ice in the jar is 1.3e+2 g.

Explanation: Let’s denote the mass of the remaining ice as m_ice. The heat gained by the ice is equal to the heat lost by the tea. The heat gained by the ice is given by m_ice * L_f, where L_f is the latent heat of fusion of water (334000 J/kg). The heat lost by the tea is given by m_tea * c_w * (T_initial - T_final), where m_tea is the mass of tea (0.187 kg), c_w is the specific heat capacity of water (4186 J/kg·°C), T_initial is the initial temperature of the tea (33.3°C), and T_final is the final temperature of the tea (31.8°C).

Equating the heat gained by the ice to the heat lost by the tea, we get:

m_ice * L_f = m_tea * c_w * (T_initial - T_final)

Substituting in the values, we get:

m_ice * 334000 = 0.187 * 4186 * (33.3 - 31.8)

Solving for m_ice, we get:

m_ice = 0.187 * 4186 * (33.3 - 31.8) / 334000

m_ice ≈ 0.130 kg

Converting to grams and rounding to two significant figures, we get:

m_ice ≈ 130 g

Hope this helps, and have a great day! =)

Answer:

A uniformly charge d insulating rod of length 14.0cm is bent into the shape of a semicircle as shown in Figure. The rod has a total charge of −7.50μC. Find (a) the magnitude and (b) the direction of the electric field at O, the center of the semicircle.

1859579

expand

Medium

Solution

verified

Verified by Toppr

Due to symmetry, E

y

=∫dE

y

=0, and E

x

=−∫dEsinθ=−k

e

∫

r

2

dqsinθ

where dq=λds=λrdθ; the component E

x

is negative because charge q=−750μC, causing the net electric field to be directed to the left.

E

x

=−

r

k

e

λ

0

∫

π

sinθdθ=−

r

k

e

λ

(−cosθ)∣

0

π

=−

r

2k

e

λ

where λ=

and r=

π

L

. Thus,

E

x

=−

L

2

2k

e

∣q∣π

=−

(0.140m)

2

2(8.99×10

9

N⋅m

2

/C

2

)(7.50×10

−6

C)π

E

x

=−2.16×10

7

N/C

(a) magnitude E=

2.16×10

7

N/C

The frequency ratio between fi = 256 Hz and f2 = 320 Hz is 4:5.Adding the interval of a fifth to f2 (320 Hz) results in fs (400 Hz). The frequency ratio falfi is 5:8.The frequency of fs is 400 Hz.

The interval of a fifth in music theory is the distance between two notes that are five notes apart in a diatonic scale. For example, the distance between C and G is a fifth.

Frequency and pitch are related in music because the pitch of a note is determined by its frequency. Lower frequencies result in lower pitches, whereas higher frequencies result in higher pitches.

The relationship between frequency and pitch is logarithmic, meaning that a doubling of frequency results in an increase of one octave (a doubling of pitch).

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Answer:

14.46°C

Explanation:

Given:

Find:

Solution:

1. Calculate the heat required to warm the ice from its initial temperature to its melting point: Heat to warm ice = Mass of ice * Specific heat of ice * (Melting point of ice - Initial temperature of ice) Heat to warm ice = 0.028 kg * 2090 J/(kg*°C) * (0°C - (-78°C)) = 4579.44 J

2. Calculate the heat required to melt the ice at its melting point: Heat to melt ice = Mass of ice * Latent heat of fusion of water Heat to melt ice = 0.028 kg * 3.33e5 J/kg = 9324 J

3. Calculate the heat lost by the water and calorimeter as they cool down to the final temperature: Heat lost by water and calorimeter = Mass of water * Specific heat of water * (Initial temperature of water and copper calorimeter - Final temperature) + Mass of copper calorimeter * Specific heat of copper * (Initial temperature of water and copper calorimeter - Final temperature)

4. The total heat gained by the ice must be equal to the total heat lost by the water and calorimeter: Heat to warm ice + Heat to melt ice + Mass of ice * Specific heat of water * (Final temperature - Melting point of ice) = Heat lost by water and calorimeter 4579.44 J + 9324 J + 0.028 kg * 4186 J/(kg°C) * (Final temperature - 0°C) = [0.562 kg * 4186 J/(kg°C) + 0.080 kg * 387 J/(kg*°C)] * (21°C - Final temperature)

Solving for the final temperature, we get: Final temperature ≈ 14.46°C

So, the final temperature of the system is approximately 14.46°C

The direction of the magnetic field with respect to your screen is d) to the left.

The upward force experienced by the proton indicates that the magnetic field is acting perpendicular to both the motion of the proton (due east) and the force it experiences. According to the right-hand rule for magnetic forces, if you point your thumb in the direction of the velocity of the charged particle (due east in this case) and your fingers in the direction of the force (vertically upward), then the direction your palm faces represents the direction of the magnetic field.

In this scenario, if you extend your left hand and point your thumb to the right (due east) and your fingers vertically upward, your palm will face to the left, indicating that the magnetic field is directed to the left. Therefore, option d) to the left is the correct answer. The magnetic field is perpendicular to the plane of the screen and points into the screen.

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to minimize the change in motion of Car A due to the collision, we should decrease the mass of Car A relative to the mass of Car B.

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that in a collision between two objects, the force that Car A exerts on Car B is equal and opposite to the force that Car B exerts on Car A.

To minimize the change in motion of Car A due to the collision, we need to minimize the force that Car B exerts on Car A. This can be achieved by decreasing the mass of Car A relative to the mass of Car B.

We can see evidence of this from the system model in the activity. When Car A and Car B have equal masses, they experience equal and opposite forces during the collision, and their velocities are both affected to the same degree. However, when Car A has less mass than Car B, Car B experiences a greater force during the collision, but Car A experiences a smaller force. As a result, Car A experiences less of a change in velocity than it would if the masses were equal.

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The wheel completes approximately 1.91 revolutions during its 2 seconds of acceleration.

The car's uniform acceleration, a = v/t, is provided. The distance it moves in the given amount of time, t, can be calculated using the kinematic equations for linear motion. By multiplying this distance by the tyre's diameter, we can calculate the number of revolutions. The formula f = vf/rtire yields the ultimate angular speed.

To resolve this issue, we can use the kinetic equation shown below:

θ = 1/2 α t²

To begin with, we can use the following method to determine the wheel's ultimate angular velocity:

ωf = ωi + αt

where i represents the starting angular speed. (which is zero in this case).

ωf = ωi + αt

ωf = 0 + 6 rad/s² × 2 s

ωf = 12 rad/s

Next, we can calculate the number of rotations made during the two seconds of acceleration using the formula for the angle the wheel made:

θ = 1/2 α t²

θ = 1/2 × 6 rad/s^2 × (2 s)²

θ = 12 rad

We can divide this by 2 (the number of radians in a rotation) to get the number of revolutions:

of revolutions = θ / 2π

of revolutions = 12 rad / 2π

of revolutions ≈ 1.91 revolutions.

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Answer:

To solve this problem, we need to use the formula: calories burned = (power expended in watts x time in seconds) / 4.184 First, we need to find the power expended in watts. We can use the formula: power = force x velocity Assuming the cyclist weighs 75 kg, the force required to maintain a speed of 7.3 m/s on level ground is: force = mass x acceleration force = 75 kg x 0 m/s^2 (since the cyclist is not accelerating) force = 0 N Therefore, the power expended by the cyclist is: power = force x velocity power = 0 N x 7.3 m/s power = 0 W Now we can plug in the values into the calories burned formula: calories burned = (power expended in watts x time in seconds) /

For a given length of the pendulum and acceleration of the cart, the maximum displacement angle can be determined using the above formulas.

What is Acceleration?

Acceleration can be positive or negative depending on the direction of the change in velocity. If an object is speeding up, the acceleration is positive, while if it is slowing down, the acceleration is negative.

(1) The maximum displacement angle observed in a pendulum experiment can be determined by the length of the pendulum and the acceleration due to gravity. According to the theory of simple harmonic motion, the period of a pendulum is directly proportional to the square root of its length and inversely proportional to the square root of the acceleration due to gravity.

The formula for the period of a pendulum is:

T = 2π * sqrt(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/[tex]s^{2}[/tex]).

For a given length of the pendulum, the maximum displacement angle occurs when the pendulum is at the highest point in its swing (i.e., when its velocity is momentarily zero). At this point, all of the energy of the pendulum is potential energy (i.e., gravitational potential energy), and the angle is known as the maximum displacement angle or the amplitude.

The maximum displacement angle (θ) can be calculated using the formula:

θ = [tex]sin^{^-1(a/g)}[/tex]

where a is the acceleration of the cart.

Therefore, for a given length of the pendulum and acceleration of the cart, the maximum displacement angle can be determined using the above formulas.

(2) If the rod is hung 8 cm from its endpoint instead of 28 cm, the length of the pendulum (L) would be 20 cm. Using the same formula as above, the period of the pendulum would be:

T = 2π * sqrt(0.2/9.8) = 0.898 seconds

The maximum displacement angle can be calculated using the same formula as above:

θ = sin^[tex]sin^{^-1(a/g)}[/tex]

where a is the acceleration of the cart.

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Answer:

Q = h . A . (T (t) - T env)

the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.

Explanation:

Q = rate of heat transfered out of the body

h = heat transfers coefficient

A = heat transfer to surface area

T = temperature of the objects surface

T env = temperature of the environment

T (t) = time dependent temperature

Because the cable was not connected properly is the most likely cause of the experiment's failure.

The coils of wire that make up an electromagnet have electricity running through them. When an electric current flows through the wire coils of an electromagnet, the coils act like a magnet because moving charges produce magnetic fields.

There are numerous factors to examine. Make sure an ordinary magnet can attract safety pins as a start. Then, verify that current is actually flowing through your wire. To do this, you need a strong enough battery, a wire with a low enough resistance, and a complete circuit connecting the two.

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Consequently, the light's wavelength that caused the multiply-slit interference pattern was around 546 nm.

Solution and Justification: Interference patterns are produced when waves of identical (or what very similar) frequencies collide. The amplitudes of these waves may then either be raised (via constructive interference) or lowered.

Fringes are the light lines that alternate with the black lines in the interference pattern. The following equation can be used to calculate the wavelength for the double-slit experiment: dissipates ≈ xd / L.

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The correct question is

Problem 4: Suppose a double-slit interference pattern has its third minimum at an angle of 0.256° with slits that are separated by 293 μm.

Randomized Variables

0 = 0.256°

d=293 μm

Calculate the wavelength of the light in nm.

Gra

Ded

Pote

Answer: The sound level produced by a chorus of 43 singers will be 97.66 dB.

Explanation:

Let I, the intensity of a sound produced by a singer, therefore, the intensity of the sound produced by 43 singers is equal to 43I. Therefore, the intensity is:

x = 10log(43I/Io)

x = 10log(43) + 10log(I/Io)

The second term in the equation is the sound intensity produced by a single singer. We calculate that the sound intensity of 36:

x = 10log(36) + 82.1  = 97.66 dB

The velocity of the ball 3 seconds after reaching the peak height is 30 m/s.

What is Velocity?

Velocity is a vector quantity that describes the speed and direction of motion of an object. It is defined as the rate of change of displacement of an object over time. In other words, velocity tells us how fast an object is moving and in what direction.

Assuming that air resistance is negligible, we can use the kinematic equations of motion to solve for the velocity of the ball 3 seconds after reaching the peak height.

Let's use the following variables:

a = acceleration = 10 m/[tex]s^{2}[/tex] (since the ball is continuing to accelerate downwards)

t = time = 3 seconds (since we want to find the velocity 3 seconds after reaching the peak)

v₀ = initial velocity = 0 m/s (since the ball has zero velocity at the peak)

v = final velocity (what we want to find)

Using the kinematic equation for velocity with constant acceleration:

v = v₀ + at

Substituting the given values:

v = 0 + 10 m/[tex]s^{2}[/tex] × 3 s

v = 30 m/s

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The zeros of the function f(x) are x = 3 and x = -12.

To find the zeros of a function, we need to solve the equation f(x) = 0. In this case, we have:

f(x) = -x^2 - 9x + 36

Setting f(x) = 0, we get:

-x^2 - 9x + 36 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula. Factoring, we get:

-(x - 3)(x + 12) = 0

Setting each factor equal to zero, we get:

x - 3 = 0 or x + 12 = 0

Solving for x, we get:

x = 3 or x = -12

These zeros represent the horizontal distances from the diving board where the vertical distance of the diver from the pool's surface is zero. In other words, they represent the points where the diver enters the water. The zero x = 3 represents the point where the diver enters the water at a distance of 3 feet from the diving board, while the zero x = -12 represents the point where the diver enters the water at a distance of 12 feet behind the diving board. However, the negative solution x = -12 is not meaningful in this context since it represents a point that is behind the diving board, so we discard it. Therefore, the zero x = 3 is the meaningful solution, which represents the point where the diver enters the water at a distance of 3 feet from the diving board.

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Answer:

x² = ((n-1)s²)/o²

x² = (39 - 1) * (3.15)² / (2.94)²

x² = 38 * 9.9225 / 8.6436

x² = 43.7598

Rounding to three decimal places, x² = 43.760. Therefore, the value of x² is 43.760 when o = 2.94, n = 39, and s = 3.15.

Explanation:

Math

The velocity of the ball 3 seconds after reaching the peak height is 30 m/s. And the right option is D. 30 m/s

Velocity is the rate of change of displacement.

To calculate the velocity the ball will travel after reaching the peak height, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the velocity is 30 m/s.

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When a transverse wave passes from a flexible spring into a heavier stiffer spring, the wave will have a greater speed in the stiffer spring due to the increased stiffness of the material. As a result, when the wave reaches the end of the stiffer spring, some of the energy from the wave will be reflected back towards the flexible spring.

The reflected wave in the flexible spring will be inverted, meaning that it will be flipped upside down. Additionally, the amplitude of the reflected wave will depend on the amount of energy that was transmitted into the stiffer spring.

If a large amount of energy was transmitted, then the reflected wave will have a higher amplitude. Conversely, if only a small amount of energy was transmitted, then the reflected wave will have a lower amplitude.

Overall, the reflected wave in the flexible spring will experience a change in both its orientation and amplitude due to the transmission and reflection of the initial wave in the stiffer spring.

When a transverse wave passes from a flexible spring into a heavier, stiffer spring where the wave has a greater speed, the reflected wave in the flexible spring will have a reduced amplitude and undergo a phase change of 180 degrees, resulting in an inverted waveform.

This occurs due to the impedance mismatch between the two springs, causing part of the wave energy to be reflected and part to be transmitted.

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To calculate the energy gained when changing the temperature of 100g of solid candle wax at 20°C to liquid at 68°C, we need to consider two processes:

(1) raising the temperature of the wax from 20°C to 68°C

(2) melting the wax at its melting point of 68°C.

The first process requires an energy input of Q1 = mcΔT, where m is the mass of the wax (100 g), c is the specific heat capacity of the wax (29 J/g°C), and ΔT is the change in temperature (68°C - 20°C = 48°C). Thus, Q1 = (100 g)(29 J/g°C)(48°C) = 139,200 J.

The second process requires an energy input of Q2 = mL, where L is the specific latent heat of fusion of the wax (220 J/g). Thus, Q2 = (100 g)(220 J/g) = 22,000 J.

Therefore, the total energy gained when changing the temperature of 100g of solid candle wax at 20°C to liquid at 68°C is Q = Q1 + Q2 = 139,200 J + 22,000 J = 161,200 J.

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The speed of the car just after the gravel is loaded is 2.8m/s.

An isolated system experiences a change in momentum to zero when the starting and final velocities are equal. The reactions between the particles are separated from the surroundings. Momentum is conserved, so we use the rule of conservation of momentum, which is expressed by the equation

   [tex]P_{f}[/tex]=[tex]P_{i}[/tex](1)

Railway is frictionless due to isolated mechanism. The thing travels at a momentum p-based speed while having mass. m

An object's bulk and velocity v are combined to form a vector.Equation of the form gives the velocity.

[tex]p=mv[/tex]

Using expression p into equation (1)

[tex]m_{f}v_{f}[/tex]=[tex]m_{i}v_{i}[/tex](2)

The final mass of a car is its original mass plus the mass of the gravel added. A car has an initial mass of.10000Kg  preliminary pace is

[tex]m_{f}[/tex]=10000Kg+4000Kg=14000Kg

initial speed 4m/s

the final speed should be found after solving the equation(2) for [tex]v_{f}[/tex]

[tex]v_{f}[/tex]=[tex]\frac{m_{i}v_{i} }{m_f} }[/tex]=[tex]\frac{10000Kg(4m/s)}{1400Kg}[/tex]=2.8m/s

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