The volume flow rate at which the water flows is 0.0188 m³/s
How to find what rate does water flow through the pipe?Since the horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter and If the pressure of the water in the larger pipe is 8.00 × 10⁴ Pa and the pressure in the smaller pipe is 6.00 × 10⁴ Pa, since we require the rate at which water flows through the pipe, we use Bernoulli's equation at constant height to find the speed of flow.
What is Bernoulli's equation?Bernoulli's equation governs flows through pipes. It is given by
P₁ + ρgh₁ + 1/2ρv₁² = P₂ + ρgh₂ + 1/2ρv₂² where
P₁ = pressure at point 1, h₁ = height at point 1, v₁ = speed at point 1, P₂ = pressure at point 2, h₂ = height at point 2, and v₂ = speed at point 2With h₁ = h₂, the Bernoulli's equation becomes
P₁ + 1/2ρv₁² = P₂ + 1/2ρv₂²
Using the volume flow rate equation
Q = A₁v₁ = A₂v₂ where
A₁ = cross- sectional area at point 1 = πd₁²/4 where d₁ = diameter at point 1v₁ = speed at point 1, A₂ = cross- sectional area at point 2 and d₂ = diameter at point 1 = πd₂²/4v₂ = speed at point 2So, A₁v₁ = A₂v₂
(πd₁²/4)v₁ = (πd₂²/4)v₂
d₁²v₁ = d₂²v₂
Making v₂ subject of the formula, we have
v₂ = d₁²v₁/d₂²
v₂ = (d₁/d₂)²v₁
Substituting v₂ into the Bernoulli equation, we have
P₁ + 1/2ρv₁² = P₂ + 1/2ρv₂²
P₁ + 1/2ρv₁² = P₂ + 1/2ρ(d₁/d₂)⁴v₁²
Making v₁ subject of the formula, we have
1/2ρv₁² - 1/2ρ(d₁/d₂)⁴v₁² = P₂ - P₁
1/2ρ[1 - (d₁/d₂)⁴]v₁² = P₂ - P₁
v₁² = √{2(P₂ - P₁)/ρ[1 - (d₁/d₂)⁴]}
Given that
P₁ = pressure in larger pipe = 8.00 × 10⁴ Pa d₁ = diameter of larger pipe = 10.0 cmP₂ = pressure in smaller pipe = 6.00 × 10⁴ Pa d₂ = diameter of smaller pipe = 5.00 cmρ = density of water = 1000 kg/m³Substituting the values of the variables into the equation, we have
v₁ = √{2(P₂ - P₁)/ρ[1 - (d₁/d₂)⁴]}
v₁ = √{2(6.00 × 10⁴ Pa - 8.00 × 10⁴ Pa)/1000 kg/m³[1 - (10.0 cm/5.0 cm)⁴]}
v₁ = √{2(- 2.00 × 10⁴ Pa)/1000 kg/m³[1 - 2⁴]}
v₁ = √{(- 4.00 × 10⁴ Pa)/1000 kg/m³[1 - 8]}
v₁ = √{(- 4.00 × 10⁴ Pa)/1000 kg/m³[-7]}
v₁ = √{(40.0 × 10³ Pa)/7 × 10³ kg/m³}
v₁ = √{(40.0/7 Pam³/kg}
v₁ = √{5.7143 Pam³/kg}
v₁ = 2.39 m/s
Since the volume flow rate Q = A₁v₁ = (πd₁²/4)v₁
Given that
d₁ = diameter of larger pipe = 10.0 cm = 0.1 m and v₁ = speed in larger pipe = 2.39 m/sSubstituting the values of the variables into the equation, we have
Q = (πd₁²/4)v₁
Q = π(0.1 m)²/4 × 2.39 m/s
Q = π × 0.01 m²/4 × 2.39 m/s
Q = π × 0.0239 m³/s/4
Q = 0.0751 m³/s ÷ 4
Q = 0.0188 m³/s
So, the water flows at a rate of 0.0188 m³/s
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An elevator lifts 2400 kg a distance of 55 m in 18.9 s. How much power does the
elevator demonstrate?
The work done by the elevator over the 55 meters is easily calculable: W = mgh = (2400)(9.8)(55) = 1293600Joules. The total time of the trip can be calculated from the velocity of the elevator: t = x/v=55/18.9 = 2.91. Thus the average power is given by: P =W/t=1293600/2.91=444536 Watts
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is 0.25. What is the net work done on the block over this distance?
The net work done on the block over the given distance is 39.4d (joules)
What is the net work done on the block over this distance?The net work done on the block over the given distance is calculated by applying the following equation as shown below:
W(net) = F(net) x d where;
F(net) is the net force on the blockd is the distance moved by the blockF(net) = F - μmgcosθ where;
μ is the coefficient of kinetic frictionm is the mass of the blockg is acceleration due to gravityθ is the angle of inclination of the planeF(net) = 50 N - (0.25 x 5 x 9.8 x cos30)
NF(net) = 50 N - 10.6 NF(net) = 39.4 N
The net work done on the block over the given distance is calculated as: W = 39.4 N x dwhere;
d is the distance moved by the block = length of the incline
W = 39.4d (joules)
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joanne drives her car at a speed of 20 m/s. when she applied her breaks, a frictional force of 2000 N brought her car to a complete stop in 10 seconds. what is the mass of her car
A) 1000 Kg
B) 1300 Kg
C) 20,000 Kg
D) 800 Kg
Answer:
A) 1000 kg
Explanation:
vf = vi + at
0 = 20 + (a)(10)
a = -2.0 m/s^2
F = ma
2000 = (m)(2)
m = 1000 kg
A 5-m long board is placed on top of two supports spaced 3 m apart. The board is placed so that one end is on the left support. The mass of the board is 30 kg. How far can a 100 kg person walk from the left end of the board without it rotating?
See below
3.15 m
When the Moments around thefulcrum , F , are equal, any increase in 'x' will cause a tip
I placed the weight of the board sections at the middle of the sections ...I think this is correct (? It has been a long time since I did simple Physics)
L moment = R moment
1.5 * 18 = 100 * x + 1 * 12
x = .15 m from the fulcrum or 3.15 m from the L end
(hope it is correct !)
A car of mass 1000 kg is travelling at a velocity of 10 ms-1. It
accelerates for 15 s, reaching a velocity of 24 ms].
Calculate:
a. The change in momentum of the car in the 15 s period.
b. The average force acting on the car as it accelerates.
(a) The change in monetum of the car of mass 1000 kg is 14000 kgm/s .(b) The average force on the car as it accelerates is 933.3 N.
(a) What is change in mometum?This can be defined as the product of the mass of a body and its change in velocity.
To calculate the change in momentum, we use the formula below.
Formula:
ΔM = m(v-u).......... Equation 1Where:
ΔM = Change in momentum of the carm = Mass of the carv = Final velocityu = Initial velocityFrom the question,
Given
m = 1000 kgv = 24 m/su = 10 m/sSubstitute these values into equation 1
ΔM = 1000(24-10)ΔM = 1000×14ΔM = 14000 kgm/s(b)Also, to calculate the average force of the car, we use the formula below.
Formula:
F = ΔM/t........ Equation 2Where:
F = Average forcet = TimeFrom the question,
Given:
t = 15 sSubstitute into equation 2
F = 14000/15F = 933.3 NHence, (a) The change in monetum of the car is 14000 kgm/s (b) The average force of the car is 933.3 N.
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5. Chad wants to investigate whether adding a solute to water affects its boiling point and freezing point. He set up an experiment and recorded the boiling and freezing point in degrees Celsius (°C), his results are in the data table.
EFFECT OF SOLUTE ON BOILING AND FREEZING POINTS
Test
A.Water
B.Water + 10 grams of salt
C.Water + 20 grams of salt
D.Water +30 grams of salt
E.Water + 40 grams of salt
Boiling Point (°C)
A.100.0
B.100.5
C.101.0
D.101.5
E.102.0
Freezing Point (°C)
A.0
B.-2
C.-4
D.-6
E.-8
Based on the data, which statement would be the best conclusion?
A. Adding salt to water decreases the boiling point.
B. Adding any solute to water increases the boiling point.
C. Adding salt to water increases the boiling point and decreases the freezing point.
D. Adding any solute to water increases the boiling point and decreases the freezing point.
Answer: C Adding salt to water increases the boiling point and decreases the freezing point
Explanation:
Stars that have a mass greater than the _____ or _____ limit will not become white dwarfs.
Stars that have a mass greater than the 1.4 solar masses or the Chandrasekhar limit will not become white dwarfs.
What is Chandrasekhar limit?The Chandrasekhar limit is the maximum mass that a stable white dwarf star can have. It was noted by E.C. Stoner and Willhelm Anderson in their works, and they gave it the name Subrahmanyan Chandrasekhar in honour of the Indian astronomer who made important, independent findings for enhancing calculation accuracy.
The limit was first disregarded by the scientific community since it would have supported the existence of black holes (technically unrealistic at this turn-off time). The white dwarf stars resist the gravitational collapse of the black hole due to the pressure of electron degeneration.
The Chandrasekhar limit is established at a mass where the gravitational field's self-attraction cannot be balanced by the pressure from electron decay. The limit that has been established these days is 1.39 solar mass.
Hence, Stars that have a mass greater than the 1.39 solar masses or the Chandrasekhar limit will not become white dwarfs.
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How massive would a black hole have to be in order for it to evaporate due to Hawking radiation in
only one year? How big is that mass compared to
some object with which you are familiar? (On the
surface of the Earth, 1 kg ≈ 2.2 lb.)
It takes a black hole an astonishingly long time to convert all of its mass into energy via Hawking radiation. A googol, or 10100 years, would be required for a supermassive black hole to completely vanish.
How are black holes able to dissipate energy?A black hole radiates, losing mass as it does so and beginning to release more radiation, which accelerates the evaporation of the black hole. It eventually contracts to a size close to the Planck mass, where its Schwarzschild radius and DeBroglie wavelength coincide.
How long does it take a black hole to be destroyed by Hawking radiation?Sagittarius A* 1087 years for Ton 618, the biggest black hole ever detected, and Sagittarius A* 1087 years for Sagittarius A* to evaporate from Hawking radiation It would take more than 10100 years for it to evaporate away (weighing a staggering 66 billion solar masses).
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An object is rotating about a fixed axis such that its rotational inertia about the fixed axis is 10 kg - m². The object has an angular velocity was a function of time t given by w(t) = at³ - w₂.
where a=2.0 and up- -4.0
The change in angular velocity for the object from t=1s to t=3s is most nearly
The change in angular velocity for the object from t=1s to t=3s is most nearly 24 rad/s².
What is the change in the angular velocity of the object?
The change in the angular velocity of the object is the angular acceleration of the object and the magnitude is calculated as follows;
α = Δω/Δt
where;
Δω is the change in the angular velocityΔt is change in time of motionα = at³ - w₂
α = d(at³ - w₂)/dt
α = 3at²
The given parameters;
a = 2t = 3 s - 1 s = 2 sα = 3(2)(2)²
α = 24 rad/s²
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What is the displacement of the iguana between 0s and 6s
Answer: Displacement between 0s and 6s = 2
Explanation:0+2=2
Write down in words the formula connecting acceleration, initial speed, final speed and time.
Formula connecting acceleration, initial speed, final speed and time.
v=u+at,
v2=u2+2as,
s=ut+1/2at2.
How many different acceleration formulas are there?For motion on a straight line with constant acceleration, there are five common formulas. The formulas are provided in terms of the initial velocity (u), final velocity (v), displacement (x), acceleration (a), and time (t).
What is the relationship between distance and acceleration?The following equation can be used to determine distance from acceleration: D = v*t + 1/2*a*t2. where an is the acceleration, t is the passage of time, and v is the velocity.
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How long has tension been building in the cascadia fault zone
Answer:
The Cascadia Subduction Zone has not produced an earthquake since 1700 and is building up pressure where the Juan de Fuca Plate is subsiding underneath the North American plate.
Explanation:
At depths shallower than 30 km (19 mi) or so, the Cascadia zone is locked by friction while stress slowly builds up as the subduction forces act, until the fault's frictional strength is exceeded and the rocks slip past each other along the fault in a megathrust earthquake. Below 30 km (19 mi) the plate interface exhibits episodic tremor and slip .
A 350 watt speaker projects sound in a spherical wave. Find the intensity of the sound at a distance of 3.0 m and 9.0 m from the speaker.
The intensity of the sound at a disatance of 3.0 m and 9.0 m from the 350 watt speaker is 3.09 db and 0.34 db respectively.
What is intensity of sound?Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
To calculate the intensity of sound, we use the formula below.
Formula:
I = P/4πr²............................................. Equation 1Where:
I = Intensity of sound r = Distance from then speakerP = PowerGiven
P = 350 WAt a distance of 3m,
I = 350/(4×3.14×3²)I = 3.09 dbAt a distance of 9.0 m,
P = 350(4×3.14×9²)P = 0.34 dbHence, the intensity of the sound at a distance of 3.0 m and 9.0 m is 3.09 db and 0.34 db respectively.
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A high diver reaches the highest point in his jump with his center of gravity 10 m above the water. Assuming that all his gravitational potential energy becomes kinetic energy during the dive, calculate his speed just before he enters the water.
According to the given statement = 14ms⁻¹ his speed just before he enters the water.
What is potential energy, exactly?Potentially energy is a type of energy that depends on how various system elements interact with one another. A spring's potential energy rises when it is crushed or stretched. A steel ball has more potential energy when it is hoisted above the soil than how it was brought closer to it.
Briefing:Since the decrease in kinetic energy equals the variation in g.p.e. out from peak of the dive to the time just before kate enters the water, we may say that.
mgh= 1/2mv²
This means that just before she enters the water, her speed is
v= √2gh
v= √2 *9.81 *10
v= √196
v= 14ms⁻¹.
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Katie pulls her wagon by the handle. She exerts a force of 60 N 30 degrees above the
horizontal. The force of friction from the sidewalk on the wagon is 30 N. The wagon has
a mass of 20 kg. What is the acceleration of the wagon?
a. 1.1 m/s²
b. 21.96 m/s²
c. 0 m/s²
d. 1.5m/s²
Answer:
a. 1.1 m/s^2
Explanation:
Force of Application = (60)(cos30)
= 51.96 N
Force of Friction = 30 N
Total Force = 51.96 - 30
= 21.56 N
F = ma
21.56 = 20a
a = 1.09
a = 1.1 m/s^2
which ways more a quarter pound hamburger on jupiter or a 12 ounce steak on venus
Answer: 12 ounce steak on venus
Explanation: venus = closer to the sun. The sun = more potential gravity, which would make it heavier than a quarter pound hamburger on jupiter.
Velocity is different from speed because it has both size and ?
Velocity is different from speed because it has both size and direction.
What is velocity and speed?Velocity is a vector quantity that denotes the rate of change of position with respect to time, combining speed with a directional component.
On the other hand, speed is the magnitude of the velocity; the rate distance is traversed in a given time.
Speed is a scalar quantity meaning that is does not have direction while velocity is a vector quantity meaning that it posseses both magnitude (size) and direction.
Therefore, speed and velocity differs in the sense that the latter is a vector quantity.
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help please
Constellations move along a celestial sphere. Which statement does not accurately represent how a person views constellations based on the celestial sphere?
A) Constellations remain in the same place in the night sky throughout the year.
B) A person's view of a constellation in the Southern Hemisphere may not look exactly the same to someone in the Northern Hemisphere who is viewing the same constellation.
C) Constellations appear to move positions each night.
D) A person in the Southern Hemisphere would see different constellations than someone in the Northern Hemisphere.
Answer: It should be B
Explanation:
The reason being that stars are constantly moving, and you may seem the see the same stars but in a different location or not see them at all. Hope this was helpful. :)
Answer:
the answer is B
Explanation:
PLEASE, PLEASE, PLEASEE!!!
EXPLAIN IN DETAIL HOW THE TWO RELATES TO THE CELL THEORY
The following lists components of the nature of science. Explain how at least two of these are related to the cell theory:
Scientific knowledge is durable yet subject to change
Science is a social activity
The foundation of biology is modern cell theory, which is a commonly recognized explanation of the relationship between cells and living things.
When scientific knowledge lasts a long time, what does that mean?Because it has been independently verified by numerous scientists working together, scientific knowledge is regarded as lasting. Independent researchers utilize the scientific method to generate factual data and knowledge that adds to the body of knowledge in their subject.
What does social science know scientifically?A generalized collection of laws and hypotheses developed using the scientific method and intended to explain a phenomenon or behavior of interest is referred to as scientific knowledge. Theories are methodical explanations of the underlying phenomenon or behavior, whereas laws are recognized patterns of occurrences or behaviors.
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Question 7: Which takes up more volume: a ton of platinum, or a ton
of graphene aerogel?
a) A ton of platinum
b) b) A ton of graphene aerogel
c) They have the same mass, so they'd take up the same volume
Answer:
b)
Explanation:
A graphene aerogel is seven times lighter than air, with the same mass, its volume is greater
The volume is inversely proportional to density. Graphene aerogel has the least density of platinum. Hence, a ton of graphene aerogel takes up more volume than a ton of platinum.
What is density?Density (ρ) is the ratio of mass and volume. Volume represents the space occupied by a substance in three-dimension. Mass is an intrinsic property that represents the quantity of a substance.
ρ = m / V. ρ represents density and its SI unit of density is kg/m³. m represents mass and its SI unit is kg. V represents volume and its SI unit is m³.
Density is inversely proportional to volume. Density increases with a decrease in volume. Density decreases with an increase in volume. Density is directly proportional to mass.
The density of graphene aerogel ranges from 0.11-0.19 g/cm³. The density of platinum is 21.45 g/cm³. Hence, volume is greater for lesser density and vice-versa.
The mass of a ton of platinum is lesser compared to the mass of a ton of graphene aerogel. Density increases with an increase in mass and density decreases with a decrease in mass.
Hence, a ton of graphene aerogel can take up a larger volume than a ton of platinum. Thus, option B is correct.
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Please help me with this looking to go over my work
0.99 joule must the work done by friction to stop the box.
m=87g
k=82N/m
x=11cm=0.11m
spring force=kx
spring force=82N/m×0.11m
spring force=9.02 N
work done= Fx
work done=9.02 N×=0.11m
work done=0.99 joule
When an item is moved across a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work done in physics. By multiplying the length of the path by the component of the force operating along the path, work may be calculated if the force is constant. The work W is equal to the force f times the distance h, or W = mgh, to mathematically describe this idea. The work is W = mas if the force is applied at an angle of to the displacement.
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A climber of mass 100 kg (including the equipment she is carrying) ascends from sea level to the top of a mountain 5500 m high. Calculate the change in her gravitational potential energy
Answer: Change in gravitational potential energy = 5500 KJ
Explanation:
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A spaceship is coasting in orbit around a planet.
A second spaceship sits motionless on the launch
pad. The two ships define frames that are accelerated with respect to each other, yet both might be
regarded as inertial frames. Explain.
As per Drag theory , one possible explanation is v=0 that means velocity of earth relative to ether is zero.
For t1=t2, as per equation
[tex]t1=2l/c [ 1 + v^{2} /c^{2} ]\\t2= 2l/c [ 1 + v^{2} /2c^{2} ][/tex]
Then there is no relative velocity between earth and ether. In other words the ether is dragged with the motion of earth with the same velocity as the earth. However if this explanation is acceptable for there should be no aberration of light. Even if the ether is considered to be dragged partially , the absence of fringes shift and value of aberration cannot be explained simultaneously.
It has been verified by experiments that newton's frame of reference taking stars to be fixed , is an inertial one , while the other one i.e. reference frame fixed to earth is not an inertial frame. Since the earth rotates about its axis as well as round the sun.
Even Galilean Transformation equations explain the structure of inertial frames.
For example - Length of a rod is invariant under Galilean transformations.
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The tune-up specifications of a car call for the spark plugs to be tightened to a torque of 50 N⋅m. You plan to tighten the plugs by pulling on the end of a 30-cm-long wrench. Because of the cramped space under the hood, you'll need to pull at an angle of 105 ∘ with respect to the wrench shaft.
With what force must you pull?
The force needed to pull the wrench of 30 cm long is 643.95 N.
What is force?Force can be defined as the product of mass and aceleration.
To calculate the force that must be pull, we use the formula below.
Formula:
F = T/Lcos∅.......... Equation 1Where:
F = ForceT = TorqueL = Length of the wrench∅ = AngleFrom the question,
Given:
T = 50 N.mL = 30 cm = 0.3 m∅ = 105°Substitute these values into equation 1
F = 50/(0.3×cos105°)F = -643.95 N.Note: The negative sign tells the direction of the force and can be ignored (Pull)
Hence, the force need to pull is 643.95 N.
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Question on dimension
Explanation:
1. Dimension formula of luminous flux matches with which of the following?
Force
Rotational impulse
Momentum
Power
Answer: d) Power
Monkey Joe and Money Jane are pulling a boat through water. Each exerts a force of 600N directed at a 30 angle relative to the forward motion of the boat. If the boat moves with constant velocity, find the resistive force Fr, exerted in the boat by the water.
Answer:
1039 N
Explanation:
The 'x' components of their pulling forces = the force of friction:
2 x 600 cos 30 = 1039 N
Being moody, depressed, or having guilty feelings would be associated with which dimension of the PEN model?
The PEN model is a biological theory of nature developed by influential psychologist Hans Eysenck (1916-1997). The model pivot on three broad personality factors: psychoticism, extraversion, and neuroticism (PEN).
which dimension of the PEN model?In the PEN model, character comprises three major dimensions: extraversion, neuroticism, and psychoticism. These pictorial dimensions have Former developing the PEN model, Eysenck chase to quantify personality based on two sizes: extraversion-introversion. Before evolving the PEN model, Eysenck sought to measure nature in two sizes: extraversion-introversion and neuroticism-emotional. Eysenck's PEN theory has suggested an influential classification for the biological basis of personality dimensions: Psychoticism
So we can conclude that The PEN model contains three personality dimensions based on psychophysiology: Psychoticism, Extraversion, and Neuroticism.
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Forces
A cyclist cannot reach terminal velocity going downhill.
Answer:
Air resistance
PLEASE GIVE BRAINLIEST THANK YOU!!!
3. An airplane accelerates from rest down a runway at 3.20 m/s² for 42.5 s until it finally lifts
off the ground. Determine how far the plane traveled before takeoff.
a. 1721.34 m
b.
968.26 m
c.
2205.47 m
d. 1115,14 m
e.
2890 m
e option is the correct answer - 2890m
Initial velocity(u) = 0[tex]m/s[/tex]
Accelaration(a) = 3.20[tex]m/s^{2}[/tex]
time(t) = 42.5s
The equation S = u t + 1 2 a t 2 is newton's second equation of motion. Here, 'S' represents the displacement of a body, 'u' represents the initial velocity of a body, 't' represents the time taken by the body to cover the displacement in t time(seconds), and 'a' represents the constant acceleration of a body throughout the movement.
[tex]s = ut + 1/2at^{2}[/tex]
[tex]s = 0(t) + 1/2(3.20)(42.5^{2}) \\s = 1/2(5780)\\s = 2890m[/tex]
The value of s is 2890m.
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The force on a particle of mass 2.0 kg varies with position according to F(x) =−3.0x^2 (x in meters, F(x) in newtons). The particle’s velocity at =2.0m is 5.0 m/s. Calculate the mechanical energy of the particle using (a) the origin as the reference point and (b) =4.0m as the reference point. (c) Find the particle’s velocity at =1.0m. Do this part of the problem for each reference point.
(a) The mechanical energy of the particle at the origin is 0 J.
(b) The mechanical energy of the particle at 4 m is 625 J.
(c) The particle’s velocity at 1.0m is 17.32 m/s.
What is the mechanical energy of the particle?
The mechanical energy of the particle is the total energy of the particle due to its motion and position above the ground such as kinetic energy and potential energy.
E = P.E + K.E
E = mgh + ¹/₂mv²
where;
h is the height of the particle above the groundg is acceleration due to gravitym is the mass of the particlev is the speed of the particleat the origin, the displacement of the particle is zero and the velocity of the particle is zero.
E = (2 x 9.8 x 0) + ¹/₂(2)(0)²
E = 0 J
The acceleration of the particle is calculated as follows;
F = ma
a = F/m
where;
F is force = 300 Nm is mass of the particle = 2 kga = (300)/2
a = 150 m/s²
The velocity of the particle at distance 4 m is calculated as follows;
v² = u² + 2as
where;
v is the velocity at 4 mu is the velocity at 2 ma is the accelerations is the distance travelled from 2 m to 4 m = 2 mv² = (5)² + 2(150)(2)
v² = 625
v = √625
v = 25 m/s
E = ¹/₂mv²
E = ¹/₂(2)(25²)
E = 625 J
The particle's velocity at 1 m is calculated as follows;
Apply the principle of conservation of energy;
Work done by force = kinetic energy of the particle
Fd = ¹/₂mv²
where;
d is the displacement of the particlev is the velocity300 x 1 = ¹/₂(2)v²
300 = v²
v = √300
v = 17.32 m/s
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