Calculate the kinetic energy of an 84-kg scooter moving at 18 m/s .

We want to study the vertical motion of a stone, to do it, we will find the motion equations of the stone.

We will find that the average velocity in the given interval is 224 ft/s.

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First, we need to find the acceleration of the stone.

The only force acting on the stone (ignoring air resistance) will be the gravitational force, then the acceleration of the stone will be equal to the gravitational acceleration.

[tex]a(t) = -32ft/s^2[/tex]

To get the velocity equation we need to integrate over time, such that the constant of integration will be equal to the initial velocity, which we know is equal to 400ft/s

Then we get:

[tex]v(t) = (-32 ft/s^2)*t + 400ft/s[/tex]

To get the position equation we integrate again, this time the constant of integration will be the initial position, 10 ft.

[tex]p(t) = (-16ft/s^2)*t^2 + (400ft/s)*t + 10ft[/tex]

Now the average velocity is defined as the quotient between the displacement and the time it took to do that displacement, then the average velocity will be:

[tex]av = \frac{p(8s) - p(3s)}{8s - 3s} \\\\av = \frac{( (-16ft/s^2)*(8s)^2 + (400ft/s)*8s + 10ft) - ((-16ft/s^2)*(3s)^2 + (400ft/s)*3s + 10ft)}{5s} = 224 ft/s[/tex]

Thus the average velocity in that interval is 224 ft/s

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Final answer:

To find the average velocity of a stone launched from a slingshot between 3 and 8 seconds, calculate the positions at both times using the given formula and then divide the change in position by the time interval. The average velocity is found to be 224 ft/s.

Explanation:

The question involves calculating the average velocity of a stone launched from a slingshot over a given time interval. Using the formula for the position of an object moving under constant acceleration, s(t) = s0 + v0t - 1/2gt², where s0 is the initial position, v0 is the initial velocity, g is the acceleration due to gravity (32 ft/s²), and t is the time in seconds, we can find the position of the stone at 3 seconds and 8 seconds. Substituting the given values into the formula, we get:

Position at 3 seconds: s(3) = 10 + 400(3) - 1/2(32)(3²) = 10 + 1200 - 144 = 1066 ft.

Position at 8 seconds: s(8) = 10 + 400(8) - 1/2(32)(8²) = 10 + 3200 - 1024 = 2186 ft.

The average velocity over the interval [3, 8] is calculated as the change in position divided by the change in time, which is (2186 - 1066)/(8 - 3) = 1120/5 = 224 ft/s.

Final answer:

To find the final speed with given acceleration and distance, use the equation v^2 = u^2 + 2as. If the initial speed is zero, it simplifies to v^2 = 2as. Then, solve for v by taking the square root.

Explanation:

How to Find Speed with Acceleration and Distance:

To determine the final speed of an object when you are given its acceleration and the distance it has traveled, you can use one of the equations of motion that relate these variables. However, the exact method will depend on whether the initial speed is zero or a known value different from zero.

If Initial Speed is Zero:

You can use the equation v^2 = u^2 + 2as, where v is the final speed, u is the initial speed (zero in this case), a is the acceleration, and s is the distance traveled. Since u is zero, the equation simplifies to v^2 = 2as. You then solve for v by taking the square root of the product of the acceleration and twice the distance.

If Initial Speed is Known:

If you have a known initial speed, use the full equation v^2 = u^2 + 2as without simplifying it. Input the known values and solve for v as previously described.

Remember to work with S.I. units (metres per second squared for acceleration and metres for distance) for consistency and to get the speed in metres per second.

The maximum height reached by the ball is 14.45 meter.

Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time. In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.

Given parameters:

Initial velocity of the ball in upward direction= 17.0 m/s.

Final speed of the ball at maximum height = 0.

Mass of the ball = 0.30 kg.

We know that acceleration due to gravity: g = 10.0 m/s²

From principle of energy conservation:

Initial kinetic energy = final potential energy

1/2 × mv² = mgH

H = v²/2g

= 17.0²/(2×10)

= 14.45 meter.

Hence, the maximum height reached by the ball is 14.45 meter.

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Answer:

[tex]v = 68.7 m/s[/tex]

angle made with the vertical

[tex]\theta = 21.3 degree[/tex]

Explanation:

Velocity of rain with respect to the car with vertical direction makes 38 degree angle

so let say rain velocity is

[tex]v_r = v_x\hat i + v_y \hat j[/tex]

[tex]v_{rc} = v_r - v_c[/tex]

[tex]v_{rc} = (v_x + 25)\hat i + v_y[/tex]

now we have

[tex]tan38 = \frac{v_x + 25}{v_y}[/tex]

while return to home

[tex]v_{rc} = (v_x - 25)\hat i + v_y[/tex]

now the angle with vertical is zero

so we have

[tex]v_x = 25[/tex]

now we have

[tex]tan38 = \frac{50}{v_y}[/tex]

[tex]v_y = 64 m/s[/tex]

so we have

[tex]v_r = 25 \hat i + 64 \hat j[/tex]

now magnitude of the speed is

[tex]v = \sqrt{25^2 + 64^2}[/tex]

[tex]v = 68.7 m/s[/tex]

angle made with the vertical

[tex]\theta = tan^{-1}\frac{25}{64}[/tex]

[tex]\theta = 21.3 degree[/tex]

In Freud’s conception, consciousness can be broken up into three distinct bands: the conscious level, the preconscious level, and the unconscious level.  The conscious level, where we process our perceptions and thoughts, is like the part of the iceberg that is above the water.  We are aware of our conscious level, just as we are aware of the top layer of an iceberg. The next level of consciousness, the preconscious level, is just below the surface of our consciousness and can be accessed when it is needed to recall memories and facts. This is similar to the level of the iceberg directly under the water: you can perceive it if you look carefully and are close enough. The last level of consciousness is the unconscious level, which a person has no active knowledge of.  Like the vast underwater portion of an iceberg, the unconscious level is unseen but can be very influential.  The unconscious mind has many urges, instincts, and desires, which it is constantly demanding be met. The unconscious mind can influence the behavior of an individual, sometimes in the disastrous ways an iceberg can threaten a ship.

Freud compared the mind to an iceberg to represent the conscious and unconscious aspects of our mind. The small, visible part of an iceberg represents the small portion of our mind that is conscious. The vast, hidden part represents our larger unconscious mind. Unconscious desires or urges may inadvertently reveal themselves, such as in a Freudian slip.

Sigmund Freud's conception of consciousness compared to an iceberg represents a recognition that much of our mental process occurs outside our conscious awareness. Only about one-tenth of our mind - comparable to the visible tip of the iceberg - is conscious, while the rest is hidden in the unconscious. The unconscious mind contains mental activity that we are unaware of and cannot readily access. It harbors our unacceptable urges and desires that are repressed or suppressed from our conscious thought. These contents could sometimes unintentionally reveal themselves, as in the case of a Freudian slip.

A Freudian slip is an error in speech or action that is interpreted as occurring due to the interference of an unconscious subdued wish, conflict, or train of thought. This concept is part of Freud's psychoanalytic theory and is used as evidence of the unconscious mind. For example, making unintended slips, like substituting another word for the one we meant to say, are seen as unconscious desires or urges accidentally slipping out.

Freud also proposed three components of our personality: the id, ego, and superego. The id and superego reside in the unconscious, while the ego mediates between them and our conscious understanding. The complex interaction between these components influences our behavior and personality.

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Answer:6x9.8m/sx2=117.6

Explanation:

An endothermic reaction is the one that makes use of chemical energy.

An endothermic reaction is defined as a chemical reaction which is a thermodynamic process  accompanied by an increase in enthalpy  of the system.In this process, a system absorbs energy from the surroundings  which is mainly thermal energy.

Thus an endothermic reaction leads to an increase in the temperature of the system with a decrease in the temperature of the surroundings.Endothermic reactions usually involve the formation of bonds which requires input of energy.In endothermic reactions, entropy of the surrounding decreases.

Many endothermic processes involve the physical changes rather the chemical changes.In an endothermic reaction ,the potential energy of products is greater than that of reactants.

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Final answer:

Bernoulli's principle describes the relationship between pressure and velocity in fluids and is applicable in various fluid flow situations.

Explanation:

Bernoulli's principle describes the property of a fluid where there is an inverse relationship between the pressure and velocity of the fluid. According to Bernoulli's equation, for an incompressible, frictionless fluid, the sum of pressure, kinetic energy, and potential energy per unit volume is constant. This principle is applicable in various situations involving fluid flow, such as in the analysis of fluid devices and systems.

Bernoulli's principle serves as a fundamental concept in fluid dynamics, providing insights into the interplay between pressure and velocity within a flowing fluid. Its application extends to understanding phenomena like lift in aviation, the operation of carburetors, and the behavior of blood flow in arteries. By recognizing the conservation of energy in fluid motion, Bernoulli's principle contributes to the analysis and design of fluid-based systems across diverse fields.

A skater moves with an initial velocity of 2 m/s, and a final velocity of 7 m/s by which he covers 12 meters, so the acceleration will be 1.875 m/s².

A vector measurement of the direction and speed of the motion is what is meant by the term "velocity" in physics. In more detail, the rate of change in an object's position relative to a frame of reference and time can also be described as the object's velocity.

Velocity, which is defined as the rate of motion of an object in a specific direction, tells us how quickly an object is traveling. The speed at which anything is traveling is determined by this.

Given information according to the question,

Initial velocity, u = 2 m/s

Final velocity, v= 7 m/s

Distance, d = 12 m

Use the equation of motion to find the acceleration of the skater,

v² - u² = 2as

7² - 2² = 24a

a = 45/24

a = 1.875 m/s².

Therefore, the acceleration of the skater is 1.875 m/s².

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The maximum height achieved by the ball thrown vertically upwards is 243.9 ft.

A time varying function is a function whose final value varies with time.

Example - f(t) = 2t + 5

Given is a ball which is thrown vertically upward from the ground with a velocity of 96 ft/s, then its height after [t] seconds is S = 96t − 16t².

We can write -

S = 96t − 16t²

Differentiating with respect to 't', we get -

dS/dt = 96 - 2 x 16 x t

dS/dt = 96 - 32t

Now, for maximum height -

dS/dt = 0

96 - 32t = 0

32t = 96

t = 96/32

t = 3 seconds

At t = 3 seconds, the height will be maximum. Now, it is given that -

[u] = 96 ft/sec

[v] = 0  (at maximum height)

[g] = - 9.8 m/s²

Using the second equation of motion, we get -

S = ut + 1/2 gt²

S [max] = 96 x 3 - 0.5 x 9.8 x 3 x 3

S [max] = 288 - 44.1

S [max] = 243.9 ft

Therefore, the maximum height achieved by the ball thrown vertically upwards is 243.9 ft.

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Answer:

a vector.

Explanation:

The arrow labeled '3.5 m/s' in the given scenario, which denotes both the speed and direction of a croquet ball, is called a vector. A vector, in physics, represents a quantity showcasing both magnitude (in this case, velocity measured as '3.5 m/s') and direction.

In the context of the question, the arrow labeled '3.5 m/s' that is indicating both the speed and the direction of the croquet ball is known as a vector. In physics, a vector is a quantity that possesses both magnitude (size or quantity) and direction. In this case, the '3.5 m/s' is the magnitude of the vector (the speed of the ball), and the direction the arrow is pointing indicates the direction the ball is moving. This is as opposed to a scalar quantity, which only has magnitude.

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The earth has many elements heavier than iron due to the hypothesis that the explosions of sun have become more massive to man kind over a period of time, thus creating heavier elements found on Earth.

Heavy elements such iron are formed by nuclear fusion reaction. Example include the heavy element of iron.

Source of these heavy elements are:

Many elements that are heavier than iron has been formed over the years due to the sun explosions.

The formation of these heavy elements occurs due to the process called neutron capture, where neutrons penetrate an atomic nucleus in explosions of the sun.

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According to law of conservation of energy, energy of motion is described by kinetic energy as the kinetic energy is displayed only when the object is in motion as per how much energy is stored in the object which are equal.

According to law of conservation of energy, it is evident that energy is neither created nor destroyed rather it is restored at the end of a chemical reaction .

Law of conservation of mass and energy are related as mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of energy is widely used in field of chemistry, fluid dynamics.

Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Julius Robert Mayer in the year 1842.

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Explanation:

It is given that,

Initial position of the Apple, [tex]h_o=1.4\ m[/tex]

Initial velocity, u = 3.1 m/s

Position of friend, Y = 4.2 m

Using second equation of motion as :

[tex]Y=ut-\dfrac{1}{2}gt^2+h_o[/tex]

[tex]4.2=3.1t-\dfrac{1}{2}\times 9.8t^2+1.4[/tex]    

[tex]3.1t-4.9t^2-2.8=0[/tex]..............(1)

On solving the above quadratic equation we get t = 2.02 seconds

Since, the value of t is real. So, the apple will reach a friend in a tree house. Hence, this is the required solution.                                    

To calculate the force needed to budge the stubborn pig, we need to consider the frictional forces acting on it. Given the given values of μs and the weight of the pig, the force required to budge the pig can be found by subtracting the force of friction from the maximum force the farmer can exert.

To calculate the force needed to budge the stubborn pig, we need to consider the frictional forces acting on it. The friction force can be calculated using the formula F_friction = μs ×F_normal, where F_normal is the normal force acting on the pig. The normal force is equal to the weight of the pig, which is given by F_weight = m × g, where m is the mass of the pig and g is the acceleration due to gravity.

Using the given values of μs and the weight of the pig, we can calculate the force of friction. Given that the maximum force the farmer can exert is 800 N, the force required to budge the pig can be found by subtracting the force of friction from the maximum force.

Let's calculate the force:

The force required to budge the pig is approximately 520 N.