What is sustainability? How can we make sustainable development a reality? How sustainability can be measured?​

Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.  

Answer:

(C) because the elevator is not accelerating

Note  F = M a = M g (the resultant force on the elevator is due to gravity)

or  Fup = Fc   the force exerted on the elevator by the cable

and Fdown = Fe    the force exerted on the elevator by gravity

F = M a = Fup - Fdown = zero    resultant force on elevator

Answer:

d. 60

Explanation:

If a body of mass 2 kg is moving with a velocity of 30 m/s, then

on doubling its velocity the momentum becomes

a 30 kgm/s

b 90 kgm/s

C 120 kgm/s

d 60 kgm/s

HALPLPLPPLL

Answer:

120

Explanation:

Answer:

\(1.62\times 10^{-8}\ \text{s}\)

Explanation:

\(\epsilon_0\) = Vacuum permittivity = \(8.854\times 10^{-12}\ \text{F/m}\)

\(A\) = Area = \(10\times 2\times 10^{-4}\ \text{m}^2\)

\(d\) = Distance between plates = 1 mm

\(V_c\) = Changed voltage = 60 V

\(V\) = Initial voltage = 100 V

\(R\) = Resistance = \(1000\ \Omega\)

Capacitance is given by

\(C=\dfrac{\epsilon_0A}{d}\\\Rightarrow C=\dfrac{8.854\times 10^{-12}\times 10\times 2\times 10^{-4}}{1\times 10^{-3}}\\\Rightarrow C=1.7708\times 10^{-11}\ \text{F}\)

We have the relation

\(V_c=V(1-e^{-\dfrac{t}{CR}})\\\Rightarrow e^{-\dfrac{t}{CR}}=1-\dfrac{V_c}{V}\\\Rightarrow -\dfrac{t}{CR}=\ln (1-\dfrac{V_c}{V})\\\Rightarrow t=-CR\ln (1-\dfrac{V_c}{V})\\\Rightarrow t=-1.7708\times 10^{-11}\times 1000\ln(1-\dfrac{60}{100})\\\Rightarrow t=1.62\times 10^{-8}\ \text{s}\)

The time taken for the potential difference to reach the required level is \(1.62\times 10^{-8}\ \text{s}\).

Answer:

B

Explanation:

If both have the same charge they would move away from eachother.

Answer:

The rate of change of distance between the two ships is 18.63 km/h

Explanation:

Given;

distance between the two ships, d = 140 km

speed of ship A = 30 km/h

speed of ship B = 25 km/h

between noon (12 pm) to 4 pm = 4 hours

The displacement of ship A at 4pm = 140 km - (30 km/h x 4h) =

140 km - 120 km = 20 km

(the subtraction is because A is moving away from the initial position and the distance between the two ships is decreasing)

The displacement of ship B at 4pm = 25 km/h x 4h = 100 km

Using Pythagoras theorem, the resultant displacement of the two ships at 4pm is calculated as;

r² = a²   +  b²

r² = 20²  +  100²

r = √10,400

r = 101.98 km

The rate of change of this distance is calculated as;

r² = a²   +  b²

r = 101.98 km, a = 20 km, b = 100 km

\(2r(\frac{dr}{dt} ) = 2a(\frac{da}{dt} ) + 2b(\frac{db}{dt} )\\\\r(\frac{dr}{dt} ) = a(\frac{da}{dt} ) + b(\frac{db}{dt} )\\\\101.98(\frac{dr}{dt} ) = 20(-30 ) + 100(25 )\\\\101.98(\frac{dr}{dt} ) = -600 + 2,500\\\\101.98(\frac{dr}{dt} ) = 1900\\\\\frac{dr}{dt} = \frac{1900}{101.98} = 18.63 \ km/h\)

Answer:

At zero kelvin (minus 273 degrees Celsius) the particles stop moving and all disorder disappears. Thus, nothing can be colder than absolute zero on the Kelvin scale. Physicists have now created an atomic gas in the laboratory that nonetheless has negative Kelvin values.

Explanation:

Answer:

"light year" - about 6 million million miles

The nearest star is alpha Centauri - about 24 million million miles away

Answer:

300

Explanation Hope I'm not wrong.

Wavelength of the given wave is 8 cm and frequency is  37.5 *\(10^{8}\) Hz.

The number of vibrations counted per second is called frequency. A wave is a group of vibrations that are referred to as energy. The bottom node is known as the crest, and the top node is known as the trough.

The frequency of an alternating current is the number of full cycles per second. The hertz, also known as Hz, is the accepted unit of frequency. The frequency of a current is 1 Hz if one cycle is completed per second; 60 cycles per second equals 60 Hz.

There are 8 waves so assume one wave is 1 cm so wavelength is 8 cm and frequency of wave = speed of light/ wavelength

frequency = \(3*10 ^{8} / .08\)

Frequency = 37.5 *\(10^{8}\) Hz

Wavelength of the given wave is 8 cm and frequency is  37.5 *\(10^{8}\) Hz.

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Answer:

mass

Explanation:

Answer: Mass is the amount of mass an object contains. Mass is measured using a scale. Volume is the amount of space matter takes up.

hope this help!! :) :)

Speed of sound is maximum on solid.

Correct option.

A) steel Solid

Answer:

Momentum - Momentum is a measurement of mass in motion. Momentum is equal to the mass times the velocity of an object.

It is highly recommended that this friend who is suffering from insomnia visits the doctor and eat foods rich in serotonin.

Insomnia is a medical condition in which an individual is unable to sleep or has short periods of interrupted sleep.

A friend who falls asleep easily and then has difficulty going to sleep is probably suffering from insomnia.

It is recommended that this friend who is suffering from insomnia visits the doctor and eat foods rich in serotonin.

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The sign set after the slowdown of the bicycle will be positive for the position,  negative for velocity, and negative for acceleration.

The rate at which an object's position changes when observed from a specific point of view and when measured against a specific unit of time is known as its velocity.

According to Que, when a bicyclist moves in a straight line and slows down, then the velocity decrease as displacement is decreasing, and the acceleration also decreases only displacement increases.

Therefore, the sign set for the position is +ve, for velocity it is -ve, and for acceleration also -ve

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A biker slows down after traveling in a long, straight line at initial velocity v0. Which of the following the best \sdescribes the signs set for the initial position, initial velocity and the acceleration? Initial position Initial velocity Acceleration

A. Positive Negative Negative

B. Positive Positive Negative

C. Negative Positive Negative

D. Negative Negative Positive

E. Negative Negative Negative

A car with a mass of 1200 kg enters a banked turn covered with ice at a velocity of 65.0 km/h. The road is banked at an angle of 20°. The radius of the turn is found to be 91.9 m using the equation r = v²/gtanθ.

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Answer:

a) v = 4.9 m/s at 62° above the horizontal

b) h = 0.94 m above the board or 4.94 m above the water

c) v = 10 m/s at 77° below the horizontal

Explanation:

Assume UP and FOREWARD are positive and the diving board is the origin.

Ignore air resistance.

s = s₀ + v₀t + ½at²

In the vertical

-4 = 0 + vy₀(1.3) + ½(-9.8)(1.3²)

vy₀ = 4.281 m/s

in the horizontal

3.0 = 0 + vx₀(1.3) + ½(0)(1.3²)

vx₀ = 2.307... m/s

v = √(4.281² + 2.307²) = 4.863...

tanθ = 4.281 / 2.307

θ = 61.680...

v² = u² + 2as

s = (v² - u²) / 2a

h = (0² - 4.281²) / 2(-9.8) = 0.9350...

v² = 4.863² + 2(9.8)(4)

v = 10.1019...

cosθ = 2.307/10.1019

θ = 76.798

(a) The initial velocity of Samuel is 4.02 m/s

(b) The maximum height reached by Samuel is 0.55 m

(c)  The final velocity when he enters the water is 5.20 m/s

The given parameter:

(a) The initial velocity of Samuel is calculated as;

\(h = v_o_y t + \frac{1}{2} gt^2\\\\\)

Assume downward motion to be in negative direction

The vertical component of the velocity is calculated as;

\(4 = 1.3\times v_0_y + 0.5\times 9.8\times 1.3^2\\\\4 = 1.3v_{0y} + 8.281\\\\1.3v_{0y} = 4- 8.281\\\\1.3v_{0y} = -4.281\\\\v_{0y} = \frac{-4.281}{1.3} \\\\v_{0y} = -3.293 \ m/s\\\\v_{0y} = 3.293 \ m/s \ \ \ (downwards)\)

The horizontal component of the velocity is calculated as;

Assume forward motion to be in positive direction

\(x = v_{0x}t \\\\3 = 1.3v_{0x}\\\\v_{0x} = \frac{3}{1.3} \\\\v_{0x} = 2.308 \ m/s\)

The resultant of initial velocity is calculated as;

\(v_0 = \sqrt{v_{0y}^2 + v_{0x}^2} \\\\v_0 = \sqrt{3.293^2 + 2.308^2} \\\\v_0 = \sqrt{16.17} \\\\v_0 = 4.02 \ m/s\)

(b) The maximum height reached by Samuel is calculated as;

\(v_f_y^2 = v_0_y^2 + 2gh\\\\at \ maximum \ height \ v_{fy} = 0\\\\0 = v_0_y^2 + 2gh\\\\-2gh = v_0_y^2\\\\h = \frac{v_0_y^2}{-2g} \\\\h = \frac{(3.293)^2}{-2\times 9.8} \\\\h = -0.55 \ m\\\\h = 0.55 \ m \ (downwards)\)

(c) The final velocity when he enters the water;

The height traveled before he hits the water, h = 0.55 m

\(v_f^2 = v_{0}^2 + 2gh\\\\v_f^2 = (4.02)^2 + (2\times 9.8\times 0.55)\\\\v_f^2 = 26.94\\\\v_f = \sqrt{26.94} \\\\v_f = 5.20 \ m/s\)

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Answer:

.66354 T

Explanation:

Use F=ILB

B =  \(\frac{F}{IL}\)

B = Magnetic field

F= force due to magnetic

I= current

L= length in meters

F = mg

Final formula:

B=\(\frac{mg}{IL}\)

B=\(\frac{(.13)(9.8)}{(6)(.32)}\)

B= .66354

ayo btw ion know how to find direction, my b G

The minimum magnetic field required to move the wire is 66354 T.

The direction of magnetic field is normal to the page outwards.

The region surrounding a magnet that experiences the effects of magnetism is known as the magnetic field. When describing the distribution of the magnetic force within and around a magnetic object in nature, the magnetic field is a useful tool.

Given parameter:

Current passing through the wire, I = 6.0 A.

Length of the wire ,L = 32 cm = 0.32 m.

Mass of the wire, m = 0.13 Kg.

Acceleration due to the gravity, g = 9.8 m/s².

We know that, force acting on a current caring wire due to magnetic field is,  F=ILB

Where,

B = Required magnetic field.

To find the minimum magnetic field that is required to move the

wire, force acting on a current caring wire due to magnetic field is equal to weight the wire, that is, mg.

Hence, we can write,

mg = ILB

⇒ B = mg/IL

= (0.13 * 9.8)/(6.0 * 0.32)

=0.66354 Tesla

Hence, the minimum magnetic field is 0.66354 Tesla.

b) By using Maxwell's right hand thumb Rule along current flow, the direction of magnetic field is  determined as normal to the page pointing outwards.

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The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J

First, we shall list out the given parameters from the question. This is shown below:

The quantity of heat energy that must be transferred can be obtained as follow:

Q = MCΔT

= 2.25 × 394 × 220

= 195030 J

Thus, we can conclude quantity of heat energy that must be transferred is 195030 J

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From pressure definition,  the area of the car tires that are in contact with the road is 0.079 m

Pressure can be defined as the ratio of force to area. It is measured in Pascal.

Given that a car weighs 15,000 N and its tires are I flared to a pressure of 190 kPa. How large is the area of the cars tires that are in contact with the road ?

From the definition of Pressure, P = F/A

Where

190000 = 15000/A

A = 15000/190000

A = 0.079 m

A car will have 4 tires. The area of one in contact with the road will be

A = 0.079/4

A = 0.02 m

Therefore, the area of the car tire that is in contact with the road is 0.02 m

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Since the rope is parallel to the table, the tension in the rope is also equal to the force acting on the cart.  The acceleration of the cart will be obtained as 1.32 m/s².

Since the rope is parallel to the table, the forces acting on the system are the tension in the rope (T) and the weight of the hanging block (m1g). Since the rope is parallel to the table, the tension in the rope is also equal to the force acting on the cart.

The acceleration of the system can be found using Newton's second law:

ΣF = ma

where ΣF is the net force on the system, m is the total mass of the system, and a is the acceleration of the system.

The net force on the system is given by:

ΣF = T - m₁g

Substituting the given values, we get:

ΣF = T - m₁g = ma

To solve for the acceleration, we need to find the tension in the rope (T). We can do this by considering the torque on the pulley. The torque on the pulley is equal to the product of the force and the radius of the pulley (τ = Fr). The torque due to the weight of the hanging block is equal to m1g * r, and the torque due to the tension in the rope is equal to T * r. Since the pulley is not accelerating, the net torque on the pulley must be zero:

Στ = m₁g * r - T * r = I * α

where I is the moment of inertia of the pulley and α is the angular acceleration of the pulley. Since the pulley is not slipping, the linear acceleration of the cart is equal to the angular acceleration of the pulley divided by the radius of the pulley (a = α * r).

Substituting for α and a, we get:

m₁g * r - T * r = I * a / r

Solving for T, we get:

T = (m₁g + I * a / r)

Substituting this expression for T into the equation ΣF = T - m₁g, we get:

ma = (m₁g + I * a / r) - m₁g

Simplifying, we get:

a = g * m₁ / (m₂ + I / r²)

Substituting the given values, we get:

a = (9.81 m/s²) * 2.0 kg / (4.0 kg + 0.4 kg-m² / (0.2 m)²) = 1.32 m/s²

Therefore, the acceleration of the cart is 1.32 m/s².

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The dangling mass will not move and the puck will keep rotating in its orbit, Therefore, V = √(mgR/M)  will be an algebraic expression that includes the variables mentioned above.

A centripetal force that causes a body to travel along a curved path. The centripetal force always acts orthogonally to the motion of the body and towards the fixed point of the path's instantaneous centre of curvature. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". Gravity is the centripetal force that causes astronomical orbits, according to Newtonian mechanics theory.

A common example of centripetal force is when a body moves at a constant speed along a circular path. The centripetal force is directed at right angles to the motion as well as along the radius of the circular path towards the centre.

Fc = mg

Now, centripetal force on the puck is equal to the mass of the puck times the centripetal acceleration, or

Fc = Mac

centripetal acceleration is related to the tangential velocity of the puck as

ac = V²/R

where R is the radius of the orbit. Then we have

Fc = M ac =M ω² R = M V² / R

and, thus

M V² / R = mg

and, solving for V, we get

V = √(mgR/M)

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Answer:

true it all changes

Explanation:

________________________

The correct matches for the given words are:

1. grand unified theory - predicts the strong, weak, and electromagnetic forces

2.electroweak force

3. Inflation

4. Olbers' paradox

5. cosmic microwave background

6. annihilation

Physical interactions between electrically charged particles are known as the electromagnetic force. It is the result of the interaction of all magnetic and electrical forces and operates between charged particles.

Both visible light and radiation in other wavebands that the human eye cannot see are produced by the electromagnetic field.

A faint glow of light known as the Cosmic Microwave Background radiation, or CMB for short, permeates the entire cosmos and falls on Earth with a remarkably consistent intensity from all directions.

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Answer:

Photovoltaic detection is a technique that converts light into electrical energy. It is a process that involves the use of a photovoltaic cell, which is made up of semiconductor materials, to generate an electric current when exposed to light.

The photovoltaic cell absorbs the photons of light, which then knock electrons out of their orbits, creating a flow of electricity. The amount of electricity produced is proportional to the intensity of the light. The photovoltaic cell is commonly used in solar panels to generate electricity from sunlight. The efficiency of the photovoltaic cell is dependent on several factors, including the type of semiconductor material used, the purity of the material, and the thickness of the cell.

The photovoltaic cell has many applications, including in solar power generation, telecommunications, and remote sensing. The technique of photovoltaic detection is an important area of research, as it has the potential to provide a clean and renewable source of energy that can help mitigate climate change.

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The correct statement is Molecular collisions transfer thermal energy between the system and its surroundings. Thus, option D is correct.

The energy moves between a system of reacting substances and the surroundings by the collision of molecules. The transfer of heat or thermal energy between the system and its surroundings by the process of Conduction. Conduction is the process of transmitting the heat to the neighboring atoms or collisions by the process of collisions.

The conduction takes place more steadily in solids and liquids where the molecules are closer together. When the molecules are collided with the nearby molecules, the potential energy is converted into kinetic energy and hence the heat energy is transferred between the system and its surroundings.

Hence, Molecular collisions transfer thermal energy between the system and its surroundings. Thus, the correct option is D.

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Answer:

2

Explanation:

The polynomial relationship between position and time for the bowling ball is linear.

A linear relationship between two variables is a term used to describe a straight-line relationship between the two variables.

Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

From the equation of linear relationship between two variable, the highest power of x is one.

The given equation for position and time;

x(t) = vot + xo

From this given equation, the highest power of t is one, hence it is called linear relationship.

Thus, the polynomial relationship between position and time for the bowling ball is linear.

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