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You used three methods of analysis to find the acceleration of the cart on the track: a two-point difference from v(t), an average of a(t) that was itself calculated by a succession of first differences of the v(t) data, and a line fit to v(t). some criteria to help you consider which method is best are part a in which type of graph(s) is it easiest to see whether the acceleration was constant?

The best way to find that you want is the line fit. When acceleration is constant the speed(v) changes smoothly every moment, so the v line must be straight. Differently, the accelaration changes.

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In the combined gas law, if the pressure in the system is increased, what happens to the volume if temperature remains constant?

In the combined gas law, if the pressure in the system is increased, what happens to the volume if temperature remains constant?

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Every female chicken lays 4 eggs. What is the constant of proportionality for the ratio of eggs to female chickens? 4, 3, 1/3, 1/4.

Every female chicken lays 4 eggs. What is the constant of proportionality for the ratio of eggs to female chickens? 4, 3, 1/3, 1/4.

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Determine whether the function is linear or quadratic. identify the quadratic, linear, and constant terms y= (x-5)(5x+4)-5x^2

Linear means that it is 1st degree, means it has x¹ basically the highest number is 1 for the power of the placeholder

quadratic means it is 2nd degree, means it has x² in it

so expand and simlfiy
(x-5)(5x+4)-5x²=
5x²-21x-20-5x=
-21x-20

so y=-21x¹-20
it’s linear because the squared terms cancel each other out

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Eric drove his fishing boat into a large cove and dropped the anchor in 52 feet of water the anchor descends at a constant rate of 3.8 feet per second, how long will it take for the anchor to hit the bottom of the lake? Round your answer to the nearest tenth If of a second if necessary.

Eric drove his fishing boat into a large cove and dropped the anchor in 52 feet of water the anchor descends at a constant rate of 3.8 feet per second, how long will it take for the anchor to hit the bottom of the lake? Round your answer to the nearest tenth If of a second if necessary.

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In which country has constant ethnic conflict between Arabs and black Africans been the most important obstacle to democracy? A. the Democratic Republic of the Congo B. South Africa C. Kenya D. Sudan

In which country has constant ethnic conflict between Arabs and black Africans been the most important obstacle to democracy? A. the Democratic Republic of the Congo B. South Africa C. Kenya D. Sudan

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Calculate the ph of 0.375 l of a 0.18 m acetic acid-0.29 m sodium acetate buffer after the addition of 0.0090 mol of koh. assume that the volume remains constant.

To calculate the pH of this solution, we use the
Henderson-Hasselbalch equation:

pH = pKa + log ([A-]/[HA])

Where,

[A-] = Molarity of the conjugate base =
CH3COO- = 0.29 M
[HA] = Molarity of the weak acid  = CH3COOH = 0.18 M

pKa = dissociation constant of the weak acid =
4.75

When KOH is added to the buffer, the chemical
reaction is:

CH3COOH + KOH = CH3COO-K+ + H2O

Therefore when 0.0090 mol KOH is added, 0.0090
mol acid is neutralized, and 0.0090 mol CH3COO- is produced.

[CH3COO-] = [0.0090 mol + 0.375 L (0.29 mol/L) ]
/ 0.375 L = 0.314 M

[CH3COOH] = [-0.0090 mol + 0.375 L (0.18 mol/L) ]
/ 0.375 L = 0.156 M

Going back to Henderson-Hasselbalch
equation:

pH = 4.75 + log (0.314 / 0.156)

pH = 5.054

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A sample of carbon dioxide gas, co2 (g), occupies a volume of 5.75 l at 0.890 atm. if the temperature and the number of moles remain constant, calculate the volume when the pressure a. increased to 1.25 atm b. decrease to 0.350 atm

According to Boyle’s law;
P1V1 = P2V2
P1 is the pressure of the gas in the first case.
V1 is the volume of the gas in the first case.
P2 is the pressure of the gas in the second case.
V2 is the volume of the gas in the second case.

P1 = 0.890 atm, V1 = 5.75l

a. P2 = 1.25 atm,
0.890*5.75 = 1.25*V2
V2 = 4.094 l

b. P2 = 0.350 atm,
0.890*5.75 = 0.350*V2
V2 = 14.621 l.

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Operation Rolling Thunder was an unsuccessful strategy to get North Vietnam to submit as a result of constant: a. diplomatic pressure c. guerilla operations b. bombing d. blockading

Operation Rolling Thunder was an unsuccessful strategy to get North Vietnam to submit as a result of constant: a. diplomatic pressure c. guerilla operations b. bombing d. blockading

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A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. the platform drops 6.00 cm before the person comes to rest. what is the spring constant of the spring?

Draw a diagram to illustrate the problem s shown in the figure below.

At state A, the person has potential energy relative to the spring of
PE = (60 kg)*(9.8 m/s²)*(1.2 m)
= 705.6 J

At state B, the PE is converted to kinetic energy which is equal to the potential energy.
Assume that aerodynamic losses are ignored during the free fall.

At state C, the potential energy (or kinetic energy) is converted into strain energy in the spring. Assume that energy losses are negligible.
The spring deflects by  6 cm = 6×10⁻² m, and its spring constant = k N/m.
Therefore
(1/2)(k N/m)(6×10⁻² m)² = 705.6 J
k = 705.6/0.03 = 23520 N/m = 23.52 kN/m

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A machine that provides both constant speed and maximum resistance throughout the full range of motion provides what type of muscular contraction?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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The rate constant for the second-order reaction 2no2(g) ? 2no(g) o2(g) is 0.540/(m · s) at 300°c. how long (in seconds) would it take for the concentration of no2 to decrease from 0.500 m to 0.250 m

The coefficient of CO₂ is 5.

Explanation:

Balancing the reaction:

___C₅H₁₂ + ___O₂ → ___CO₂ + ___H₂O

There are 5 C in the left side, so we put 5 on the right side:

___C₅H₁₂ + ___O₂ →  5CO₂ + ___H₂O

There are 12 H in the left side, so we put 6 as the coefficient of H₂O:

___C₅H₁₂ + ___O₂ →  5CO₂ + 6H₂O

Finally, there are 16 O in the right side, so we put 8 as the coefficient of O₂

___C₅H₁₂ + 8O₂ →  5CO₂ + 6H₂O

The coefficient of CO₂ is 5.

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A gas has a volume of 25 ml at a pressure of 100 kpa. what will the new volume of the gas be at a pressure of 150 kpa if the temperature remains constant?

This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.

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The decomposition of so2cl2 is first order in so2cl2 and has a rate constant of 1.42 x 10^-4 if the initial concentration of so2cl2 is 1.00 m how long will it take for the concentration to decrease to .78 m

The unknown of this problem is the experimental percent of water in the compound in order to remove the water of hydrogen, given the following:

Mass of crucible, cover and contents before heating                               23.54 g
Mass of empty crucible and cover                                                            18.82 g
Mass of crucible, cover, and contents after heating to constant mass     20.94 g

In order to get the answer, determine the following:

Mass of hydrated salt used                          = 23.54 g – 18.82 g = 4.72 g
Mass of dehydrated salt after heating          = 20.94 g – 18.82 g = 2.12 g
Mass of water liberated from salt                 = 4.72 g – 2.12 g = 2.60 g

Then solve the percent of water in the hydrated salt by:

% water = (mass of water / mass of hydrated salt) x 100
% water = 2.60 g / 4.72 g x 100
% water = 55.08 % in the compound

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An older client complains of a constant headache. a physical examination shows papilledema. what may the symptoms indicate in this client

Charlie had a waist circumference of 47 inches and a BMI of 29 this shows that she is overweight. BMI test level is high from normal ranges shows that she is at higher risk of disease. She should lose weight and concern to the doctor.

Further Explanation:

Body mass index (BMI) is a measured value derived from the height of a person and mass.

BMI indicates whether the person is healthy or overweight mainly used by physicians.

• Range of BMI in a normal person is 18.5-25

• Range of BMI in skinfold person is 25-30

• Range of BMI in underweight person is 15-18.5

The skinfold measurement test is used to determine a person’s body fat percentage and body composition.

In this test, we are the proportion of body fat by determining skinfold thickness at pinches specific part of the body. The estimate of these folds is determined the fat beneath the skin, also called subcutaneous adipose tissue.

The tester pinches the skin at the site and drags the fold of skin away from the muscle so only the fat tissue and skin are being held. The skinfold thickness is measured by skinfold calipers in millimeters.

Skin test includes the seven locations of the body:

1. Triceps

3. Suprailiac

4. Pectoral

5. Subscapular

6. Midaxilla

7. Abdomen

Charlie had a waist circumference of 47 inches and a BMI of 29 this shows that she is overweight. Females with waist size 47 inches have higher risk of having disease. BMI test level is high from normal ranges shows that she is at higher risk of disease.She should lose weight and concern to the doctor.

Subject: Health

Chapter: Physical Fitness

Keywords:

Body index mass, weight, doctor, triceps, abdomen, midaxilla, Quadriceps, skinfold, mass, height, pectoral.

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A gas with a volume of 4.0 liters at a pressure of 205 kilopascals is allowed to expand to a volume of 12.0 liters. What will the pressure in the container be if the temperature remains constant?

This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.

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~~20 Points~~ If c is a constant such that x^2+25x+c is equal to the square of a binomial, then what is c?

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6. Applying Newton’s cooling model, the temperature of the tea after 2 hours will be ___ ºF. round to the nearest integer.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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An airplane is flying at a constant speed in a positive direction. It slows down when it approaches the airport where it’s going to land. Which term describes the slowing of the plane? 1.stationary positive velocity 2.positive acceleration 3.negative acceleration 4.constant velocity

The equation of the car is given by the equation,

x(t) = 2.31 + 4.90t² – 0.10t⁶

If we are going to differentiate the equation in terms of x, we get the value for velocity.

dx/dt = 9.8t – 0.6t⁵

Calculate for the value of t when dx/dt = 0.

dx/dt = 0 = (9.8 – 0.6t⁴)(t)

The values of t from the equation is approximately equal to 0 and 2.

If we substitute these values to the equation for displacement,

(0)   , x = 2.31 + 4.90(0²) – 0.1(0⁶) = 2.31

(2)    , x = 2.31 + 4.90(2²) – 0.1(2⁶) = 15.51

Thus, the positions at the instants where velocity is zero are 2.31 and 15.51 meters.

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An object is moving north at a constant speed. A force of 5 N begins to push the object east at the same moment that a force of 5 N begins to push it west. What will happen to the object?

The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

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In a real world trampoline, how do gymnasts keep a constant bounce height

In a real world trampoline, how do gymnasts keep a constant bounce height

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25. From left to right across a period in the periodic table, elements become less ___________ and more ______________ in their properties. 26. Francium has 36 isotopes, but only francium-223 occurs in nature. Francium-223 spontaneously emits particles and energy, so francium-223 is a(an) _____________ of francium. 27. At sea level, water ______________ at 100°C. 28. Cooking requires continuous addition of energy to the chemical reactions that are taking place. The chemical reactions involved in cooking can be described as __________________. 29. The ________________ theory of matter states that all particles of matter are in constant motion. 30. In Rutherford’s experiments, some of the _______________ aimed at gold atoms bounced back, suggesting that a solid mass was at the center of the atom. 31. You are given the melting points of three unknown substances and are asked to predict which one is an ionic compound. You would select the compound with the ________________ melting point. 32. A flight simulator that helps astronauts prepare for a shuttle launch is an example of a(an) __________________. 33. In the symbol ■([email protected]) He, the superscript 4 is the _________________ for helium, and the subscript 2 is the ___________________ for helium.

25) Answer is: less metallic and more nonmetallic.

Electronegativity increases from left to right across a period, atoms have tendency to attract electrons.

Electronegativity (χ) is a property that describes the tendency of an atom to attract a shared pair of electrons.

Radioisotope has an unstable atomic nucleus and emit energy and particles when it changes to a more stable form.

Francium (Fr) is element with atomic number 87 (87 protons and 87 electrons).

Boiling is the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere.

The Celsius scale was based on 0°C for the freezing point of water and 100°C for the boiling point of water at 1 atm pressure.

There are two types of reaction:

1) endothermic reaction (chemical reaction that absorbs more energy than it releases, ΔH>0).

2) exothermic reaction (chemical reaction that releases more energy than it absorbs).

For example, the breakdown of ozone is an endothermic process. Ozone has lower energy than molecular oxygen (O₂) and oxygen atom, so ozone need energy to break bond between oxygen atoms.

The average kinetic energy of molecules depends on the temperature.

As temperature increases, molecules gain more energy from surrounding and move faster.

Kinetic energy (standard unit is the joule J) depends on speed of the molecule.

Solid gains kinetic energy to become a liquid and then becomes a gas.

This was famous Rutherford’s Gold Foil Experiment: he bombarded thin foil of gold with positive alpha particles.

Rutherford observed the deflection of alpha particles on the photographic film.

Alpha particles are helium atom particles, consist of two protons and two neutrons.

According to Rutherford model of the atom: atoms have their charge concentrated in a very small nucleus.

For example, calcium oxide.

Calcium oxide (CaO) has ionic bonds between calcium cations (Ca²⁺) and oxygen anions (O²⁻).

Because it has strong ionic bonds, it has high melting point (around 2600°C).

Ionic bond is the electrostatic attraction between oppositely charged ions (cations and anions).

32) Answer is: a scientific model.

A scientific model is a representation of an idea, an object, a process or a system that is used to describe and explain phenomena that cannot be experienced directly.

33) Answer is: the superscript is mass number and the subscript is atomic number.

Atomic number(Z) is the number of protons, which is characteristic of a chemical element..

Mass number (A) is the total number of protons and neutrons in a nucleus.

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The gas in a cylinder has a volume of 5 liters at a pressure of 101 kPa. The pressure of the gas is increased to 202 kPa. Assuming the temperature remains constant, what would the new volume be? L

This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.

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The rate constant of a first-order process that has a half-life of 3.50 min is __________ s-1.

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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What would be your estimate of the age of the universe if you measured a value for hubble’s constant of h0 = 30 km/s/mly ? you can assume that the expansion rate has remained unchanged during the history of the universe. express your answer using two significant figures. yr?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m