A spring in a toy gun has a spring constant of 10 N/m and can be compressed 4 cm.
It is then used to shoot a 1 g ball out of the gun. Find the velocity of the ball as it
leaves the gun

Answers

Answer 1
F=ma
We know from this that a=10,000m/s2

V=at
X=vt


You end up with v^2=ax

Plug in 10,000 and 0.04 and solve for v =20m/s

Related Questions

What must your speed be in order to travel 400 km in 3 hrs?

Answers

Answer:

\(\boxed {\tt s=133 \frac{1}{3} \ or \ 133.333333 \ km/hr}\)

Explanation:

We want to find speed, so we can use the following formula.

\(s=\frac{d}{t}\)

where \(d\) is the distance traveled and \(t\) is the time.

We traveled 400 kilometers in 3 hours. Therefore,

\(d= 400 \ km \\t= 3 \ hrs\)

Substitute the values into the formula.

\(s=\frac{400 \ km }{3 \ hrs}\)

Divide

\(s= 133.33333 \ km/hr\)

\(s= 133 \frac{1}{3} \ km/hr\)

The speed is 133 1/3 or 133.33333 kilometers per hour.

three carts of masses 2 kg, 18 kg, and 9 kg move on a frictionless horizontal track with speeds of 10m/s, 8m/s, and 2m/s. the carts stick together after colliding. find the final velocity of the three carts. answer in units of m/s.

Answers

Answer:

V = 6.3 m/s

Explanation:

Given:

m₁ = 2 kg

m₂ = 18 kg

m₃ = 9 kg

V₁ = 10 m/s

V₂ = 8 m/s

V₃ = 2 m/s

__________

V - ?

Let us write the momentum conservation law for an inelastic impact:

m₁·V₁ + m₂·V₂ + m₃·V₃ = (m₁ +m₂ + m₃) ·V

Cart speed after interaction:

V = ( m₁·V₁ + m₂·V₂ + m₃·V₃ ) / (m₁ +m₂ + m₃)

V = (2·10 + 18·8 + 9·2) / ( 2 + 18 + 9) = 182 / 29 ≈  6.3 m/s

A horse has a kinetic energy of 29/400 J. If the horse has a mass of 300 kg.
what is the horse's speed?
OA. 98 m/s
OB. 33.1 m/s
O C. 14 m/s
OD. 9.9 m/s

Answers

OB. 33.1 m/s

To calculate the horse's speed, you can use the formula for kinetic energy:

KE = (1/2)mv^2

where m is the mass of the horse and v is its velocity. Rearranging the formula to solve for velocity:

v = √(2KE/m)

Plugging in the given values:

v = √(2 * 29/400 J / 300 kg) = √(58/300 kg m^2/s^2) = √(0.194 m^2/s^2) = 33.1 m/s

If the same amount of force was applied to an object that was twice the mass,​

If the same amount of force was applied to an object that was twice the mass,

Answers

Answer:

the object with greater mass will experience a smaller acceleration and the object with less mass will experience a greater acceleration.

Explanation:

According to Newton's second law, when the same force is applied to two objects of different masses, the two objects will change mass.

A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.70 kg and 2.50 kg, and the length of the wire is 1.21 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

Answers

Just before the collision, the ball has a velocity of 9.3 m/s, downward. After the collision, the ball has a velocity of 6.2 m/s, upward.

To solve this problem, we can analyze the motion of the ball and block before and after the collision using the principles of conservation of energy and momentum. Since the collision is elastic, the total kinetic energy of the system is conserved. The ball has gravitational potential energy before the collision, which is converted to kinetic energy as it falls.

The block has no kinetic energy before the collision, but gains some after the collision due to the transfer of momentum from the ball. By equating the total kinetic energy before and after the collision and using the principle of conservation of momentum, we can solve for the velocities of the ball and block.

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you made $100,000 this year. you have $0 in adjustments, $11,500 in deductions and $7,300 in exemptions. What is your taxable increase?

Answers

The tax rate you will pay is displayed in tax brackets for each category of taxable income.

Thus, For instance, in 2022, the first $10,275 of your taxable income is subject to the lowest tax rate of 10% if you are single.

Up until the maximum amount of your taxable income, the following portion of your income is taxed at a rate of 12%.

As taxable income rises, the tax rate rises under the progressive tax system. Overall, this has the result that taxpayers with higher incomes often pay a greater rate of income tax than taxpayers with lower incomes.

Thus, The tax rate you will pay is displayed in tax brackets for each category of taxable income.

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Please help me in questions 4_5_6

Please help me in questions 4_5_6

Answers

Yes, the force of the engine does work on the car as it accelerates the car forward. Work is defined as the transfer of energy that occurs when a force is applied over a distance, and in this case, the force of the engine is causing the car to move, so it is doing work.

How to explain the force

As the car gains speed, its kinetic energy increases, which means it has more energy of motion. Kinetic energy is defined as one-half of the mass of an object times its velocity squared, so as the car's speed increases, so does its kinetic energy.

The gravitational potential energy of the car will remain constant as long as it stays on a horizontal road, assuming there is no change in elevation. Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, and since the car's position relative to the ground is not changing, its gravitational potential energy will remain constant.

The tractive force of the engine may change depending on the speed of the car and the resistance to motion that the car is encountering. As the car speeds up, the air resistance acting on the car will increase, which will require more force from the engine to maintain the same acceleration. Additionally, if the road surface is rough or there are inclines, the tractive force required to maintain the same speed or acceleration will also increase.

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fm radio frequencies accentuated the pitch, or distance, between radio waves and offered greater fidelity and clarity than am radio.

Answers

The statement "FM radio frequencies accentuated the pitch, or distance, between radio waves and offered greater fidelity and clarity than AM radio" is true.

What is FM radio?

Frequency modulаtion (FM) is а type of rаdio аnd sound trаnsmission thаt offers stаtic-less reception аnd greаter fidelity аnd clаrity thаn АM rаdio by аccentuаting the pitch or distаnce between rаdio wаves.

АM (or Аmplitude Modulаtion) аnd FM (or Frequency Modulаtion) аre wаys of broаdcаsting rаdio signаls. Both trаnsmit the informаtion in the form of electromаgnetic wаves. АM works by modulаting (vаrying) the аmplitude of the signаl or cаrrier trаnsmitted аccording to the informаtion being sent, while the frequency remаins constаnt. This differs from FM technology in which informаtion (sound) is encoded by vаrying the frequency of the wаve аnd the аmplitude is kept constаnt.

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What is the kinetic energy of a 72.2 kg cheetah moving at a velocity of 25.9 m/s?
935 J
5450 J
48,400 J
24,200 J

Answers

Given:

Mass of cheetah (m) = 72.2 kg

Speed of cheetah (v) = 25.9 m/s

Equation:

\( \rm KE = \dfrac{1}{2} mv^2\)

Answer:

By substituting values in the equation, we get:

\( \rm KE = \dfrac{1}{2} \times 72.2 \times (25.9)^2 \\ \\ \rm = \dfrac{1}{2} \times 72.2 \times 670.81 \\ \\ \rm = 36.1 \times 670.81 \\ \\ \rm = 24,216.241 \\ \\ \rm \approx 24,200 \ J\)

\( \therefore \) Kinetic energy of cheetah = 24,200 J

A Mexican jumping bean jumps with the aid of a small worm that lives insidethe bean. a) If a bean of mass 2.0 g jumps 1.0 cm from your hand into the air,how much potential energy has it gained in reaching its highest point.b) What is its speed as the bean lands back in the palm of your hand?

Answers

Given:

The mass of the bean is

\(\begin{gathered} m=2.0\text{ g} \\ m=2.0\times10^{-3}\text{ kg} \end{gathered}\)

The distance during which it traveled is

\(\begin{gathered} h=1.0\text{ cm} \\ h=0.010\text{ m} \end{gathered}\)

Required: (a) Potential energy gained

(b) the speed of the bean when lands back in the palm.

Explanation:

we have to apply conservation of energy to solve the problem.

when the bean is in our hand it has zero potential energy and after reaching its highest point has only potential energy.

look at the free body diagram

The potential energy is given as

\(P.E=mgh\)

here,

\(h\)

is the height and

\(g\text{ }\)

is the acceleration due to gravity which is equal to

\(9.8\text{ m/s}^2\)

Plugging all the values in the above relation, we get

\(\begin{gathered} P.E=mgh \\ P.E=2.0\times10^{-3}\text{ kg}\times9.8\text{ m/s}^2\times0.010\text{ m} \\ P.E=0.196\times10^{-3}\text{ J} \\ P.E=1.96\times10^{-4}\text{ J} \end{gathered}\)

(a) Potential energy is

\(1.96\times10^{-4}\text{ J}\)

(b)

By energy conservation,

when a bean comes down in the hand, total potential energy is converted into kinetic energy.

\(K.E=P.E\)

Kinetic energy is given as

\(K.E=\frac{1}{2}mv^2\)

put this into the above relation, we get

\(\begin{gathered} K.E=P.E \\ \frac{1}{2}mv^2=P.E \\ \end{gathered}\)\(v=\sqrt[2]{2\times\frac{P.E}{m}}\)

Plugging all the values in the above relation, we get

\(\begin{gathered} v=\sqrt[2]{2\times1.96\times\frac{10^{-\frac{4}{}}\text{ J}}{2\times10^{-3}\text{ kg}}} \\ \\ v=\sqrt[2]{1.96\times10^{-1}} \\ v=0.44\text{ m/s} \end{gathered}\)

Thus, the speed of the bean as lands back in the palm is

\(0.44\text{ m/s}\)

A Mexican jumping bean jumps with the aid of a small worm that lives insidethe bean. a) If a bean of

Momentum conservation often assumes that the mass of an object remains
constant throughout a process or event. However, a change in momentum can
also occur when mass changes. Consider an automobile with a full tank of
gasoline traveling at a velocity of 88.0 km/h to the east. The mass of the car when
the fuel tank is full is 1292 kg. Suppose that the car travels along a highway that
extends eastward for 600 km. By the time the car has traveled this distance, its
mass is 1255 kg. What is the car's velocity at the end of the journey?

Answers

The law of conservation of momentum states that in an isolated system, the total momentum of two or more bodies acting on each other remains constant unless an external force acts on them. Therefore, it cannot create or destroy momentum.

What is the speed of the car at the end of the trip?Velocity is the percentage of time an object moves along a path, and Velocity is the speed and direction of an object's movement.If the car is moving at a constant speed, the car is also moving at a constant speed. The confusion between the two rates, which are actually measured in the same units, is:Velocity is a vector quantity, but velocity is a scalar quantity.This is just Newton's first law. An object at rest will remain stationary and an object in motion will continue to move in the same direction at a constant speed unless an unbalanced force acts on it. The car tends to keep moving at a constant speed and direction because the two forces are canceling (i.e. balanced).

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In this table, the molecules of which object move fastest?
O Object
O Object B
O Object C
O Object D

In this table, the molecules of which object move fastest?O ObjectO Object BO Object CO Object D

Answers

Answer:

D. Object D

Explanation:

The hotter the temp the faster the molecules move

An automobile moves forward and backward on the street highway. The graph shows the velocity of this automobile as a function of time. At t equals five seconds, how far is the automobile from its t = 0 initial position? (round to 3 significant digits)

An automobile moves forward and backward on the street highway. The graph shows the velocity of this

Answers

The velocity of this automobile as a function of time. At t = 5 seconds, the automobile is 90 meters from its initial position.

To determine the distance traveled by the automobile from its t = 0 initial position, we need to calculate the area under the velocity-time graph up to t = 5 seconds.

The graph shows the velocity of the automobile as a function of time. Let's assume that positive velocity represents forward motion, and negative velocity represents backward motion.

Since velocity represents the rate of change of displacement, the area under the velocity-time graph represents the displacement or distance traveled. In this case, the area will consist of two parts: the area above the x-axis (forward motion) and the area below the x-axis (backward motion).

To calculate the area, we can break it down into two separate integrals:

1. The area above the x-axis (forward motion):

Since the velocity is constant at 20 m/s for the first 4 seconds, the area is a rectangle:

Area1 = velocity * time = 20 m/s * 4 s = 80 m

2. The area below the x-axis (backward motion):

The velocity changes to -10 m/s at t = 4 seconds. From t = 4 seconds to t = 5 seconds, the velocity is -10 m/s. The area is a rectangle:

Area2 = velocity * time = -10 m/s * 1 s = -10 m

To find the total distance traveled, we add the absolute values of the areas:

Total distance = |Area1| + |Area2| = |80 m| + |-10 m| = 80 m + 10 m = 90 m

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An astronaut measure the period of a mass spring system on Earth. How would the period be affected if the astronaut measured the period of the same mass spring system on the moon? (Moon's gravity = 1/6 Earth's gravity.)

Answers

An astronaut measure the period of a mass spring system on Earth.

The period of a mass spring system on the moon would be longer than the period on Earth. This is because the period of a mass spring system is dependent on the square root of the ratio of the mass to the spring constant, and the acceleration due to gravity. Since the acceleration due to gravity on the moon is only 1/6th of that on Earth, the restoring force on the mass will be weaker, resulting in a longer period. Therefore, the astronaut would measure a longer period for the same mass spring system on the moon than on Earth.

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If Bugs bunny can accelerate at a rate of 10m/s?, how long (in seconds) will it take him to
reach a speed of 300m/s, if starting from rest?
HELPPPP ME PLS NEED WORK SHOWN

Answers

I believe that it would take 30 seconds, as he accelerates at 10 m/s and 10 x 30 = 300

hope this helps! good luck :)

The kinematic equation is vf=vi+at
This leaves the answer being time=30sec
If Bugs bunny can accelerate at a rate of 10m/s?, how long (in seconds) will it take him toreach a speed

A stone is dropped from a bridge 45 meters above the surface of a river. What is the time required for the stone to reach the water’s surface?

Answers

Answer:

C.  3.0 s

Explanation:

Well, I've taken this question before, so I went back and this was the answer I put, which was correct.

Hope this helps! <3 May I have brainliest if it helps you enough?

It will take 3 s for the stone to get to the surface of the water.

We'll begin by listing out what was given from the question. This includes:

Height (h) = 45 m

Time (t) =?

NOTE: Acceleration due to gravity (g) is 10 m/s²

From the data above, we can obtain the time taken for the stone to get to the surface of the water as follow:

H = ½gt²

45 = ½ × 10 × t²

45 = 5 × t²

Divide both side by 5

\(t^{2} = \frac{45}{5} \\\\t^{2} = 9\)

Take the square root of both side

\(t = \sqrt{9}\)

t = 3 s

Therefore, it will take 3 s for the stone to get to the surface of the water.

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why does sound travel faster in metal than in air

Answers

Sound travel faster in metal than air becoz molecules of metal i.e solid are closely packed and it will take less time for sound waves to travel from one molecule to another whereas in air i.e in gas,molecules are far apart so it will take more time for sound waves to travel.In case of vacuum there are no molecules at all so sound is not there.that is why in space we cannot hear anything.

HOPE THIS HELP<3

organisms are able to maintain their normal internal temperatures because their bodies contain water, which protects them from rapid temperature changes. it is water's heat

Answers

Water's high specific heat capacity helps it resist changes in temperature, making it a useful tool for organisms to regulate their body temperature.

How does water regulate the body temperature?

Water helps regulate body temperature through several mechanisms.

Cooling through sweating: When the body becomes too warm, water in the form of sweat is secreted through the sweat glands onto the surface of the skin. As the sweat evaporates, it takes heat away from the body, cooling it down.Retaining heat through shivering: When the body becomes too cold, water in the form of blood is circulated to muscles, which can contract rapidly and generate heat through shivering.Distributing heat through blood flow: Water in the form of blood is circulated throughout the body, carrying heat away from warmer areas and distributing it to cooler areas. This helps maintain a consistent internal temperature.

In addition, water's high specific heat capacity allows it to resist changes in temperature, which helps the body maintain a constant internal temperature even in the face of external temperature fluctuations.

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Which of the following statements is true?
a Penicillin is produced by fungal fermentation.
b
The effects of too much beer or wine can be
countered with antibiotics.
с
The deadly Death Cap mushroom can be treated
with penicillin.
d Antibiotics do not treat fungal diseases.

Answers

Answer:

a Penicillin is produced by fungal fermentation.

Explanation:

The industrial production of penicillin (PEN) occurs via fermentation using the filamentous fungus Penicillium chrysogenum

Penicillin G (benzylpenicillin) was first produced from a penicillium fungus that occurs in nature. The strain of fungus used today for the manufacture of penicillin G was created by genetic engineering to improve the yield in the manufacturing process.

Why is math so hard?

Answers

Answer:

its just built different

I could give you a big, fancy scientific answer, but it often comes down to the fact that the way that most instructors teach math is not the way the student(s) can most easily understand it.

What is the frequency of light that has a wavelength of 682 nm? Round to 3 sig figs and put your answer in scientific notation (e.g. 6.11E14). (note: the velocity of light is 3.0E8 m/s) Hz​

Answers

Answer:

439.6 THz

Explanation:

A 0.0400 kg meter stick is placed on a thin rod at the 30.0 cm mark. What is the minimum mass required to be placed on the 0.00 cm mark on the stick to maintain equilibrium?

Answer in kg

Answers

The minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.

To maintain equilibrium, the torques acting on the meter stick must balance each other. The torque is given by the formula:

τ = r * F * sin(θ)

where τ is the torque, r is the distance from the pivot point to the point where the force is applied, F is the force applied, and θ is the angle between the force vector and the lever arm.

In this case, the meter stick is in equilibrium when the torques on both sides of the pivot point cancel each other out. The torque due to the weight of the meter stick itself is acting at the center of mass of the meter stick, which is at the 50.0 cm mark.

Let's denote the mass to be placed on the 0.00 cm mark as M. The torque due to the weight of M can be calculated as:

τ_M = r_M * F_M * sin(θ)

where r_M is the distance from the pivot point to the 0.00 cm mark (which is 30.0 cm), F_M is the weight of M, and θ is the angle between the weight vector and the lever arm.

Since the system is in equilibrium, the torques on both sides of the pivot point must be equal:

τ_M = τ_stick

r_M * F_M * sin(θ) = r_stick * F_stick * sin(θ)

Substituting the given values:

30.0 cm * F_M = 20.0 cm * (0.0400 kg * 9.8 m/s^2)

Solving for F_M:

F_M = (20.0 cm / 30.0 cm) * (0.0400 kg * 9.8 m/s^2)

F_M = 0.0264 kg * 9.8 m/s^2

F_M = 0.25872 N

Finally, we can convert the force into mass using the formula:

F = m * g

0.25872 N = M * 9.8 m/s^2

M = 0.0264 kg

Therefore, the minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.

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Tom weighs 830 N here on Earth. His suit that he will wear on the moon has a mass of 50 kg. The acceleration due to gravity is 9.81 m/s2 on Earth and 1.67 m/s2 on the moon. What would be the total weight of Tom in his moon suit when he is on the moon?224 N141 N0 N467 N

Answers

Given

Tom weighs 830 N here on Earth

Suit has a mass of 50 kg

g = 9.81 m/s2

gm = 1.67 m/s2

Procedure

First let's calculate Tom's mass with the help of the earth's acceleration.

\(\begin{gathered} W=mg \\ m=\frac{W}{g} \\ m=\frac{830N}{9.81m/s^2} \\ m=84.60kg \end{gathered}\)

Now let's calculate Tom's weight on the moon as the sum of his weight plus the weight of his suit.

\(\begin{gathered} W=(84.6+50)\cdot1.67 \\ W=224.8N \end{gathered}\)

The answer would be 224 N

Answer: 224N

Explanation: Hope this was helpful

Question 11 of 29
According to Newton's second law of motion, how much force will be required
to accelerate an object at the same rate if its mass is doubled?
A. Twice the amount of force will be required.
B. No change in the amount of force is needed.
C. Half the amount of force will be required.
D. Four times the amount of force is needed.

Answers

The force is directly proportional to the acceleration hence, at twice the amount of force will be required.

Newton's second law;

The Newton's second law of motion states that the rate of change of momentum is directly proportional to the impressed force. From this law we obtain that F = ma

Since the force is directly proportional to the acceleration, at constant mass, twice the amount of force will be required.

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which of the following is not a good working habit in doing an embroidery

Answers

Answer:

Where is following ??

Post proper Ques

How does work affect energy between objects so it can cause a change in the form of energy?
O Work transfers energy.
O Work changes energy.
O Work increases energy.
O Work decreases energy.

Answers

Answer:

Work transfers energy

Explanation:

Work can affect energy by transfering energy between objects to result to a change in the amount and form of energy

A person walks 15.0 m in 5.00 s and then
walks 12.0 m in 10.00 s. What is the
average speed of the person?

Answers

Answer:

Explanation:

Given:

D₁ = 15.0 m

t₁ = 5.00 s

D₂ = 12.0 m

t₂ = 10.00 s

___________

V - ?

The average speed of the person:

V =(D₁ +D₂) / (t₁ + t₂)

V =(15.0 + 12.0) / (5.00 + 10.00) = 27.0 / 15.00 ≈ 1.8 m/s

Describe 3 methods how asteroids can be deflected to protect Earth?

Answers

Answer:

atmosphere, gravitational pull, magnetic field

Explanation:

the astroids burn up in the atmosphere, gravitational pull alters the path of the astroids, and the magnanetic field deflects them of path.

When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, e = -1.60 × 10-19 C, 1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg)
(a) What is the work function of the metal, in eV?
(b) What is the maximum speed of the ejected electrons?

Answers

The work function of the metal is found to be 1.13eV and the speed of the ejected electrons is found to be 7.8 x 10⁵ m/s.

The wavelength of the light used for illumination is 437 nm.

The stopping potential is given to be 1.67V.

The required values are also given,

(a) The work function is found as,

Ve + W = E

E is the energy of the light,

V is the stopping potential,

W is the work function,

Putting values,

1.67eV + W = 1240/437eV

W = (2.8- 1.67)eV

W = 1.13eV.

The work function of the metal is 1.3eV.

(b) The maximum speed of the ejected electrons,

Kinetic energy = stopping potential

1/2mv² = 1.67 eV

v² = 1.67 x 1.67 x 10⁻¹⁹ x 2/9.1 x 10⁻³¹

v₂ = 6.1 x 10¹¹ m/s

v = 7.8 x 10₅ m/s.

So, the speed of the electron is 7.8 x 10⁵ m/s.

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Two bacteria are next to each other moving in the same direction. One moves with an initial velocity of 20 μm/s, accelerating at a rate of 5 μm/s2. The other starts with a velocity of 60 μm/s and is decelerating at a rate of 2 μm/s2. 1 μm=10-6 m.
(a) Find the time and position at which the bacteria meet again for an epic battle

I just started 1-D Kinematics, stuff like this just confuses me. I'd more so like the "how to do" rather than just the answer so I can still learn.

Answers

We want to find the motion equations for two bacteria, and use these to see when the two bacteria will meet again.

We will see that the bacteria meet again after 26.67 seconds.

Let's call bacteria number 1 at the one that moves with an initial velocity of 20 μm/s and that accelerates at 5 μm/s^2.

Remember that the acceleration is the rate of change of the velocity, then the velocity equation of this bacteria is:

\(v_1(t) = (5 \mu m/s^2)*t + 20 \mu m/s\)

The position equation is given by the integration of the above equation:

\(p_1(t) = (1/2)* (5 \mu m/s^2)*t^2 + (20 \mu m/s)*t + p0\)

Where p0 is the constant of integration, this is the initial position of the bacteria number one. We can define this equal to zero, because we can decide where the zero of our axis is.

\(p_1(t) = (1/2)* (5 \mu m/s^2)*t^2 + (20 \mu m/s)*t\)

Similarly, for the other bacteria we can write the equations:

\(v_2(t) = (-2 \mu m/s^2)*t + 60 \mu m/s\)

Again we integrate to get the position equation:

\(p_2(t) = (1/2)* (-2 \mu m/s^2)*t^2 + (60 \mu m/s)*t\)

a) We want to see when the bacteria meet again, then we just need to solve:

\(p_1(t) = p_2(t)\)

\((1/2)* (5 \mu m/s^2)*t^2 + (20 \mu m/s)*t = (1/2)* (-2 \mu m/s^2)*t^2 + (60 \mu m/s)*t\\\\(1/2)*(5 \mu m/s^2)*t^2 + (1/2)*(2 \mu m/s^2)*t^2 + (20 \mu m/s)*t - (60 \mu m/s)*t = 0\)

We will get a quadratic equation, simplifying the above we get:

\((1.5 \mu m/s^2)*t^2 - (40 \mu m/s)*t = 0\\\\(1.5 \mu m/s^2)*t - (40 \mu m/s) = 0\\\\(1.5 \mu m/s^2)*t = (40 \mu m/s) \\\\t = (40 \mu m/s)/(1.5 \mu m/s^2) = 26.67s\)

We can conclude that the bacteria will meet again after 26.67 seconds.

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