Why do you lurch forward in a bus that suddenly slows? why do you lurch backward when it picks up speed? what law applies here?

Answers

Answer 1
The law applied here is Newton's first law, also known as, law of inertia.
This law states that: A body will retain its state of rest or motion unless acted upon by an external force.

If you are moving and the bus suddenly stops, your body will lurch forward trying to retain its state of motion until it comes to rest and changes its state by the external force acted on it.

If you are at rest and the bus suddenly moves, your body will lurch backwards trying to retain its state of rest and opposing the force of motion until it is forced to change its state by this force.
Answer 2

Final answer:

You lurch forward in a bus that suddenly slows due to Newton's First Law of Motion, or the law of inertia, which suggests an object in motion stays in motion unless acted on by an unbalanced force. When the bus accelerates, inertia causes you to feel pushed back as your body prefers to remain at rest. Understanding this law helps in recognizing the importance of safety measures like seatbelts.

Explanation:

Understanding Movement in a Bus: Newton's First Law of Motion

When a bus suddenly slows down, you lurch forward because of Newton's First Law of Motion, also known as the law of inertia. This law states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Since your body wants to keep moving at the same speed the bus was going before it slowed down, you lurch forward when the bus decelerates.

Similarly, when the bus speeds up, you might feel like you are being pushed back into your seat. This is again due to the law of inertia. Your body wants to remain at its state of rest (or moving at a constant speed if the bus was already moving), so when the bus accelerates, it creates a temporary imbalance, making you feel pushed back.

Using seatbelts or holding onto something stable inside the bus can counteract these effects by providing the necessary force to keep you in place, thereby preventing injury and ensuring safety.

Why Understanding Newton's First Law is Important

The applications of Newton's First Law are seen in everyday life, not just in theoretical physics. It explains a wide range of phenomena, from why it's crucial to wear a seatbelt to the importance of headrests in preventing whiplash injuries. Understanding these principles can help improve personal safety and awareness in moving vehicles.


Related Questions

A compound microscope uses A. a convex mirror and a lens to enlarge an image. B. a mirror that flips up to let light through the lens. C. two convex lenses to magnify a small object. D. a mirror to reflect an image of a small object.

Answers

Answer:

Option (c)

Explanation:

A compound microscope is an optical instruments which can use to see the highly magnified image of very tiny objects.

It consists of two convex lenses.

1. Objective lens: It is a convex lens of short focal length and of short aperture.

It is located at the object side.

2. Eyepiece: It is a convex lens of comparatively large focal length and of large aperture.

It is located at the side from where we can see the image of the object.

Consider a sample of gas in a container on a comfortable spring day in chicago, il. the celsius temperature suddenly doubles, and you transfer the gas to a container with twice the volume of the first container. if the original pressure was 12 atm, what is a good estimate for the new pressure?

Answers

To solve this problem, we must first assume that the gas acts like an ideal gas so that we can use the ideal gas equation:

 P V = n R T

where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the absolute temperature

 

Assuming that the number of moles is constant, then we can write all the variables in the left side:

P V / T = k            where k is a constant (n times R)

 

Equating two conditions or two states:

P1 V1 / T1 = P2 V2 / T2

We are given that V2 = 2 V1 therefore

P1 V1 T2 = P2 (2V1) T1

P1 T2 = 2 P2 T1

 

Additionally we are given that the temperature in Celsius is doubled, however in the formula we use the absolute temperature in Kelvin, therefore:

T1 (K) = T1 + 273.15

T2 (K) = 2T1 + 273.15

and P1 = 12 atm

 

Substituting:

12 (2T1 + 273.15)  = 2 P2 (T1 + 273.15)

P2 = 6 (2T1 + 273.15) / (T1 + 273.15)

 

Assuming that a nice spring day in Chicago has a temperature of 15 Celsius, therefore:

P2 = 6 (2*15 + 273.15) / (15 + 273.15)

P2 = 6.312 atm

Final answer:

When the Celsius temperature of a gas in a container doubles, and the gas is transferred to a new container with twice the original volume, the new pressure of the system can be computed using the combined gas law.

Explanation:

This Physics question involves understanding how gas laws work. Given the scenario where the Celsius temperature doubles and the gas is transferred to a container functioning at twice the original volume, several gas laws come into play such as Boyle's law and Charles's law, which relate pressure, volume, and temperature.

Let's look at Charles's law first. It states that volume is proportional to the absolute temperature, assuming constant pressure. From this law, we know that the gas's volume will increase when the temperature doubles. Meanwhile, according to Boyle's law, at constant temperature, the pressure and volume of a gas are inversely proportional. In other words, if you double the volume of the container, the pressure will be halved.

The new pressure will be derived by applying the combined gas law which factors the changes in both temperature and volume. Using Combined Gas law which is (P1V1)/T1 = (P2V2)/T2 where the pressures are in atmospheres, volumes in liters, and temperature in Kelvin, you can solve the new pressure in the system.

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What should you do immediately if a boat motor catches fire?

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 If a boat motor catches fire, you should immediately shut off the fuel supply, and try to put out the fire with an extinguisher. It is very important to have fully charged fire extinguishers on hand. As soon as you notice the fire activate the extinguisher and do not panic. In order to prevent fire remember to clean the bilges often and maintain proper gear stowage, make sure short-tie cables are properly connected...
Final answer:

In the event of a boat motor catching fire, prioritize personal safety by ensuring lifejackets are worn, cut off the fuel source if possible, and use a fire extinguisher at the fire's base. If necessary, evacuate the boat.

Explanation:

The immediate actions if a boat motor catches fire should be focused on ensuring personal safety and then attempting to extinguish the fire. Firstly, ensure everyone on board is wearing a lifejacket for safety. Secondly, turn off the fuel source if possible to prevent the fire from spreading. Following this, use a fire extinguisher if one is available, aiming it at the base of the fire. Be cautious and prioritize evacuating the boat if the fire becomes uncontrollable.

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How many series-connected cells does a typical 12 V storage battery contain?

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does anyone know the answer?

An interstate highway loop meets the primary route at both ends. the first digit of its route number is always

Answers

The first number indicates that the highway is an  East - West or South -North highway. East - West always have an even number and increasing from East going to West while odd numbers are designated to South - North highways with the same incremental pattern. 

The first digit of an interstate highway loop route number that meets the primary route at both ends is always an odd number, indicating it is a spur or a loop off of the main interstate route.

The question relates to the numbering system of interstate highways in the United States. If an interstate highway is a loop that reconnects with the primary interstate route, the first digit of its route number will always be an odd number.

Specifically, these loops are usually three-digit numbers with the last two digits matching the main interstate and the first digit signifying it is a loop or spur.

For example, Interstate 495 would be a loop off of Interstate 95.

Which is an homogeneous mixture?
A) a jar of mixed nuts
B) a bowl of salsa
C) a slice of cheese
D) a bowl of fruit salad

Answers

So which of those items listed above you cannot separate into different parts?
Slice of cheese, I think, because you can not break it up into its original contents. You can do it with the other ones though.

Which statement best describes scientific theories? Select one: A. Scientific theories are what laws are called before they are proven. B. Scientific theories attempt to explain why natural events occur. C. Scientific theories are based on opinions. D. Scientific theories describe natural events.

Answers

C. Scientific theories are based on opinions. 

Laws are not based on opinions. They are proven.
I think A fits the best, coz a theory is capable of producing experimental predictions. and are based on postulates.

A brass wire is to withstand a tensile force of 350N without breaking? A brass wire is to withstand a tensile force of 350N without breaking.

Answers

Final answer:

Tensile force refers to the stretching force experienced when forces pull on both ends of a material like wire. Equal and opposite forces lead to tension that is equally distributed across the material, as seen in Figure 5.24. The example of a tightrope walker underscores that most of the tension resides in the wire itself rather than supporting the walker's weight.

Explanation:

In Physics, the term tensile force is used to describe the stretching force a material experiences when forces are applied on opposing sides, such as a wire being pulled on both ends. In your case, the brass wire has to withstand a tensile force of 350N without breaking.

Considering the principles behind tensile force, the concept of equal and opposing forces holds significant value as depicted in Figure 5.24. This is due to Newton's third law which states that every action has an equal and opposite reaction, ensuring that the tension in the wire is equal throughout. If the tension at one spot in the brass wire could handle 350N, this could be applied across the entire wire.

The tightrope example illustrates a situation where the tensile force is employed. However, not all this tension is used to support the weight of the tightrope walker as the horizontal components are in opposite directions and cancel out. Hence, most of the tension resides in the wire itself.

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Before passing another vehicle, the first major step is to ________.

Answers

Answer:Explained

Explanation:

Before Passing the another vehicle

make sure it is safe to do it.For instance a single lane road make sure the lane is clear for sufficient distance.Make sure to honk before passing another vehicleMake sure no other vehicle is overtaking you by checking in Rear view mirror.

Before passing another vehicle, the first major step is to ensure proper signaling and check blind spots. Signaling is crucial as it communicates your intention to the drivers behind and ahead of you.

Activating the turn signal in the direction you plan to pass alerts others of your intentions. Checking blind spots is equally important to ensure there are no vehicles present in the adjacent lanes that may be hidden from your mirrors.

This step involves a quick glance over your shoulder to verify that the lane is clear and safe for passing. Only after completing these steps should you proceed with passing the vehicle.

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The national high magnetic field laboratory holds the world record for creating the strongest magnetic field. for brief periods of time, their largest multi-shot pulsed magnet can produce magnetic fields in excess of 85 t. to see if such a strong magnetic field could pose health risks for nearby workers, calculate the maximum acceleration the field could produce for na ions (of mass 3.8 × 10-26 kg) in blood traveling through the aorta. the speed of blood is highly variable, but 45 cm/s is reasonable in the aorta

Answers

Newton’s 2nd law states that Force is equal to the product of mass (m) and acceleration (a):

F = m a                                  ---> 1

While in magnetic forces, force can also be expressed as:

F = q v B                               ---> 2

where,

q = total charge

v = velocity = 45 cm / s = 0.45 m / s

B = the magnetic field = 85 T

First we solve for the total charge, q:

q = 3.8 × 10^-23 g (1 mol / 23 g) (6.022 × 10^23 electrons / mol) (1.602 × 10^-19 C / electron)

q = 1.594 × 10^-19 C

 

We equate equations 1 and 2 then solve for acceleration a:

m a = q v B

a = q v B / m

a = [1.594 × 10^-19 C * 0.45 m / s * 85 T] / 3.8 × 10-26 kg

a = 160,437,862.2 m/s^2

 

Therefore the maximum acceleration of Na ions is about 160 × 10^6 m/s^2.

Answer:

[tex]a = 1.61 \times 10^8 m/s^2[/tex]

Explanation:

Force due to magnetic field on the position of Na+ ions is given as

[tex]F = qvB[/tex]

here we know that

[tex]q = 1.6 \times 10^{-19} C[/tex]

[tex]v = 45 cm/s[/tex]

[tex]B = 85 T[/tex]

now the force will be given as

[tex]F = (1.6 \times 10^{-19})(0.45)(85)[/tex]

[tex]F = 6.12 \times 10^{-18} N[/tex]

now we know that acceleration is given as

[tex]a = \frac{F}{m}[/tex]

[tex]a = \frac{6.12 \times 10^{-18}}{3.8 \times 10^{-26}}[/tex]

[tex]a = 1.61 \times 10^8 m/s^2[/tex]

Therefore, the force that the sun exerts on earth is ____ that earth exerts on the sun.

Answers

The gravitational force between earth and the sun

F = (G*Me*Ms)/Des

So exerting force will be same on each other.

Whether or not you actually exercise each week is greatly influence by _____.

Answers

Whether or not you actually exercise each week is greatly influence by your motivation. You can lose face fat just by living a healthy lifestyle. A healthy lifestyle involves exercising AND eating the right amount of foods. If you are busy enough to exercise, at least walk for 30 minutes a day. When eating a balanced diet, follow the food pyramid. Eat more at the bottom level and eat less at the top level. Avoid foods that zero nutrients such as ice cream, chocolates, and cakes. Stay away from salty foods too because it retains water into your body making you feeling bloated all the time. This is an indicator that your body could not digest the food properly in your system.

Answer:

Whether or not you actually exercise each week is greatly influence by your mindset.

Explanation:

Mindset refers to the way you organize your thoughts and decide to face everyday situations. The way you reflect on a particular situation, and especially how you choose to act upon that personal analysis, can determine your success or failure. So if you can work out each week without fail, it is a big influence by your mindset.

A kayaker needs to paddle north across a 100-m-wide harbor. the tide is going out, creating a tidal current that flows to the east at 2.0 m/s.the kayaker can paddle with a speed of 3.0 m/s.

a. in which direction should he paddle in order to travel straight across the harbor?

b. how long will it take him to cross?

Answers

Refer to the diagram shown below.

Part a.
In order for the kayaker to travel straight north across the river, the kayak should travel at angle θ west of north.
By definition,
sinθ = 2/3   =>  θ = sin⁻¹(2/3) = 41.8°.

Answer: The kayaker should paddle at an angle of about 42° west of north.

Part b.
The resultant traveling velocity is
  v = 3 cosθ
     = 3cos(41.8°)
     = 2.236 m/s

The time required to cross the river is
t = (100 m)/(2.236 m/s)
  = 44.7 s

Answer: It will take the kayaker about 45 s to cross.

The kayaker needs to paddle at an angle of 41.81º opposite to the current so that he can travel straight across the harbor, and it will take him 44.73 seconds to cross.

Further explanation

This is a 2-dimensional problem, since the kayaker can move in 2 dimensions over the river. For our study, we will model how does the kayaker move in the direction transversal to the river (meaning across the river), and longitudinal to the river (meaning along the river).

On the first part of this problem, we're asked to compute the direction at which the kayaker needs to paddle so that he moves only transversal to the river flow. Since the river flow has a velocity of 2 meters per second on the longitudinal direction, then the kayaker must have a velocity opposite to the river flow on the longitudinal direction of 2 meters per second.

Since he can paddle with a speed of 3 meters per second, we can make a right triangle (check the attached figure), and through trigonometry find the angle at which he needs to paddle against the river to only move in the transversal direction. Therefor we can write:

[tex]sin(\theta) = \frac{2}{3}[/tex]

Therefor [tex]\theta[/tex] is 41.81 degrees. This means that the kayaker moves across the river with a velocity 2.24 meters per second. With this velocity and the width of the river, we can easily find that the time it will take to cross is 44.73 seconds.

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Right triangle, velocity, sine of angle.

Which of the following statements most accurately differentiates potential and kinetic energy?
   

Answers

Kinetic is flowing energy while potential is stored energy
It's really hard to decide without seeing the statements.

When a plant is entering the calvin cycle of photosythesis______.

light energy is required to proceed
light energy is not required to proceed
light energy cannot be present to proceed
light energy and stored energy is required to proceed

Answers

The Calvin cycle refers to the light-independent reactions in photosynthesis that take place in three key steps. Although the Calvin Cycle is not directly dependent on light, it is indirectly dependent on light since the necessary energy carriers (ATP and NADPH) are products of light-dependent reactions.

So basically it indirectly needs the light, even it's called light-independant reaction.

So the answer is the last one.

Plants do not need light energy during the Calvin Cycle of photosynthesis.

When a plant is entering the calvin cycle of photosynthesis, light energy is not required to proceed. The Calvin cycle, also known as the light-independent reactions, utilizes energy stored during the light-dependent reactions to convert carbon dioxide into glucose.

A man drops a rock into a well. (a) the man hears the sound of the splash 2.40 s after he releases the rock from rest. the speed of sound in air (at the ambient temperature) is 336 m/s. how far below the top of the well is the surface of the water? (b) what if? if the travel time for the sound is ignored, what percentage error is introduced when the depth of the well is calculated?

Answers

Part (a)
Let h =  depth of water surface from the top of the well, m

Because the stone is dropped, its initial velocity is zero.
Let t₁ =  time for the stone to drop, s
Then
h = (1/2)*(9.8 m/s²)*(t₁ s)²
t₁ = √(h/4.9) s = 0.4518√h s

The velocity of sound is 336 m/s.
The time for the sound wave to travel from the water surface to the top of the well is
t₂ = h/336 m/s 

Because the time before the sound is heard is 2.4 s, therefore
t₁ + t₂ = 2.4
0.45181√h + h/336 = 2.4
Multiply through by 336.
151.8082√h + h = 806.4
h - 806.4 = -151.8082√h
h² - 1612.8h + 6.5028 x 10⁵ = 2.3046 x 10⁴h
h² - 2.4659 x 10⁴h + 6.5028 x 10⁵ = 0

Solve with the quadratic formula.
h = 0.5[2.4659 x 10⁴ +/- 2.4606 x 10⁴]
   = 24632 m or 26.5 m

Test the two answers.
When h = 24632,
   t₁ = 0.4518√(24632) = 70.9 s (Not acceptable)
When h = 26.5 m,
   t₁ = 0.4518√(26.5) = 2.3258 s, t₂ = 26.5/336 = 0.0789 s,
   t₁+t₂ = 2.4 s (CORRECT)

Answer:  h = 26.5 m

Part (b)
If travel time for the sound is ignored, then
0.4518√h = 2.4
h = (2.4/0.45118)² = 28.2 m
The percent error is 100*[(28.2 - 26.5)/26.5] = 6.42%

Answer: The error is  6.4%

Final answer:

The distance below the top of the well is 806.4 meters. When taking into account the time for sound to travel up the well, the distance is 0 meters.

Explanation:

(a) To calculate the distance to the water, we can use the formula:

Distance = Speed of Sound x Time

Distance = 336 m/s x 2.40 s

Distance = 806.4 m

(b) To calculate the distance taking into account the time for sound to travel up the well, we subtract the time for sound to travel up:

Distance = (Speed of Sound x Time) - Speed of Sound x Time for Sound to Travel Up

Distance = 336 m/s x 2.40 s - 336 m/s x 2.40 s

Distance = 0 m

Why is a steam burn more damaging than a burn from boiling water at the same temperature?

Answers

The phase change (from gas to liquid) that the steam undergoes right when it touches your skin releases a lot of energy right onto your skin so it burns a ton. The boiling water would just burn you until it reaches the same temperature as your skin.
Final answer:

A steam burn is more damaging than a burn from boiling water at the same temperature due to the release of latent heat energy when steam comes into contact with the skin.

Explanation:

A steam burn is more damaging than a burn from boiling water at the same temperature because steam carries more energy due to its phase change from water to steam. When water is heated to boiling point, it absorbs a significant amount of heat energy to change from liquid to gas. When this steam comes into contact with the skin, it releases the latent heat, causing a more severe burn.

A box of mass m slides down an inclined plane that makes an angle of φ with the horizontal. if the coefficient of kinetic friction is μk, find an expression for the acceleration of the box down the slope. the acceleration due to gravity is g.

Answers

In a force diagram set-up, we name the angle of inclination theta, g as the acceleration due to gravity. In this case, the forces acting on the box going down is the weight itself impeded by the friction between the box and the inclined plane.

The weight of the box is expressed as mg sin theta
The frictional force is expressed as the normal force times the coefficient of friction that is expressed as mu g cos theta.

By Newton's second law of motion,  F = ma = mg sin theta - mu g cos theta
Thus, a = g (sin theta - u cos theta

According to newton's second law of motion acceleration of an object depends upon the?

Answers

It depends on the force that is applied to the object.

Night vision glasses detect energy given off by objects as (2 points)
Select one:
a. ultraviolet waves.
b. radio waves.
c. microwaves.
d. infrared waves.

Answers

the answer here would be infrared waves. Hot objects and humans give off heat in the form of infrared light, thermal imaging technology in the goggles enable them to catch this light emitted by these objects 

Low sun angles result in reduced solar energy because:

Answers

Solar energy is a form of renewable energy that is harnessed using the technology of the photovoltaic cells. These cells are composed of semiconductors. When the light from the sun hits the semiconductor, the energy from the light particles, or photons, cause the electrons in the semiconductor to be 'excited'. When the electron moves across the semiconductor platforms, the electron flows, thus creating electricity.

Therefore, as much as possible, you want to capture all of the sun's light. This can be achieved when the Sun is high up the sky. But if there is low sun angle, then the concentration of the sun's energy that strike the PV cells would be lesser. 
Final answer:

Low sun angles spread sunlight over a larger area and through more of Earth's atmosphere, reducing its intensity. The Rosetta spacecraft observed this effect, receiving only 4% of the sunlight intensity experienced on Earth. Other phenomena, like solar activity and volcanic activity, can also impact solar energy on Earth's surface.

Explanation:

Low sun angles result in reduced solar energy due to a fundamental physics principle: the intensity of sunlight is spread over a larger area when it strikes the Earth at a more oblique angle. This occurs, for example, during winter when the Sun is low in the sky. As depicted in Figure 4.6, the Sun's rays spread out over a much wider area, becoming less effective at heating the ground. Moreover, when the sun is low in the sky, the sunlight must travel through more of the Earth's atmosphere, which can scatter the light, reducing the intensity of the sunlight that reaches the ground.

Another point to consider is the observed phenomenon reported by the Rosetta spacecraft at 800 million kilometres from the sun. Rosetta’s solar cells had to be specifically designed to function in these cold, low-light conditions as it receives only 4 percent of the light strength received on Earth.

However, while this explains the reduction in the intensity of solar energy at low angles, it's important to note that other phenomena, such as solar activity and volcanic aerosols, can also affect the global temperatures and solar energy received on Earth's surface.

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For thermometers to read temperatures correctly they must be

Answers

For thermometers to read temperatures correctly, they must be immersed in the substance being measured while reading the temperature. When they are taken out the substance, there is a possibility that the fluid inside would change its level due to the sudden change in the temperature. Thus, giving you an erroneous reading of the temperature. 

For the measurement of the temperatures correctly the thermometers Should Fully dipped into Fluids  So that it is dipped into the Fluids and give you Correct reading.

Further Explanation:

Explanation:

First of all we should check that the liquid in the thermometer should be at below the room temperature. If it is not below this temperature please bring its temperature below the room temperature by shaking the thermometer.

When the temperature below the room Temperature:

When the Temperature of the thermometer is below the room temperature then dipped the thermometer into the fluid of which you have to checked the temperature. Make sure that the Thermometer dipped into the fluid properly.

Difficulties:

If thermometer is not dipped properly in the fluid then the temperature of fluid should not be measured correctly an there should be an error in the measurement.

When you take off the thermometer from the fluid then the Liquid in the thermometer can be leveled down because of sudden change of Temperature of the temperature of fluid to the room Temperature.

Answer Details:

Subject: Physics

Level: High School.

Key Words:

Explanation:

When the temperature below the room Temperature:

Difficulties:

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Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of an automatic washing machine? what about the direction of the force on the water?

Answers

an outward force is exerted

The death of a star occurs when its _____ stops

Answers

energy producer ...is the answer

How would you expect energy to change her in a chemical reaction?
Energy will be increased
Energy Will be decreased
Energy will be converted into another form
Energy will be consumed

Answers

The correct answer is option (c) i.e. Energy will be converted into another form.

During a chemical reaction, energy remains unchanged, It just gets converted into another form and doesn’t increases or decreases. Excess energy is released in the form of heat, light during a chemical reaction and thus, proving the law of conservation of energy which says, energy can neither be created nor destroyed. It just gets converted from one form to another form. 

Calculate the period (T) of uniform circular motion if the velocity is 40.0 m/s and centripetal acceleration is 20.0 m/s2.

Answers

T is the time for a whole round.

centripetal acceleration = V^2/R,

20 = 40^2 / R, find R = 40^2/20 = 40*40/20 = 80 m, right?

Now, one round is L = 2*pi*R = 2*pi*80 = 160*pi

And T = L/v (distance/speed) = 160*pi/40 = 4*pi seconds, or ~ 12.57 s

The period (T) of uniform circular motion if the velocity is [tex]40.0 m/s[/tex] and centripetal acceleration is [tex]20.0 m/s^2[/tex] is approximately 8.9 seconds.

Finding the Period (T) in Uniform Circular Motion

To calculate the period (T) of an object in uniform circular motion, we need to relate the given velocity and centripetal acceleration to the formula involving period and radius.

First, let's use the centripetal acceleration formula:

[tex]|a| = |v|^2 / r[/tex]

We know:

Velocity (v) = 40.0 m/sCentripetal acceleration [tex](a) = 20.0 m/s^2[/tex]

By rearranging the formula to solve for the radius (r):

[tex]r = v^2 / a[/tex]

Now, substitute the given values:

[tex]r = (40.0 m/s)^2 / 20.0 m/s^2 = 1600 / 20 = 80 m[/tex]

Next, we use the relationship between the period and radius:

[tex]a = 4\pi^2r / T^2[/tex]

Rearranging to solve for T:

[tex]T^2 = 4\pi^2r / a[/tex]

Substitute the known values:

[tex]T^2 = 4\pi^2 * 80 / 20\\T^2 = (4 \times 9.87 \times 80) / 20 = 1583 / 20 = 79.16[/tex]

Therefore:

[tex]T = \sqrt{79.16} = 8.9 s[/tex]

A train moving at a constant speed of 55.0 km/h moves east for 35.0 min, then in a direction 55.0° east of due north for 10.0 min, and then west for 45.0 min. what is the average velocity of the train during this run? (let the +x-axis point towards the east and the +y-axis point towards the north.)

Answers

When you illustrate the problem description, the direction of distance travelled is shown in the picture. But actually, since you are asked of the average velocity, you really don't need the drawing. It is given that the constant speed is 55 km/h. Since distance is speed multiplied with time, then you only have to multiply the constant speed and the respective time so you can find the distance. The average velocity, on the other hand, is the total distance per total time travelled. So since there is a constant speed, all the terms for time will be cancelled. Therefore, the average velocity is the constant speed. But we have to add the direction, which is south so it will denote a negative sign. The final answer for average velocity is -55 km/h.

When approaching a hillcrest where you can not see the other side..?

Answers

When approaching a hillcrest where you cannot see the other side, approach the crest in the rightmost lane.
It is important to be able to see on both sides, so as to avoid possible collisions with other drivers. So, it is for the best to approach this crest using the rightmost lane, in order to drive safely.

Teresa wanted to test the effects of liquid density on the speed of sound waves. what is the dependent variable in her experiment?

Answers

Given that Teresa wanted to test how the speed of sound waves change that is the dependent variable.

The independent variable is the liquid density, which means that Teresa will vary the liquid density and then will measure the resultant liquid density.

The dependent variable is that that changes is response to a change on other variable (the independent one), that is why the dependent variable in this experiment is the speed of sound waves.

Your swimming pool is 8 ft long, 6 ft wide and 1.5 ft deep. how many gallons of water will be needed to fill it?

Answers

538 gallons of water will be needed.
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