The acceleration of a particle is given by a = c1 + c2v, where a is in millimeters per second squared, the velocity v is in millimeters per second, and c1 and c2 are constants. If the particle position and velocity at t = 0 are s0 and v0, respectively, determine expressions for the position s of the particle in terms of the velocity v and time t.

Answers

Answer 1

The expression for the position of the particle in terms of velocity and time is given as, s = vt

The given expression:

[tex]a = c_1 + c_2v[/tex]the unit of a = mm/s²the velocity, v = mm/sc₁ and c₂ are constantthe position of the particle at time, t = 0, is s₀ and v₀

To find:

The expression for the position s of the particle in terms of the velocity v and time t

Determine the value of the constants from second equation of motion given as:

[tex]s = vt + \frac{1}{2}at^2\\\\substitute \ the \ given \ value \ of \ a\\\\s = vt + \frac{1}{2}(c_1 + c_2v)t^2\\\\s = vt + \frac{1}{2} c_1 t^2 + \frac{1}{2} c_2vt^2\\\\divide \ through\ by \ t^2\\\\\frac{s}{t^2} = \frac{v}{t} + \frac{1}{2} c_1 + \frac{1}{2} c_2v\\\\multiply \ through \ by \ 2\\\\\frac{2s}{t^2} = \frac{2v}{t} + c_1 + c_2v\\\\when \ t = 0\\\\0 = 0 +c_1 + c_2v\\\\c_1 + c_2v = 0\\\\from \ the \ original \ equation;\\\\s = vt + \frac{1}{2} (c_1 + c_2v)t^2\\\\[/tex]

[tex]s = vt + \frac{1}{2}(0)^2\\\\s = vt[/tex]

Thus, the expression for the position of the particle in terms of velocity and time is given as, s = vt

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Related Questions

An automobile starts at rest and accelerates at 3.5 m/s/s after a traffic light turns green. How far will it have gone when it is traveling at 25 m/s?

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Please find attached photograph for your answer. Please do comment whether it helped you or not

iii A load of 2.5 N is hung on the spring.
1. What does the letter N stand for?
[1]
2. Use the graph to estimate the overall length in mm of the spring when 2.5 N is hanging from it. [2]
[Cambridge IGCSE Physics 0625/22 Question 2, October/November, 2010)

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N stands for Newton
2- upload the graph..

suppose you start with an initial velocity of 10 m/s and have an acceleration of -2m/s. what is your final velocity after 9 seconds?

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Please find attached photograph for your answer. Please do comment whether it is useful or not

what is inertia? what are the relations between mass and inertia​

Answers

Answer:

Inertia is the tendency of an object to continue in uniform motion or remain in its state of rest. Mass is a measure of inertia,so the more huge the mass of an object is the more inertia it has.

Inertia is the tendency of an object to resist a change in its motion. Because of inertia, a resting object will remain at rest, and a moving object will keep moving. Objects with greater mass have greater inertia.

A bicyclist is traveling at +25m/s when he begins to decelerate at -4m/s2. How fast is he traveling after 5 seconds

Answers

Answer:

+5m/s

Explanation:

When doing the math we figure out that e is going to be slowing down at -4m/s² for 5 seconds. In total he is slowing down -20m/s which we take from the total speed of +25m/s to get his current new speed.

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

A. Kinetic energy is a form of mechanical energy, while gravitational potential energy isn't.
B. Gravitational potential energy is a form of mechanical energy, while kinetic energy isn't.
C. Any object that has motion has potential energy, while any object not in motion but with the potential to do work has kinetic energy.
D. Any object that has motion has kinetic energy, while any object not in motion but with the potential to do work has potential energy.

Answers

Answer:

D) Both parts are true.

Hey there, hope my answer helps :)

Answer: D) Any object that has motion has kinetic energy, while any object not in motion but with the potential to do work has potential energy.

In your own words, provide two examples of scientific data that scientists use to explain how the Big Bang could
have been the birth of the Universe.

Answers

Explanation:

One example of how the big bang could have been the birth of the universe is the expansion of it... (Expand on it) (It says in your own words)

A bus travels 6km east and then 8km south. The magnitude of the bus’s resultant displacement is _ km

Answers

Hey there! Here's your answer:

10 km

Here's why:

The bus's displacement has two components, a number of km and the direction of the final position from the initial position.

The bus's displacement is the hypotenuse of the triangle, 10 km southeast of the initial position.

But southeast is only a rough estimate of the direction.

The tangent of the angle is 6/8 or .75, so the amount of angle to the east of south is 37 degrees.

South (180 degrees) minus 37 degrees is 143 degrees.

The car’s displacement is more accurately called 10 km in a direction of 143 degrees from the initial point.

Have a good day!

Group 2 elements have two valence electrons. Which kind of bond will they most likely form, and why?(1 point)

A covalent bond is likely because they want to share those two valence electrons in order to become stable.

An ionic bond is likely because they will want to give away two valence electrons in order to become stable.

An ionic bond is likely because they are metals and will want to bond with nonmetals.

A metallic bond is likely because they are metals and can bond with other metals.

Answers

Answer:

An ionic bond is likely because they will want to give away two valence electrons in order to become stable.

Considering the octet rule and the definition of ionic bond,   the correct option is the second option: "An ionic bond is likely because they will want to give away two valence electrons in order to become stable."

Consider first the octet rule, which states that atoms combine or form ions with the goal of obtaining 8 electrons at their last level. In this way, an electronic configuration similar to that of the closest noble gas in the periodic table is reached. This happens because this configuration, of full electronic level, is very stable from the energy point of view

On the other hand, an ionic bond is a type of chemical bond that occurs when one atom gives up an electron to the other, in order for both to achieve electronic stability.

This union normally occurs between metal and nonmetal elements with different electronegativity, which means that the elements have different capacity to attract electrons. In general, metal elements are willing to donate an electron while nonmetals are willing to receive it.

In summary, an ionic bond is produced between metallic and non-metallic atoms, where electrons are completely transferred from one atom to another. During this process, one atom loses electrons and another one gains them, forming ions. Usually, the metal gives up its electrons forming a cation to the nonmetal element, which forms an anion.

Finally,  the correct option is the second option: "An ionic bond is likely because they will want to give away two valence electrons in order to become stable."

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đo cường độ dòng điện bằng dụng cụ gì

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Answer:

Explanation:

Dhdhfhfjjfjffj

What do you notice about where the independent and dependent variables are located on each hypothesis above?!

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Answer:

sorry

sorryndd

&#

8383

48484

8484

4848844

44 the 48844

48484848

4

Why is the sun considerad as the main source of energy?​

Answers

Answer:

The sun is considered as the main source of energy since it is the source of nearly all the earth's energy. Plants produce food using sunlight, and the food we get from plants and animals also has its primary sunlight source.

Hoped it helps you.

Answer:

It is because it supplies most of our energy that we use today, directly or indirectly. It radiates light and heat or solar energy, which makes it possible to exist life on earth.

Define upstroke and downstroke?

Answers

Answer:

The upstroke is a mechanism that helps to raise the plunger and downstroke helps to help lower the plunger. On the up-stroke of the plunger, the lower valve opens and the upper valve is closed. Whereas, on the downstroke, the lower valve closes and the upper one opens.

Need help ASAP!!! Need graphs drawn and the answers to the question on top of each table

Answers

Answer:

1) 8s

2).8cm/s/s

3)3.5?

Explanation:

not sure about answer 3 FYI

Can someone please answer this real quick:
Who has the greater velocity, an astronaut who has just completed an orbit of the Earth or you when you have just traveled from home to school? Explain.

Answers

Answer:

An astronaut have greater velocity.

Which option is a microscopic property that helps determine whether or not two substances will dissolve with each other? (1 point)

volume

polarity

molecular mass

state of matter

Answers

Answer:

The answer is polarity

Answer:

B: Polarity

Explanation:

6. What type of stretching would require you to hold a position for a period of time, like doing a split for two minutes and breathing into the pose? h short-term stretching dynamic stretching static-active stretching ballistic stretching​

Answers

The answer would be C: Static- Active Stretching

The answer is C: static-active stretching

A person is pushing a book lying on a table. Identify the different forces that act on
the book and hence mark their directions.

Answers

Explanation:

There are two forces acting upon the book. One force - the Earth's gravitational pull - exerts a downward force. The other force - the push of the table on the book (sometimes referred to as a normal force) - pushes upward on the book.

There are mainly 3 forces which acts on a book.

Listed below are the forces and their points:-

Earth's Gravitational force of attraction- Usually, we may not consider or notice this force, but when a book falls, we understand this, because the book falls due to this gravitational force.

Force exerted on book while pushing it- While we push a book, we apply Push Force, due to which the book moves on the pushing it on a table.

Frictional Force- We notice that while pushing a book, it does not continuously move in motion. At a certain distance, this Frictional force increases and therefore, the book comes to a halt.

Location- Opposite of exerted force in all directions

a hot metal block is placed into 50g of water in an insulated container the water increases in temperature from 20c to 32c the specific heat capacity of water is 4200j/kgk calculate the quantity of heat energy supplied to the water from the metal​

Answers

Answer:

25,000 joules

given the formula

Q=Mc(final temperature - initial temperature)

M=50 grams convert to kilogram 0.5

c= 4200 j/kg/k

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Which two elements in the list would bond together based on their ionic charges? (30 points) potassium and iodine potassium and iodine potassium and neon potassium and neon calcium and neon calcium and neon calcium and potassium

Answers

Answer: Ionic bonds usually occur between metal and nonmetal ions.

Explanation:

4.You decide to flip a coin to determine whether to do your physics or English homework first. The coin is flipped
straight up.
a. What is the velocity of the coin at the top of its trajectory?
b. If the coin reaches a high point of 0.25 m above where you released it, what was its initial speed? c. If you
catch it at the same height as you released it, how much time did it spend in the a

Answers

For the coin that is flipped straight up we have:

a. The velocity at the top of its trajectory (at the maximum height) is 0.

b. When it reaches a high point of 0.25 m above where it was released, the initial velocity is 2.21 m/s.

c. The time that the coin spends on the air is 0.44 s.

a. The velocity of the coin at the top of its trajectory is zero because in the maximum height the ball will stop and then will start to move down.

b. When the coin reaches a high point of 0.25 m above where it was released, the initial velocity can be calculated as follows:

[tex] v_{f}^{2} = v_{0}^{2} - 2gh [/tex]

Where:

[tex] v_{f}[/tex]: is the final velocity = 0 (at the maximum height)

[tex] v_{0}[/tex]: is the initial velocity =?

g: is the acceleration due to gravity = 9.81 m/s² (it is negative because its direction is the opposite to the direction of motion of the coin)

h: is the height = 0.25 m

Hence, the initial velocity of the coin is:

[tex] v_{0} = \sqrt{2gh} = \sqrt{2*9.81 m/s^{2}*0.25 m} = 2.21 m/s [/tex]

c. The time that the coin spends on the air is given by the sum of the rise time and the fall time:

Rise time

[tex] t_{s} = -\frac{v_{f} - v_{0}}{g} = -\frac{0 - 2.21 m/s}{9.81 m/s^{2}} = 0.22 s [/tex]

Since the ball is caught at the same height as it was released, the rise time is the same as the fall time, so the total time is:

[tex] t = 0.22 s*2 = 0.44 s [/tex]  

Therefore, the coin spend 0.44 seconds in the air.

You can find another example of initial and final velocity here: https://brainly.com/question/13275688?referrer=searchResults

I hope it helps you!                      

what is pulley? How does it help in lifting weight?​

Answers

Hey there!

A pulley is a "system" that has a rope attached to carry heavy materials off the ground. Once you pull the rope, the heavy item will be carried.

Hope this helps!

Have a great day!

Using a pulley greatly multiplies the force of your physical efforts. A pulley with one wheel allows you to reverse the direction of your lifting force by pulling down on a rope (that's looped over the wheel), lifting your weight. ... The more wheels your rope can loop around, the more weight you will be able to lift.

True or false: Venus is the hottest planet

Answers

True. Venus is the hottest planet in the solar system. Venus is the second closest planet to the sun, Mercury is first.

d) All of the
The volume of solid is measured in
a) Litters
b) Grams
c) Cubic centimeters
d) All of the above

Answers

a) Liters ... It COULD be.  The "Liter" is a perfectly good unit of volume, but it's typically used for liquids and gases, not solids.

b) Grams ... definitely NOT.  The "gram" is a unit of mass, not volume.

c) Cubic centimeters ... Yes. This is a unit of volume.

d) All of the above ... No.

The volume of solid is measured in

a) Litters

b) Grams

c) Cubic centimeters

d) All of the above

2246.7 milliseconds to seconds

Answers

Answer:

2.2467

Explanation:

Divide the value of time by a thousand

Complete the table below. Place an X in the appropriate box to
indicate the type of each measurement unit.

Answers

Answer:

Gram per centimeter cubed: Derived Unit

Decimeter: SI Unit

Liter: Derived Unit

Meter Cubed: Derived Unit

Kilogram: SI Unit

Explanation:

Look in Quizlet

It is easy to cut curry by a sharp knife,why?

Answers

The sharper the knife, the less effort is required to cut the item.

9. A train is moving with the velocity of 45 km Ihro The osives applies brace and the train gets stopped in 6 second. Now, calculate as distance covered by the train before coming to
the rest.​

Answers

((12.5 + 0)/2)(6)
D= 37.5 m
I think it’s 37.5 m
I basically just converted 45 km/h to m/s then used the formula d =( (initial velocity + final velocity)/ 2)(t)

When is the pressure of the man on the ground more – lying position or standing position? Explain.

Answers

The man on the ground in standing position has more pressure. This is because when he stands, only his legs are in contact with the ground. While lying, his body is more in contact with the ground, therefore, he exerts less pressure.

To the point, a manin standing position on the ground had more pressure.

More is the area of contact, less is the pressure efforted.

Thank you...

A crowbar having the length of 1.75 m is used to balance a load of 500 N. If the distance between the fulcrum and the load is 0.5 m, calculate: (Friction is neglected] i. effort applied to balance the load
ii. MA
iii. VR
iv. efficiency​

Answers

Answer:

L=load LA=load arm

E=effort EA=effort arm

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