This argument is valid because the bar is a homogeneous linear conductor, and the magnetic field around it must be constant.
What is magnetic field?A magnetic field is a region of space in which a magnetic force is exerted on any magnet, electric current, or magnetic material. It is created by an electric current, such as the electric current in a wire. It is also created by the motion of electric charges, such as those found in an electromagnet. The strength of the magnetic field increases as the electric current increases. The direction of the magnetic field is determined by the direction of the electric current.
The field at any point along the bar is proportional to the current passing through it, which remains constant for a homogeneous conductor. Therefore, the field at any point along the bar must be the same as at the midpoint, just with a larger magnitude. This implies that the average effective magnetic field along the bar is five times larger than the field at the midpoint.
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Coherent light with wavelength of 580 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is at 4.81 mm from the center of the central bright fringe. For what wavelength of light will the first-order dark fringe be observed at this same point on the screen?
Answer:
the required wavelength is 1.15815 μm
Explanation:
Given the data in the question;
The position of bright fringes [tex]y_m[/tex] on screen in double slit experiment is expressed as follows;
[tex]y_m[/tex] = mλD / d
solving for d, we substitute 1 for m
y₁ = (1)λD / d
d = λD / y₁
given that λ = 580 nm = 5.8 × 10⁻⁷ m, D = 3.00 m and y₁= y₀ = 4.81 mm = 0.00481 m
so we substitute
d = λD / y₁
d = ( 5.8 × 10⁻⁷ m × 3.00 m ) / 0.00481 m
d = 0.00000174 m² / 0.00481 m
d = 3.6117 × 10⁻⁴ m
Now, position of dark fringe [tex]y_m[/tex] on screen in double slit experiment is expressed as;
[tex]y_m[/tex] = ( m + 1/2 )λD / d
we substitute 0 for m
y₀ = ( 0 + 1/2 )λD / d
y₀ = λD / 2d
2y₀d = λD
λ = 2y₀d / D
we substitute
λ = ( 2(0.00481 m) ( 3.6117 × 10⁻⁴ m) ) / 3.0 m
λ = 1.15815 × 10⁻⁶ m
λ = 1.15815 μm
Therefore, the required wavelength is 1.15815 μm
the magnet below is cut in half. what will be the result?
Answer:
C.
Explanation:
This is what we call a permanent magnet. By the way, the magnetic phenomena were first observed about 2500 years ago near the ancient city of Magnesia, what is today Manisa, located in western Turkey, when people saw fragments of magnetized iron. So what happens if you cut a magnet in half? Well, a magnet has two ends, the first one is called a north pole or N pole while the other end is a south pole or S pole, so if you break a bar magnet, each piece has a north and south pole, no matter the size of each new bar although the smaller the piece, the weaker its magnetism. This is true because unlike electric charges, you always find magnetic poles in pairs, that is, ¡they can't be isolated! The option is C. because in the great bar the north pole is to the left while the south pole is to right.
Which lists the springs in order of increasing spring constant?
W, Y, X, Z
OW, Y, Z, X
O Z, X, Y, W
OX,Z,Y, W
Answer:
is there supposed to be a picture?
Explanation:
The correct order of the springs in increasing spring constant is: W, Y, X, Z. The correct option is A.
What is the spring constant?Spring constant, also known as force constant or stiffness, is a measure of the resistance of a spring to deformation when a force is applied to it. It is defined as the amount of force required to stretch or compress a spring by a given distance.
The formula for the spring constant is:
k = F/x
Where
k = is the spring constant,
F = is the applied force,
x =is the displacement or deformation of the spring.
The unit of spring constant is newtons per meter (N/m) in the SI system of units, or pounds per inch (lb/in) in the Imperial system.
A higher spring constant means that a spring is stiffer and requires more force to be stretched or compressed by a given distance. A lower spring constant means that a spring is more flexible and requires less force to be stretched or compressed by a given distance. The spring constant is an important property of springs, which are used in various applications, such as in suspension systems, mattresses, and mechanical watches.
Here in the Question,
In order to determine the order of increasing spring constant, we need to compare the given springs and see which one requires more force to stretch or compress.
Therefore, The correct order of the springs in increasing spring constant is: W, Y, X, Z. This is because the spring constant increases as we move from W to Z.
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This force will cause the path of the particle to curve. Therefore, at a later time, the direction of the force will ____________. This force will cause the path of the particle to curve. Therefore, at a later time, the direction of the force will ____________. have a component along the direction of motion remain perpendicular to the direction of motion have a component against the direction of motion first have a component along the direction of motion; then against it; then along it; etc.
Answer:
have a component along the direction of motion that remains perpendicular to the direction of motion
Explanation:
In this exercise you are asked to enter which sentence is correct, let's start by writing Newton's second law.
circular movement
F = m a
a = v² / r
F = m v²/R
where the force is perpendicular to the velocity, all the force is used to change the direction of the velocity
in linear motion
F = m a
where the force is parallel to the acceleration of the body, the total force is used to change the modulus of the velocity
the correct answer is: have a component along the direction of motion that remains perpendicular to the direction of motion
calculate power disspated by the element of an electric fire (heater) of resistance 30 ohms when a
current of 10 amps flows in it. if is on for 30 hours in a week determine the energy used. determine the weekly cost of energy if eletricity costs K 13 per unit
Answer:
Weekly cost = K 8,190
Explanation:
Given the following data;
Resistance, R = 30 Ohms
Current, I = 10 Amps
Time, t = 30 hours
Cost = K13
I. To find the power dissipated;
Power = current² * resistance
Power = 10² * 30
Power = 100 * 30
Power = 3000 Watts
II. To find the energy consumption;
Energy = power * time
Energy = 3000 * 30
Energy = 90,000 Watt-hour = 90 KWh (1 Kilowatts is equal to 1000 watts).
III. To find the weekly cost;
Daily cost = Energy consumption * cost
Daily cost = 90 * 13
Daily cost = K 1170
Therefore, weekly cost = 1170 * 7
Weekly cost = K 8,190
please helppp:((( PLEASEEEEE
Answer:
is the amount of matter in this object
Question Set: Waves and Wave Properties
Answer:
The basic properties (parts) of a wave include: frequency, amplitude, wavelength and speed. Frequency is a measure of how many waves pass a point in a certain amount of time.
A is a hot object. B is a cold object. the two are brought into contact with each other so that heat is developed
A) which of the two gets hotter and why?
B) when does the exchange of heat stop?
Answer:
A) Cold object will start getting hot
B) Heat exchange will stop as the two object acquire the same temperature.
Explanation:
A) When one hot object and one cold object are kept in contact then the heat is transferred from the hot object to the cold object via different modes of heat transmission. Hence, the cold object starts getting hot
B) The transmission of heat from the hot object to the cold object will stop as the temperature of the two object becomes equal to each other.
The plates of a capacitor are charged using a battery, and they produce an electric field across the separation distance d between them. The two plates are now to be pushed together to a separation of d/2. The pushing together can be done either with the battery connected or with it disconnected. In which case, with the battery connected or disconnected. Is the electric field magnitude greater with the battery connected with the battery disconnected?
Answer:
Explanation:
The equation of the capacitance of the capacitor can be represented as:
[tex]C = \dfrac{\varepsilon_oA}{d}[/tex]
Also, the electric field between the plates can be expressed as:
[tex]E = \dfrac{\sigma}{\varepsilon_o}[/tex]
[tex]= \dfrac{Q}{A \varepsilon _o} \ \ (surface \ charge\ density \ \sigma =\dfrac{Q}{\varepsilon_o})[/tex]
However;
when pushed to a distance d/2, the new capacitance of the capacitor is:
[tex]C = \dfrac{\varepsilon _oA}{(d/2))}[/tex]
[tex]=\dfrac{2 \varepsilon_oA}{d}[/tex]
[tex]=2C \\ \\ Q' = CV \\ \\ = 2CV \\ \\ =2Q[/tex]
SImilarly, the new electric field between the plates is:
[tex]E' = \dfrac{\sigma'}{\varepsilon_o} \\ \\ = \dfrac{Q'}{A \varepsilon_o} \\ \\ = \dfrac{2Q}{A \varepsilon_o} \\ \\ =2E[/tex]
For Battery disconnected:
The electric field between the plates doesn't rely upon the distance between the plates yet relies upon the magnitude of the charge. At the point when the battery is detached, the charge on the capacitor stays as before, so does the electric field.
Therefore, the magnitude of the electric field when the battery is associated is twice however much the magnitude of the electric field when the battery is separated and disconnected.
Hence, the ratio is :
[tex]\dfrac{E_{connected}}{E_{disconnected}} =\dfrac{2E}{E} \\ \\ \dfrac{E_{connected}}{E_{disconnected}} = 2[/tex]
Hence, the ratio is = 2
List two types of current
Answer:
static and current electricity
how to measure the weight of an object?? PLEASE HELP I'LL GIVE BRAINLEST
Answer:
Weight is a measure of the force of gravity pulling down on an object. It depends on the object's mass and the acceleration due to gravity, which is 9.8 m/s2 on Earth. The formula for calculating weight is F = m × 9.8 m/s2, where F is the object's weight in Newtons (N) and m is the object's mass in kilograms.
What is the Lorentz force law used for? A. To find the voltage of a battery B. To find the magnitude of a magnetic force C. To find the velocity of an electromagnetic wave. D. To find the direction of a magnetic field
Answer:
B
Explanation:
The Lorentz force is the sum of the electric force and magnetic force.
F = qE + qvB
qE represents electric force and qvB represents magnetic force
Assignment: Calculating Speed Investigation
Data Analysis:
Note: Please submit your data table with this assignment.
1. Write your original hypothesis here.
2. Calculate the average time for vehicle 1 from the information in your data table. Show all work.
3. Calculate the average time for vehicle 2 from the information in your data table. Show all work.
4. Calculate the average speed for vehicle 1 from the information in your data table. Show all work, including the formula used.
5. Calculate the average speed for vehicle 2 from the information in your data table. Show all work, including the formula used.
Conclusion:
Think about this information and then write a conclusion based on the data of this experiment. Don’t forget to connect the conclusion to the original hypothesis.
Were you able to support your hypothesis or not? Be sure to base your answer on the data you collected. Consider whether your conclusion is the only explanation for the data you collected or if there could be alternate explanations. Don’t forget to mention any scientific laws or theories you have studied that would apply to this experiment.
Follow-up Questions:
1. If your experiment did not seem to match the expected results, what did you learn from the experience?
2. Instantaneous speed is the rate of motion of an object at a particular moment in time. What change(s) to the experimental procedure would be necessary if you wanted to gather data on instantaneous speed?
and as for the data can you please make your own
Answer:
Assignment: Calculating Speed Investigation
Data Analysis:
Note: Please submit your data table with this assignment.
1. Write your original hypothesis here.
2. Calculate the average time for vehicle 1 from the information in your data table. Show all work.
3. Calculate the average time for vehicle 2 from the information in your data table. Show all work.
4. Calculate the average speed for vehicle 1 from the information in your data table. Show all work, including the formula used.
5. Calculate the average speed for vehicle 2 from the information in your data table. Show all work, including the formula used.
Conclusion:
Think about this information and then write a conclusion based on the data of this experiment. Don’t forget to connect the conclusion to the original hypothesis.
Were you able to support your hypothesis or not? Be sure to base your answer on the data you collected. Consider whether your conclusion is the only explanation for the data you collected or if there could be alternate explanations. Don’t forget to mention any scientific laws or theories you have studied that would apply to this experiment.
Follow-up Questions:
1. If your experiment did not seem to match the expected results, what did you learn from the experience?
2. Instantaneous speed is the rate of motion of an object at a particular moment in time. What change(s) to the experimental procedure would be necessary if you wanted to gather data on instantaneous speed?
and as for the data can you please make your own
Explanation:
Assignment: Calculating Speed Investigation
Data Analysis:
Note: Please submit your data table with this assignment.
1. Write your original hypothesis here.
2. Calculate the average time for vehicle 1 from the information in your data table. Show all work.
3. Calculate the average time for vehicle 2 from the information in your data table. Show all work.
4. Calculate the average speed for vehicle 1 from the information in your data table. Show all work, including the formula used.
5. Calculate the average speed for vehicle 2 from the information in your data table. Show all work, including the formula used.
Conclusion:
Think about this information and then write a conclusion based on the data of this experiment. Don’t forget to connect the conclusion to the original hypothesis.
Were you able to support your hypothesis or not? Be sure to base your answer on the data you collected. Consider whether your conclusion is the only explanation for the data you collected or if there could be alternate explanations. Don’t forget to mention any scientific laws or theories you have studied that would apply to this experiment.
Follow-up Questions:
1. If your experiment did not seem to match the expected results, what did you learn from the experience?
2. Instantaneous speed is the rate of motion of an object at a particular moment in time. What change(s) to the experimental procedure would be necessary if you wanted to gather data on instantaneous speed?
and as for the data can you please make your ownWhich sentence uses a superlative adjective correctly?
Anthony is running more quickly than anyone else on the field.
Shalon is a very talented pianist.
That is the best chocolate cake I have ever tasted.
Ani is the better gymnast of the two.
Which statement best compares and contrasts the purpose of "PROSERPINE" to that of "How Old Man Winter Was Driven Back"?
The Greek myth explains the creation of the earth, while the Iroquois myth also explains why there is evil in the world.
The Greek myth explains the creation of the earth, while the Iroquois myth also explains the creation of the moon.
The Greek myth explains the changing of the seasons as well as the existence of the underworld, while the Iroquois myth also explains the changing of the seasons.
The Greek myth explains the creation of the moon, while the Iroquois myth explains the creation of the sun.
Read the passages:
from "How Old Man Winter Was Driven Back"
"I, too, am powerful, and I am young! I do not fear you. When I touch the earth, it grows soft and warm. Every living thing stirs in its sleep,—birds and bees, flowers and trees, animals and men. When I speak, the sleeping sun awakes. See! Already he begins to send down his arrows. Hasten! that they may not find you, on the trail to the North Sky."
from "How the World Was Made"
Even some of the trees went to sleep. Only the cedar, the pine, the spruce, the holly, and the laurel were awake all seven nights. Therefore they are always green. They are also sacred trees. But to the other trees it was said, “Because you did not stay awake, therefore you shall lose your hair every winter.”
Which best uses textual evidence to compare and contrast these two myths?
Both myths show the change in seasons as a violent battle.
In "How Old Man Winter Was Driven Back," the change in
Course hero N4M.6 A board has one end wedged under a rock having a mass of 380 kg and is supported by another rock that touches the bottom side of the board at a point 85 cm from the end under the rock. The board is 4.5 m long, has a mass of about 22 kg, and projects essentially horizontally out over a river. Is it safe for an adult with a mass of 62 kg to stand at the unsupported end of the board
Answer:
Therefore it is save to carry a 62kg adult
Explanation:
From the question we are told that:
Mass [tex]m=380kg[/tex]
Height of supporting Rock [tex]X=85cm[/tex]
Length of Board[tex]L_r=4.5m[/tex]
Mass of board [tex]M_b=22kg[/tex]
Mass of adult [tex]M_a=62[/tex]
Generally the moment of balance about wedge part about is mathematically given by
[tex]N -Q + R = Mg + mg[/tex]
[tex]0.85*N - Mg*2.25 - mg*(2.25 + x) = 0[/tex]
[tex]0.85*N = + Mg*2.25 + mg*(2.25 + x)[/tex]
where
[tex]N+R=4547[/tex]
therefore
[tex]N = 570.70588 + 1608.3529 + 714.823 x[/tex]
if N=0 at fallen person
[tex]x=3.04m[/tex]
Therefore it is save to carry a 62kg adult
2. What does SCA stand for? (1 Point) Student Conservation Association h Securities Class Action Sudden Cardiac Arrest Solar Cell Array:',)
Answer:
sudden cardiac arrest
Explanation:
A uniform 4.50 kg square solid wooden gate 1.50 m on each side hangs vertically from a frictionless pivot at its upper edge. A 1.20 kg raven flying horizontally at 4.50 m/s flies into this door at its center and bounces back at 1.50 m/s in the opposite direction. Part A What is the angular speed of the gate just after it is struck by the unfortunate raven
Answer:
A. 1.17
B.
the angular momentum is conserved because there is n o external force doing torque on the pivot
Linear momentum is not conserved because this is not an example of elastic collision where the final and initial kinetic energies are the same
Explanation:
A.
1.17 rad/s
B.
the angular momentum is conserved because there is n o external force doing torque on the pivot
Linear momentum is not conserved because this is not an example of elastic collision where the final and initial kinetic energies are the same
I will mark you brainlist! Use your own word
What is the weathering, erosion, and deposition?
Weathering is the breaking down or dissolving of rocks and minerals on Earths surface.
Erosion is the process by which the surface of the Earth gets worn down. Erosion can be caused by natural elements such as wind and glacial ice
Deposition is the dropping of sediment by wind, water, ice, or gravity.
Answer:
Weathering: refers to the process of breaking down and disintegrating rocks, minerals, soils, as well as several other materials.
Erosion: refers to the process of wearing down the surface of the earth due to glacial ice, wind and other natural elements.
Deposition: refers to the geological process, of sediments and soil, added to landforms due to wind, ice and other natural elements to build up layers od sediments.
Explanation:
Which of the following would be most likely to contribute to molecules
experiencing intermolecular forces?
O A. Containing oxygen
B. Containing charged regions
O C. Electric neutrality
O D. Being made of atoms
Answer:
B. Containing charged regions
Explanation:
The term i.e. intermolecular forces would be used to explain the attraction forces. Here the interaction would be done between molecules etc that acts between the acts & the other types of particles i.e. neighboring like atoms or ions
So in the given case, the option b would be contributed to the molecules that have intermolecular forces
hence, the option b is correct
Convert the following angles in degrees to radians:
(a) 300°
(b) 18°
(c) 105°
Answer:
a) 5.23599
b) 0.314159
c) 1.8326
Explanation:
Answer:
a. 5.236 rad
b. 0.314 rad
c. 1.833 rad
Explanation:
300° × π/180 = 5.236rad
18° × π/180 = 0.3142rad
105° × π/180 = 1.833rad
when a wave is bent by traveling from one medium to another
a- reflection
b- refraction
c- absorption
d- propagation
Answer:
B. Refraction
Explanation:
Jope this helps
a man in a lift is moving upwards in a constant speed.the weight of the man is W.Acc
ording to Newtons third law,the reaction force of the weight W is the force of ?
Answer:
Normal force=mg
Explanation:
The reaction force of weight is the normal force.
in order to find the normal for we need to write all the forces and set it equal to the net force:
N-mg=ma (since it is a constant speed the a=0)
N=mg
In which direction does the magnetic field in the center of the coil point?
Answer:
Right
Explanation:
Coil move right yes
Explain how grality and electric charge are different
During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26cm.
a. Determine the speed (in m/s) of the clothes which are located on the wall of the spin barrel.
b. Determine the acceleration of the clothes.
To answer the two questions, we need to know two important equations involving centripetal movement:
v = ωr (ω represents angular velocity in radians)
a = [tex]\frac{v^{2}}{r}[/tex]
Let's apply the first equation to question a:
v = ωr
v = ((1800*2π) / 60) * 0.26
Wait. 2π? 0.26? 60? Let's break down why these numbers are written differently. In order to use the equation v = ωr, it is important that the units of ω is in radians. Since one revolution is equivalent to 2π radians, we can easily do the conversion from revolutions to radians by multiplying it by 2π. As for 0.26, note that the question asks for the units to be m/s. Since we need meters, we simply convert 26 cm, our radius, into meters. The revolutions is also given in revs/min, and we need to convert it into revs/sec so that we can get our final units correct. As a result, we divide the rate by 60 to convert minutes into seconds.
Back to the equation:
v = ((1800*2π)/60) * 0.26
v = (1800*2(3.14)/60) * 0.26
v = (11304/60) * 0.26
v = 188.4 * 0.26
v = 48.984
v = 49 (m/s)
Now that we know the linear velocity, we can find the centripetal acceleration:
a = [tex]\frac{v^{2}}{r}[/tex]
a = [tex]\frac{49^{2}}{0.26}[/tex]
a = 9234.6 (m/[tex]s^{2}[/tex])
Wow! That's fast!
We now have our answers for a and b:
a. 49 (m/s)
b. 9.2 * [tex]10^{3}[/tex] (m/[tex]s^{2}[/tex])
If you have any questions on how I got to these answers, just ask!
- breezyツ
create a poem that incorporates those ten words. Feel free to make it as silly as you like! MINIMUM of 6 lines with a MINIMUM of 5 words and 10 should come from your book. These do not have to rhyme, but can if you wish.
I could make a poem for you if you actually gave the words...... what 10 words do i need to incorporate???☹︎
un
A block of 48kg 18
is resting
a slope of a 23° angle.
khat is the normal reachion Force?
The sensor on a door for a home security system consisted of a small coil of wire
embedded in the doorframe, and a small steel disk on the door opposite the coil.
When the door was opened, what characteristic of the coil changed for the home
security system?
Answer:
Probably electromagnetism
Explanation:
When the door is closed, the steel disk on the door is in close proximity to the coil of wire in the doorframe. This creates a magnetic field around the coil, which induces a small current in the coil.
What is the magnetic field?Ampere's law, which says that the magnetic field created by a current-carrying wire is proportional to the current and inversely proportional to the distance from the wire, may be used to describe the magnetic field produced by a long straight wire carrying a current.
When the door is opened, the steel disk moves away from the coil, which causes the magnetic field to weaken. As a result, the current induced in the coil decreases. This change in current is detected by the home security system as a change in the magnetic field and is interpreted as the door being opened.
In other words, the characteristic of the coil that changes when the door is opened is the amount of current induced in it. The decrease in the magnetic field as the steel disk moves away from the coil results in a decrease in the induced current, which signals to the home security system that the door has been opened.
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Guys can you please help me with this
A tennis ball with mass 57 g is travelling at 25 m/s [S] when it is intercepted by a tennis racquet for 4.0 ms after which the ball travels at 32 m/s [N]. What is the average force applied to the ball by the racquet?
Answer:
F = 812.25 N
Explanation:
Given (convert to SI units):
m = 57 g = 0.057 kg
[tex]v_{1}[/tex] = -25 [tex]\frac{m}{s}[/tex]
[tex]v_{2}[/tex] = 32 [tex]\frac{m}{s}[/tex]
t = 4 ms = 0.004 s
Find acceleration:
a = [tex]\frac{v_{2}-v_{1} }{t}[/tex] = [tex]\frac{32-(-25)}{0.004}[/tex] = 14250
Find force:
F = ma = 0.057(14250) = 812.25 N
The function s(t)=−t3+3t+3 gives the distance from a starting point at time t of a particle moving along a line. Find the velocity and acceleration functions. Then find the velocity and acceleration at t=0 and t=1. Assume that time is measured in seconds and distance is measured in centimeters. Velocity will be in centimeters per second (cm/sec) and acceleration in centimeters per second per second (cm/sec2).
Answer:
v(t)=3t²+3, and a(t)=6t
v(0)=3cm/sec, and a(0)=0cm/sec²
v(1)=6cm/sec, and a(1)=6cm/sec²
Explanation:
Find velocity and acceleration functions ( v(t) and a(t) )
(Relevant background: Let's say f(t) is a function of y with respect to x. Think of the derivative of this function, f'(t) , as representing the rate at which y changes with respect to x)
s(t) is a function of distance with respect to time. Therefore, s'(t) - the derivative of this - represents the rate at which distance changes with time, which is just the definition of velocity. So we can say velocity v(t) = s'(t).
s(t)=t³+3t+3
s'(t)=v(t)=3t²+3
Similarly, if v(t) is a function of speed with respect to time, then v'(t) represents the rate at which speed changes with time, which is acceleration. So we can say that acceleration a(t)=v'(t)=s''(t)
v(t)=3t²+3
v'(t)=a(t)=6t
Find velocity and acceleration at t=0 and t=1
t=0
v(t)=3t²+3
v(0)=3(0²)+3
v(0)=3 cm/sec
a(t)=6t
a(0)=6(0)
a(0)=0 cm/sec²
t=1
v(t)=3t²+3
v(1)=3(1²)+3
v(1)=3+3
v(t)=6 cm/sec
a(t)=6t
a(1)=6(1)
a(1)=6 cm/sec²
The function s(t)=−t3+3t+3 gives the distance from a starting point at time t of a particle moving along a line.
v(t)=3t²+3, and a(t)=6t
v(0)=3cm/sec, and a(0)=0cm/sec²
v(1)=6cm/sec, and a(1)=6cm/sec²
What is velocity and acceleration functions ( v(t) and a(t)?Relevant background: Let's say f(t) is a function of y with respect to x. Think of the derivative of this function, f'(t) , as representing the rate at which y changes with respect to x.
s(t) is a function of distance with respect to time. Therefore, s'(t) - the derivative of this - represents the rate at which distance changes with time, which is just the definition of velocity. So we can say velocity v(t) = s'(t).
s(t)=t³+3t+3
s'(t)=v(t)=3t²+3
Similarly, if v(t) is a function of speed with respect to time, then v'(t) represents the rate at which speed changes with time, which is acceleration. So we can say that acceleration a(t)=v'(t)=s''(t)
v(t)=3t²+3
v'(t)=a(t)=6t
Find velocity and acceleration at t=0 and t=1
t=0
v(t)=3t²+3
v(0)=3(0²)+3
v(0)=3 cm/sec
a(t)=6t
a(0)=6(0)
a(0)=0 cm/sec²
t=1
v(t)=3t²+3
v(1)=3(1²)+3
v(1)=3+3
v(t)=6 cm/sec
a(t)=6t
a(1)=6(1)
a(1)=6 cm/sec²
Therefore, The function s(t)=−t3+3t+3 gives the distance from a starting point at time t of a particle moving along a line.
v(t)=3t²+3, and a(t)=6t
v(0)=3cm/sec, and a(0)=0cm/sec²
v(1)=6cm/sec, and a(1)=6cm/sec²
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