A particle moves along a straight line and its position at time t is given by s(t) = 2t^3 - 18t^2 + 30t where s is measured in feet and t in seconds.
finally, what is the total distance the particle travels between time 0 and time 18
Answers
The particle travels a total distance of 190 feet between time 0 and time 18.
To find the total distance the particle travels between time 0 and time 18, follow these steps:
1. Find the velocity function, v(t), by differentiating the position function, s(t), with respect to time t:
v(t) = ds/dt = 6t^2 - 36t + 30.
2. Find the critical points of the velocity function by setting v(t) equal to 0 and solving for t:
6t^2 - 36t + 30 = 0
t^2 - 6t + 5 = 0
(t-5)(t-1) = 0
t = 1, 5
3. Evaluate the position function, s(t), at each of the critical points and the endpoints of the interval [0, 18]:
s(0) = 2(0)^3 - 18(0)^2 + 30(0) = 0
s(1) = 2(1)^3 - 18(1)^2 + 30(1) = 14
s(5) = 2(5)^3 - 18(5)^2 + 30(5) = -5
s(18) = 2(18)^3 - 18(18)^2 + 30(18) = -162
4. Calculate the differences in position for each subinterval:
From 0 to 1: |14 - 0| = 14
From 1 to 5: |(-5) - 14| = 19
From 5 to 18: |-162 - (-5)| = 157
5. Add the distances from each subinterval to find the total distance traveled:
Total distance = 14 + 19 + 157 = 190 feet.
So, the particle travels a total distance of 190 feet between time 0 and time 18.
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Related Questions
Two metal spheres that are initially uncharged are mounted on insulating stands as shown above. A negatively charged rubber rod is brought close to but does not make contact with sphere X. Sphere Y is then brought close to X on the side opposite to the rubber rod. Y is allowed to touch X and then is removed some distance away. The rubber rod is then moved far away from X and Y. What are the final charges on the spheres?Sphere XSphere Y
A. ZeroZero
B. NegativeNegative
C. NegativePositive
D. PositiveNegative
E. PositivePositive
Answers
The final charges on the spheres are: Sphere X: Positive, Sphere Y: Negative. Option D
Initially, both spheres X and Y are uncharged. When the negatively charged rubber rod is brought close to sphere X, it induces a separation of charge in sphere X. This means that the electrons in sphere X are repelled by the negative charge of the rod and move to the opposite side of the sphere, leaving the near side of the sphere positively charged.
When sphere Y is brought close to X on the side opposite to the rubber rod, the positive charges in sphere X attract the negative charges in sphere Y. This causes the electrons in sphere Y to move towards the positively charged side of sphere X, resulting in a transfer of electrons between the two spheres. Sphere Y becomes negatively charged and sphere X becomes positively charged.
After sphere Y is removed some distance away, the charges on the spheres will remain the same since there are no external forces acting on them to change their charges. Therefore, sphere X will remain positively charged and sphere Y will remaiWhen the rubber rod is moved far away from X and Y, it has no effect on the charges of the spheres since they are already charged and there is no electrical connection between them and the rod. Therefore, the final charges on the spheres are:Sphere X: Positive, Sphere Y: Negative.The correct answer is D) PositiveNegative.
So, the option option D is correct
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Which of the following is an example of a dry lubricant? oil grease graphite petroleum
ANSWER ASAP WILL GIVE BRAINLIEST!
Answers
Answer:
Dry lubricants or solid lubricants are materials that, despite being in the solid phase, are able to reduce friction between two surfaces sliding against each other without the need for a liquid oil medium.
Explanation:
Answer:
Your answer is graphite :) Have a nice day
Explanation:
What must change in order for electromagnetic induction to occur in a wire coil?.
Answers
Answer:
The magnetic field through the coil must change.
Explanation:
The ramp has an efficiency of 80%. If you perform 600 J of work, how much useful work does the ramp do
Answers
The ramp does 480J of useful work with an efficiency of 80% .
What is efficiency of work done ?Efficiency is the ratio of the useful energy released by a system to the input energy .Mathematically, efficiency of energy = out put energy/ input energy What is the useful work done by the ramp having efficiency 80% and an input work done 600J?The efficiency =output work done/ input work done 80% =output work done/ 600Joutput work done =( 80×600)/100=480J
Thus, we can conclude that the useful work done by the ramp is 480J.
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What do all heterotrophs have in common?
A: Their diets must include meat incorrect answer
B: They must drink at least one liter of water each day to survive incorrect answer
C: They must consume nutrients to survive incorrect answer
D: They must breathe oxygen to survive
Answers
Answer:
c
Explanation:
your welcome dude good luck
what happen when I put a coloured ice cube in warm water
Answers
Answer:
it would melt with the hot weather
Explanation:
It melts and the water changes color
a person walks first at a constant speed of 5.10 m/s along a straight line from point circled a to point circled b and then back along the line from circled b to circled a at a constant speed of 3.20 m/s.
Answers
Let's assume it took 10 seconds to walk from A to B. Using the formula, the distance covered would be 5.10 m/s × 10 s = 51 meters. The distance covered would be 3.20 m/s × 15 s = 48 meters. Adding the distances, the total distance traveled is 51 meters + 48 meters = 99 meters.
A person walks at a constant speed of 5.10 m/s from point A to point B along a straight line.
Then, they walk back from point B to point A at a constant speed of 3.20 m/s.
To find the total distance traveled, we need to calculate the distance covered from A to B and then add it to the distance covered from B to A.
To find the distance from A to B, we can use the formula distance = speed × time.
Since we know the speed is 5.10 m/s, we need to find the time it took to cover the distance.
Unfortunately, the time is not provided in the question, so we cannot calculate the exact distance.
However, if we assume the time taken to walk from A to B is 10 seconds, the distance covered would be 5.10 m/s × 10 s = 51 meters.
Similarly, to find the distance from B to A, we can use the same formula. Assuming it took 15 seconds to walk back, the distance covered would be 3.20 m/s × 15 s = 48 meters.
Therefore, the total distance traveled is 51 meters + 48 meters = 99 meters.
A person walks at a constant speed of 5.10 m/s along a straight line from point A to point B and then back along the line from point B to point A at a constant speed of 3.20 m/s.
To find the total distance traveled, we need to calculate the distance covered from A to B and then add it to the distance covered from B to A.
The formula to find the distance is distance = speed × time.
However, the question does not provide the time taken for each segment of the walk, so we cannot calculate the exact distances.
We can, however, make assumptions about the time taken.
Let's assume it took 10 seconds to walk from A to B.
Using the formula, the distance covered would be 5.10 m/s × 10 s = 51 meters.
Now, let's assume it took 15 seconds to walk back from B to A.
The distance covered would be 3.20 m/s × 15 s = 48 meters.
Adding the distances, the total distance traveled is 51 meters + 48 meters = 99 meters.
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which of the following could not be measured from a single photograph? group of answer choices the number of bright stars in a nearby cluster. the general shape of an interstellar gas cloud. the color of a planet. the brightness of a star in our sky. the rate at which a variable star brightens and dims.
Answers
The number of bright stars in a nearby cluster can also be determined from a single photograph by analyzing the cluster's luminosity function.
It is impossible to measure the rate at which a variable star brightens and dims from a single photograph. The rate at which a variable star brightens and dims cannot be measured from a single photograph. A variable star is a star that changes brightness over time, and their light curves are often used to study them. Light curves are plots of brightness over time, and they are used to study the properties of variable stars.
It is difficult to measure the rate at which a variable star brightens and dims from a single photograph because it is necessary to observe the star over a long period to obtain a complete light curve. Variable stars can be used to study a variety of phenomena in astronomy, including the evolution of stars, the structure of galaxies, and the expansion of the universe. The brightness of a star in our sky can be measured from a single photograph by measuring its apparent magnitude.
The apparent magnitude of a star is a measure of its brightness as seen from Earth. The general shape of an interstellar gas cloud can also be determined from a single photograph by analyzing its morphology. The color of a planet can also be determined from a single photograph by analyzing the wavelengths of light reflected by its atmosphere. Finally, the number of bright stars in a nearby cluster can also be determined from a single photograph by analyzing the cluster's luminosity function.
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(3+j4)x+(4-j5)y=18+j13
(4-j2)x-(4+j5)y=-5+j10
What is the magnitude of x?
Answers
X has a magnitude of around 1.11.
What is the X component's magnitude?The cosine and sine of a vector's direction angle can be used to calculate the scalar x-component, while the magnitude and cosine of the vector's direction angle can be used to calculate the scalar y-component.
By multiplying the first equation by (4+j5) and the second equation by (3+j4) and adding the resulting equations, we can use the method of elimination to solve this system of equations:
(3+j4)(4-j5)x + (3+j4)(4+j5)y = (18+j13)(3+j4)
(4-j2)(3+j4)x - (4+j5)(3+j4)y = (-5+j10)(4+j5)
Simplifying, we get:
53x + 47y = 78 + 43j
10x - 29y = 15 - 37j
By multiplying the first equation by 29 and the second equation by 47, then removing, we may eliminate y and arrive at the solution for x:
1537x = 1695 - 1150j
Therefore, x = (1695 - 1150j)/1537.
To find the magnitude of x, we calculate the absolute value:
|x| = |(1695 - 1150j)/1537| = √((1695/1537)² + (-1150/1537)²) = 1.11
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At what rate must the potential difference between the plates of a parallel-plate capacitor with a 2.3 uF capacitance be changed to produce a displacement current of 1.6 A? V/s
Answers
The potential difference between the plates of the parallel-plate capacitor needs to change at a rate of 0.696 V/s to produce a displacement current of 1.6 A.
The required rate of change is calculated by using the formula for displacement current in a parallel-plate capacitor :
I_d = ε₀ * A * dV/dt,where I_d is the displacement current, ε₀ is the vacuum permittivity (8.85 x 10^(-12) F/m), A is the area of the plates, and dV/dt is the rate of change of the potential difference.
Rearranging the formula, we can solve for dV/dt:
dV/dt = I_d / (ε₀ * A).Given that the capacitance C = ε₀ * A / d, where d is the separation between the plates, we rewrite the formula as:
dV/dt = (I_d * d) / (C * ε₀).Substituting the given values, with C = 2.3 x 10^(-6) F and I_d = 1.6 A, we have:
dV/dt = (1.6 A * d) / (2.3 x 10^(-6) F * 8.85 x 10^(-12) F/m).Calculating the result gives:
dV/dt ≈ 0.696 V/s.To know more about parallel-plate capacitors, refer to the link:
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A furniture crate of mass 60 kg is at rest a loading ramp that makes an angle of 25° with the horizontal
The coefficient of kinetic friction between the crate and the ramp is 0.2. What force, applied parallel to the incline, is required to push the crate up the incline at a constant speed?
Answers
Answer:
furniture crate of mass 60 kg is at rest a loading ramp that makes an angle of 25° with the horizontal
The coefficient of kinetic friction between the crate and the ramp is 0.2. What force, applied parallel to the incline, is required to push the crate up the incline at a constant speed?
Explanation:
furniture crate of mass 60 kg is at rest a loading ramp that makes an angle of 25° with the horizontal
The coefficient of kinetic friction between the crate and the ramp is 0.2. What force, applied parallel to the incline, is required to push the crate up the incline at a constant speed?
\( \huge \boxed{ \sf lol}\)
On a cosmic calendar, in which the history of the universe is compressed into one year, how long is the average human life span?.
Answers
Answer:
If one were to use 5 billion years as the age of the universe and 75 years as the average human life span then
T = 75 / 5 E9 = 1.5E-8
The number of seconds in a year is 3600 * 24 * 365 = 3.2E7
If t = N * T seconds in a year * fraction of human life span
t = 1.5E-8 * 3.2E7 = .48
A human life span is about 1/2 second compared to the life of the universe if the universe were compressed to a single year
(8.86 + 1.0 x 10^-3)÷3.610×10^-3
Answers
Answer:
2454.57
Explanation:
Step 1: Solve
\(\frac{(8.86+0.001)}{(3.610)(10^{-3}) }\)
\(\frac{8.861}{0.003.61 }\)
2454.57
Therefor the answer to this equation is 2454.57
A spring is stretched 10 cm from the resting position. The spring's constant of proportionality is 40 N/m. What is the spring potential energy?
Answers
Answer:
0.2 J
Explanation:
Elastic potential energy of a spring is:
EE = ½ kx²
where k is the spring stiffness and x is the displacement.
EE = ½ (40 N/m) (0.1 m)²
EE = 0.2 J
Mrs. Candies notices that her husband stops breathing in his sleep, awakens slightly to gulp in the air, and then goes back to sleep. This happens several times a night. Mr. Candies is displaying which of the following sleep disorders?
Answers
Answer:
Sleep Apnea
Explanation:
I believe it is Sleep Apnea due to one of the "symptoms" of it being, "Observed episodes of stopped breathing during sleep".
familydoctor.org also says that, "People who have sleep apnea stop breathing for 10 to 30 seconds at a time while they are sleeping. These short stops in breathing can happen up to 400 times every night."
What does ADA apply to?
Answers
Ted lifts a 10N weight at a height of 1.5 m in 1 second. Johnny lifts a 10N weight at a height of 1.5 m in 2 second. Which statements are correct? A. Johnny and Ted did the same amount of work B. Ted did more work C. Johnny and Ted expanded the same power D. Ted expanded more power E Johnny did more work F. Johnny expanded more power
Answers
Answer:
he affirmations the correct ones are: A and D
Explanation:
To find out which expressions are correct, let's calculate the work and power done by each person
the expression for work is W = F and
the expression for power is P = W / t
In this case the work is positive because the beast is in the same direction of displacement.
Ted
W₁ = 10 1.5
W₁ = 15 J
P₁ = 15/1
P₁ = 15 w
Johnny
the job
W₂ = 10 1.5
W₂ = 15 J
the potential
P₂ = 15/2
P₂ = 7.5 w
therefore we see that the work of both is the same, but Ted developed twice as much power as Johnny
when resisting the affirmations the correct ones are: A and D
If the force is applied to a car, then its acceleration will ___________ because of Newton's _____________.
Answers
When solving projectiles you will often get two possible times for solutions. Sometimes a time will be negative and can be rejected. Other times both times will be positive and therefore possible. Explain why both times above make sense in the context of the given information used. Which time will you ultimately choose and why?
Context is attached below.
Answers
Answer:
The reason why times, 0.23 s, and 1.80 s makes sense is that a projectile passes through a given height level, which is lesser than the maximum height reached by the projectile, twice in its trajectory
Explanation:
The formula for the time of motion of a projectile is given as follows;
\(t = \dfrac{-V_{oy} \pm \sqrt{V_{oy} ^2 - 2 \cdot g \cdot \Delta y} }{-g}\)
Therefore, when \(V_{oy} ^2 = 2 \cdot g \cdot \Delta y}\), we have only one time value
When \(V_{oy} ^2 > 2 \cdot g \cdot \Delta y}\), two time values can be obtained and both will be positive when we have;
\(V_{oy} > \sqrt{V_{oy} ^2 - 2 \cdot g \cdot \Delta y} }\)
When \(V_{oy} < \sqrt{V_{oy} ^2 - 2 \cdot g \cdot \Delta y} }\), one of the time values will be negative and can be rejected
Therefore, given that the times obtained above are 1.80 s, and 0.23 s, and both make sense due to the following reason;
In the path of the projectile motion of the basketball, there are two points in time at which the height of the basketball above the starting point is exactly 2 meters, given that the maximum height reached is more than 2 meters
The first time the basketball is 2 meters above the point it is shot is lesser of the two calculated time values, which is during the upward motion of the basketball before it reaches the maximum height, while the second time is, which is the larger calculated time, is the time that the basketball reaches the hoop, after flying past the highest point
What law explains why a collapsing cloud usually forms a protostellar disk around a protostar?.
Answers
Explanation: quizlet!
Answer:
conservation of angular momentum
Explanation:
Quizlet
What types of cells are likely to have lots of smooth ER?
Answers
Answer:
eukaryotic cells
Explanation:
"Smooth endoplasmic reticulum (sER) is (a part of) endoplasmic reticulum that is tubular in form and lacks ribosomes. It is present in eukaryotic cells and is associated with lipid synthesis, carbohydrate metabolism, regulation of calcium concentration, and drug detoxification"
source: biologyonline
What is the maximum possible parallax of Mercury during a solar transit, as seen from either end of a 2700 km baseline on Earth?
Express your answer using two significant figures.
__________ arc seconds
Answers
The maximum possible parallax of Mercury during a solar transit, as seen from either end of a 2700 km baseline on Earth, can be calculated using the formula
Given that the average distance to Mercury from Earth is approximately 77 million kilometers, we can calculate the parallax as follows: parallax = (2700 km / 77 million km) * (180 / π) * 3600 ≈ 2.2 arc seconds
Therefore, the maximum possible parallax of Mercury during a solar transit, as seen from either end of a 2700 km baseline on Earth, is approximately 2.2 arc seconds.
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If a car travels 400m in 20 seconds how fast is it going?
What the distance
Answers
Answer:
20m/s i think this much
a boat travels east at 35 m/s while the wind blowing south is at 15 m/s find the velocity
Answers
The resultant velocity of the boat is 38.08 m/s.
What is the resultant velocity of the boat?
The resultant velocity of the boat is the single velocity that will effectively represent the velocity of the boat and effect of the wind speed on the boat in terms of magnitude and direction.
The resultant speed of the boat is calculated by applying the following formula.
V² = Vb² + Vw²
where;
V is the resultant velocity of the boatVb is the velocity of the boatVw is the velocity of the windThe given parameters;
Vb is the velocity of the boat = 35 m/sVw is the velocity of the wind = 15 m/sSubstitute the given parameters and solve for the resultant speed of the boat as shown below;
V² = 35² + 15²
V² = 1,450
V = √1450
V = 38.08 m/s
Thus, the resultant velocity of the boat is determined by applying triangular method of vector addition.
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The complete question is below:
a boat travels east at 35 m/s while the wind blowing south is at 15 m/s find the resultant velocity of the boat.
the distance between pole and position of image can denoted by___
a)u. b)v. c)R. d)C
Answers
Answer:
b) v
Explanation:
the distance between pole and position of image can denoted by v
A pendulum swings back and forth. Is there energy in the system?
Answers
Answer:
yes
Explanation:
A pendulum should be able to contain enough energy to constantly be moving
What would be true of a thermometer that always reads three degrees off?
a. It is valid but not reliable.
b. It is both reliable and valid.
c. It is neither reliable nor valid.
d. It is not valid, but you cannot determine if it is reliable from the information given.
e. It is reliable but not valid
Answers
A thermometer that always reads three degrees off, is reliable but not valid.
Reliability of a measuring instrument refers to the consistency of the measurement. It always give the same reading for the same temperature, however it is not correct as it is reads three degrees off. So we can say it is reliable, we can use it by calibrating it.
On the other hand it is not valid, as it gives the incorrect value of the temperature by reading the three degrees off. It does not give the reading that is suppose to. So it is not valid, or we can say the reading of this thermometer is not valid. Hence the correct option is E.
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a concave mirror of radius of curvature 20cm produces an inverted image three times the size of an object placed on and perpendicular to the axis. calculate the position of the object and the image
Answers
Answer:
Check attachment for your answer
Good luck
FREEE POINTS
COME HELP NOW!!!
Which of these statements about heating up water on Earth's surface is true?
Water heats up faster than land.
Water heats up by convection from Earth.
Water heats up by conduction from the sun.
Water heats up to a lower temperature than land.
Answers
Answer:
number 2
Explanation:
the 2 one is right
How much does a bowling ball weigh if it has a mass of 6 kg on Earth?
Answers
Answer: pretty sure 14 pounds
Explanation: