Answer:
(a)
[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex] --- velocity
[tex]x(t) = \frac{At^3}{6} -\frac{Bt^4}{12} + x(0)[/tex] --- position
(b) The maximum velocity is: 39.0625m/s
Explanation:
Given
[tex]a_x(t) =At -Bt^2[/tex]
[tex]A = 1.5m/s^3[/tex]
[tex]B = 0.120m/s^4[/tex]
Solving (a): The position and velocity as a function
To calculate the change in velocity, we integrate the given acceleration
i.e.
[tex]\int\limits^{v(t)}_{v(0)} {dv} = \int\limits^t_0 {a(t)} \, dt[/tex]
Integrate
[tex]v|\limits^{v(t)}_{v(0)} = \int\limits^t_0 {a(t)} \, dt[/tex]
Substitute v(t) and v(0) for v
[tex]v(t) - v(0) = \int\limits^t_0 {a(t)} \, dt[/tex]
[tex]v(0) = 0[/tex] ---- The initial velocity.
So, we have:
[tex]v(t) - 0 = \int\limits^t_0 {a(t)} \, dt[/tex]
[tex]v(t) = \int\limits^t_0 {a(t)} \, dt[/tex]
Substitute: [tex]a_x(t) =At -Bt^2[/tex]
[tex]v(t) = \int\limits^t_0 {[At -Bt^2]} \, dt[/tex]
Integrate
[tex]v(t) = {\frac{At^2}{2} -\frac{Bt^3}{3}}|\limits^t_0[/tex]
Substitute 0 and t for t
[tex]v(t) = [\frac{At^2}{2} -\frac{Bt^3}{3}] - [\frac{A*0^2}{2} -\frac{B*0^3}{3}][/tex]
[tex]v(t) = [\frac{At^2}{2} -\frac{Bt^3}{3}] - 0[/tex]
[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]
To calculate the change in position, we integrate the calculated velocity
i.e.
[tex]\int\limits^{x(t)}_{x(0)} {dx} = \int\limits^t_0 {v(t)} \, dt[/tex]
Integrate
[tex]x(t)|\limits^{x(t)}_{x(0)} = \int\limits^t_0 {v(t)} \, dt[/tex]
Substitute x(t) and x(0) for x(t)
[tex]x(t) - x(0) = \int\limits^t_0 {v(t)} \, dt[/tex]
Substitute: [tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]
[tex]x(t) - x(0) = \int\limits^t_0 {\frac{At^2}{2} -\frac{Bt^3}{3}} \, dt[/tex]
Integrate
[tex]x(t) - x(0) = \frac{At^3}{6} -\frac{Bt^4}{12}}|\limits^t_0[/tex]
Substitute t and 0 for t
[tex]x(t) - x(0) = [\frac{At^3}{6} -\frac{Bt^4}{12}] - [\frac{A*0^3}{6} -\frac{B*0^4}{12}][/tex]
[tex]x(t) - x(0) = [\frac{At^3}{6} -\frac{Bt^4}{12}] - [0][/tex]
[tex]x(t) - x(0) = \frac{At^3}{6} -\frac{Bt^4}{12}[/tex]
Make x(t) the subject
[tex]x(t) = \frac{At^3}{6} -\frac{Bt^4}{12} + x(0)[/tex]
Where x(0) represents the initial position
Solving (b): The maximum velocity
First, we calculate the time at which it attains the maximum height
Set acceleration to 0
[tex]a_x(t) =At -Bt^2[/tex]
[tex]At - Bt^2 = 0[/tex]
Factorize
[tex]t(A - Bt) = 0[/tex]
Split
[tex]t = 0\ or\ A - Bt = 0[/tex]
t can't be 0.
So, we have:
[tex]A - Bt = 0[/tex]
Solve for t
[tex]-Bt = -A[/tex]
[tex]t = \frac{-A}{-B}[/tex]
[tex]t = \frac{A}{B}[/tex]
Substitute: [tex]A = 1.5m/s^3[/tex] and [tex]B = 0.120m/s^4[/tex]
[tex]t = \frac{1.5m/s^3}{0.120m/s^4}[/tex]
[tex]t = \frac{1.5}{0.120}s[/tex]
[tex]t = 12.5s[/tex]
Substitute [tex]t = 12.5s[/tex] in v(t) to get the maximum velocity
[tex]v(t) = \frac{At^2}{2} -\frac{Bt^3}{3}[/tex]
[tex]v(t) = \frac{A*12.5^2}{2} -\frac{B*12.5^3}{3}[/tex]
[tex]v(t) = \frac{156.25A}{2} -\frac{1953.125B}{3}[/tex]
Substitute: [tex]A = 1.5m/s^3[/tex] and [tex]B = 0.120m/s^4[/tex]
[tex]vmax = (156.25*1.5)/2 -(1953.125*0.120)/3[/tex]
[tex]v_{max} = 117.1875 - 78.125[/tex]
[tex]v_{max} = 39.0625[/tex]
By using moving _____magnetic fields_________ and _________________ wire together, electric ___________________ create electricity. Electric generators essentially convert _____________________energy (the energy of motion) into _____________ energy.
The words with a blank are , magnet, coiled copper, motor, mechanical and electrical. Electric generators produce electricity by combining a moving shaft with coiled wire.
How do magnetic fields work?The magnetic field is the region where the strength of magnetism acts on a magnetic substance or a flowing electric charge. a magnetic field diagram that shows how the magnetic force is distributed both inside and outside of a magnetic substance.
Kinetic energy: What is it?When an object is moving, it has kinetic energy. If we intend to accelerate an object, we must exert a force. The task has been finished, energy has been applied to the object, and it is now moving at a fixed constant pace.
Therefore, electric generators generate electricity by combining coiled wire and moving shaft magnetic fields. Kinetic energy, or the energy of motion, is effectively transformed into electrical energy via electric generators.
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A 74 kg student, starting from rest, slides down an 11.8 meter high water slide. What is his kinetic energy at the bottom of the slide
The kinetic energy of the student at the bottom of the slide with a velocity of 15.21 m/s is 8,557.36 J
The mass of the student = 74 kg
The distance of the slide = 11.8 m
The final velocity at the bottom of the slide can be found using
v² = u² + 2ax
where v is the final velocity
u is the initial velocity
a is the acceleration due to gravity
x is the distance
Let us substitute the known values,
v² = 0 + 2 x 9.8 x 11.8
v² = 231.28
= √231.28
v = 15.21
Therefore, the kinetic energy at the bottom of the slide is
K.E = 1/2mv²
= 1/2 x 74 x 231.28
= 8,557.36 J
The kinetic energy of the student is 8,557.36 J
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We are warmed by condensation because water molecules in the air that strike our bodies
A. form an insulating layer on our bodies
B. gain kinetic energy as they change state
C. transfer some of their kinetic energy to us
Condensation warms us because airborne water molecules that impact our bodies give up some of their kinetic energy to us.
What is kinetic energy?
Kinetic energy is the energy of motion. It is the energy that a moving item possesses.It is typically measured in joules and is equal to the work done to accelerate the object from its rest state to its current state. Kinetic energy can be found by multiplying the mass of an object by its velocity squared, divided by two. The kinetic energy of an object increases as its velocity increases.Kinetic energy exists in both linear and rotational forms. Linear kinetic energy is the energy of an object moving in a straight line, while rotational kinetic energy is the energy an object has due to its spinning or rotating motion.
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how much electrical energy is converted to light and thermal energy by a 160 w light bulb in one day
13824 x 10^3 J electrical energy is converted to light and thermal energy by a 160 w light bulb in one day
What is the best way to define thermal energy?Thermal energy is the movement of the molecules within an object or substance. Every material has heat energy; the sun is the primary thermal energy source in our solar system. The transfer of thermal energy through one material or item to another is known as heat.
Given,
Power = P = 160 W
time = t = 1 day = 24 hours = 24 x 3600 sec = 86400 sec
energy = power x time = 160 x 86400 = 13824 x 10^3 J
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8. Jax bounced a dodgeball off a wall. The dodgeball has a momentum of 32. 6 kg · m/s after the
collision. What is the total momentum of the system before the collision?
32. 6 kg m/s will be the total momentum of the system before the collision.
What does "collision" mean?In physics, a collision is any circumstance in which two or more bodies rapidly apply forces to one another.
Despite the fact that the most common usage of the word "collision" relates to instances in which two or more objects smash violently, the scientific usage of the word makes no such assumptions.
If most or all of the total kinetic energy from the collision is lost (dissipated as heat, sound, etc., or absorbed by the objects themselves), the collision is said to be inelastic; such collisions result in the objects coming to a complete stop. A collision involving a car serves as an example of this type of collision since cars fold inward rather than colliding with one another.
Briefing:pf = Final momentum of the system = 32.6 kg m/s
According to the principle of conservation of angular momentum we have
pi = pf => pi = 32.6 kg m/s
The wall is not moving so the initial and final momentum of the system are equal.
Therefore, the total momentum of the system before the collision is 32.6 kg m/s
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If the starting velocity was 0 m/s and the final velocity was -7.68 m/s, what is the average velocity of the rock?
Answer:
Average velocity = -3.84 m/s
Explanation:
Given the following data;
Initial velocity = 0 m/s
Final velocity = -7.68 m/s
To find the average velocity;
Average velocity = (U + V)/2
Average velocity = (0 + [-7.68])/2
Average velocity = -7.68/2
Average velocity = -3.84 m/s
Therefore, the average velocity of the rock is -3.84 meters per seconds.
A car is traveling for 1638 km for a time period of 6.5 hours. What is the average speed of the car?
Answer:
252 km/hr
70 m/s
Explanation:
s = d/t
answer in km/hr:
s = 1638 km / 6.5 hr = 252 km/hr
if you need the answer in m/s:
s = ((1638 km)(1000 m/km)) / ( (6.5 hr)(60 min/hr)(60 s/min))
= 70 m/s
How are static and passive stretching similar?
Static stretching and passive stretching are very similar in that they both involve moving the limbs into and holding the stretch posture.
Static stretching involves the individual holding their own limbs in place, while passive stretching involves a partner assisting with the movement and holding of limbs. When you stretch to your limit and hold that position, you are engaging in a form of stretching known as static stretching. Passive stretching, on the other hand, is also a form of static stretching; however, during this technique, you remain relaxed and do not actively participate in increasing your range of motion.
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A plane flying at the speed of 150. M/s is accelerated uniformly at a rate of 5. 00 m/s^2
a. What is the plane's speed at the end of 10. 0 seconds?
b. What distance has it traveled?
The plane's speed at the end of 10.0 seconds is 200 m/s and the distance it has travelled is 1750 meters.
The initial speed of the plane, u = 150 m/s
Acceleration of the plane, a = 5 m/s²
Time, t = 10 sec
We can find the plane's speed at the end of 10. 0 seconds by the formula
a = (v - u)/ t
⇒5 = (v - 150)/ 10
⇒50 = v - 150
⇒v = 150 + 50
⇒v = 200 m/s
Now, to find the distance it has travelled we will use the kinematic equation
v² = u² + 2as
⇒200² = 150 ² + 2 × 5 × s
⇒40000 = 22500 + 10s
⇒17500 = 10 s
⇒s = 1750 m
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How do you find the acceleration of a marble down a ramp?
The marble accelerates at a constant rate as it moves down the slope because of the constant gravitational force acting on it in a major portion and the rolling tangential force on the object is acting in the smaller form.
Rolling motion of any object occurs when the marble starts sliding in a different methods from the other objects such as when the objects starts to roll from the ramp or any other sloppy surface and it rolls down due to the gravitational force and with many other forces such as the rolling tangential force. many forces are acting on the object at the same moment and we are just seeing the gravitational force which is playing a major portion. Hence by this information we can consider that the ball accelerates at a constant rate as it moves down the slope because of the constant gravitational force acting on it in a major portion and the rolling tangential force on the marble is acting in the smaller form.
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What type of protein secondary structure does the structure shown here (Fiqure 1) represent? O a-helix O a-sheet
O B- helix O B-sheet O y turn
The correct option is C. β-sheet type of protein secondary structure does the structure shown here (Figure 1) represent.
A shape is an arrangement and organization of interrelated elements in a fabric item or gadget, or the item or system so prepared. material systems encompass guy-made items consisting of homes and machines and natural items which include organic organisms, minerals, and chemical compounds. abstract structures consist of statistics structures in pc science and musical shape.
Sorts of the shape include a hierarchy (a cascade of one-to-many relationships), a network providing many-to-many links, or a lattice presenting connections among additives that can be pals in space.
Built structures are widely divided by using their various design approaches and requirements, into classes together with constructing systems, architectural structures, civil engineering structures, and mechanical structures.
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Complete Question:
What type of protein secondary structure does the structure is shown here (Figure 1) represent?
A). α-helix
B). α-sheet
C). β- helix
D). β-sheet
E). γ turn
Why does temperature have no effect on mass?
The amount of matter present is simply referred to as mass. As a result, temperature change has no direct effect on mass since the amount of matter present remains constant regardless of temperature. The mass of a material in a given volume is defined as its density.
Temperature is a physical measure that quantifies our feelings of hotness and coolness. A thermometer is used to measure temperature.
Thermometers are calibrated in a variety of temperature scales that have traditionally been defined by various reference points and thermometric substances.
The most prevalent scales are the Celsius scale (previously known as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being used mostly for scientific reasons. The kelvin is one of the International System of Units' seven basic units (SI).
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A teacher makes the following statement.
“Gasoline boils at a relatively low temperature (about 150°C). The kerosene is removed at around 200°C, followed by diesel oil at 300°C and fuel oil at around 370°C.”
What topic is the teacher most likely talking about?
distillation of a mixture
filtration of a pure substance
evaporation of a mixture
sorting of a pure substance
Answer: Distillation of mixture
Explanation: Different fractions of crude oil have different
boiling points according molecular weight of hydrocarbons
How is Pythagorean Theorem used in baseball?
Bill James came up with the Pythagorean Theorem of Baseball, which connects the amount of runs a club has scored and given up to its actual winning %.
Its uses are:The Pythagorean Theorem is the idea that a baseball team's record may be roughly estimated by taking the square of team runs scored and dividing it by the square of team runs scored plus the square of team runs allowed. Bill James, a baseball analyst, made this idea famous.
The Pythagorean Winning % approach uses the relationship between a team's victories and losses and the number of points scored and allowed to calculate the predicted winning percentage. To follow Pythagorean winning percentages for the seasons, consult the team statistics.
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The speed of light is approximately $3\times10^5$ kilometers per second. How long does it take sunlight to reach Jupiter
it takes about 26 seconds for speed of light with approximate speed of 3\times10^5 kilometers per second to reach Jupiter.
To calculate the time it takes light to reach Jupiter, we need to know the distance between the Sun and Jupiter. The average distance between the Sun and Jupiter is approximately 778 million kilometers. We can use the formula distance = speed x time to calculate the time it takes for sunlight to reach Jupiter. We know that the speed of light is approximately 3x10^5 kilometers per second and the distance between the Sun and Jupiter is 778 million kilometers.time = distance / speed
time = (77810^6 km) / (310^5 km/s)
time = 26 sec (approximately)
Therefore, it takes about 26 seconds for light to reach Jupiter.
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A 9 cm tall object is placed 16 cm from a converging lens forming an image at 13 cm. What is the height of the image?
1) A sound wave produced by an alarm is heard 668m away 2.0s later. a) What is the speed of sound of the alarm in the air? b) The sound wave has a frequency of 436Hz. What is its period? c) What is its wavelength?
Answer:
jkjkjkjkjkjkjkjkjkjkjk
Echolocation only works well when the object is as long as or longer than one wavelength of the sound produced.
a) Estimate the size of the smallest object a bat can detect using echolocation when the air temperature is 22 °C
The size of smallest object that a detect wing is 22°C bat can echolocation when air temperature is 31 mm.
Bat need to use because as high frequencies for echolocation compared to lower frequencies, higher. frequencies gives them more regarding size of the object in speed and frequency the prey direction of its waver are not early detailed information their path, range, pray. Also high detected by the prey.
For care the Jame of bat, dolphin frequency as explained in alio high radiation. Thus despite poor visibility under water, dolphin can high frequency and avoid to catch its wave it Predator. we there to find its path and to catch its prey and also to avoid its peredetor.
Bat sounds are emitted only during wing upbeat to minimize physiological costs. Air pressure in calls is just below blood pressure in lungs physiological maximum. FM is best for determining target distance Measure time delay between pulse and echo return FM sweep labels each part of pulse with a frequency value.
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they were pleased by the news.(active voice)
Answer:
They were pleased by the news. (passive voice)
The news pleased them. (active voice)
A 1kg rock is dropped 50m off a bridge. How much PE did it have
before it was dropped?
In this case, a body of mass 5 kg kept at a height of 10 m. So, the potential energy is given as 500 J.
Which energy has potential?An object's potential energy is its stored energy. This energy has the capacity to be productive. An object's potential energy is provided by gravity. Gravity's downward force is the source of this potential energy.
The acceleration brought on by gravity is known as the gravitational constant, or g. On Earth, this acceleration is equivalent to 10 metres per second. PE = mgh is the equation for potential energy resulting from gravity. The object's potential energy declines and its kinetic energy rises as it approaches the ground.
Briefing:Potential Energy = 5 x 10 x 10 = 500J.
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The table shows the values Jane obtained when she measured the thickness of a steel pipe. The known thickness of the pipe is 1.32 centimeters. Which statement about her results is true?
As the values are closed to each other, Jane's measurements are precise.
What is precision?The precision of a substance is defined as the degree to which two or more measurements agree with one another.
It is incredibly precise but not always accurate to measure something if you measured it five times and get around 1.50 cm each time. Accuracy is not necessary for precision. There are various categories of precision:
Persistence: The variation that results when the conditions are maintained constant and repeated measurements are done over a brief period of time.Reproducibility: When employing the same measurement method with various instruments and operators over longer time periods, variation occurs.Learn more about precision here:
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2. Outer planets have these characteristics:
A. Long orbits, made up of gas, have many moons
B. Long orbits, made up of gas, have few moons
C. Short orbits, made up of gas, have many moons
D. Long orbits, have a rocky crust, have many moons
Answer:
A
Explanation:
may i be marked as brnliest?
humans taste food mostly because of:
Answer:
taste buds
Explanation:
very sensitive microscopic hairs called microvilli. The tiny hairs send messages to the brain about how something tastes, so you know if it's sweet, sour, bitter, or salty
At a _________ light, after checking to the rear, stop before entering the intersection or at the stop bar. If the stop cannot be made safely, proceed through the intersection with caution.
"At a yellow light, after checking to the rear, stop before entering the intersection or at the stop bar." If stopping safely is not possible, cautiously cross the junction.
Devices that are typically located at significant sites, such as busy junctions, are used to give out traffic signals in order to control the flow of traffic.
A yellow traffic light serves as a warning that the red signal will soon be shown. As a result, as soon as you notice a yellow light, you should begin to slow down in preparation for a red light. Additionally, if for some reason you are unable to stop, you should keep an eye out for any vehicles that may be approaching the intersection at the same moment.
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Now let's think about a balloon. We know the gas particles inside of the balloon are bumping against the sides. What keeps those gas particles from forcing the balloon to expand
The elasticity of the balloon's material keeps the 1particles from forcing it to expand. The material stretches as the gas particles bump against the sides, allowing the balloon to expand to a certain point before contracting again.
The elasticity of the balloon's material is an important factor in determining the balloon's shape and size. In general, the more elastic the material is, the more the balloon will be able to stretch and expand. When the material is not elastic enough, it will not be able to stretch and the balloon will remain in its original shape.
The elasticity of the material also affects the amount of air pressure within the balloon. A more elastic material will be able to hold more air pressure, while a less elastic material will not be able to hold as much pressure. This is why balloons with a higher pressure will usually be larger than balloons with a lower pressure.
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What is the new volume of the gas if the pressure on 350 L of oxygen
at 720 mm Hg is decreased to 600 mm Hg?
Answer:
420 L
Explanation:
Applying Boyle's Law,
PV = P'V'.................... Equation 1
Where P = Initial pressure, P' = Final pressure, V = Initial volume, V' = Final volume.
make V' the subject of the equation
V' = PV/P'.................... Equation 2
From the question,
Given: P = 720 mmHg, V = 350 L, P' = 600 mmHg
Substitute these values into equation 2
V' = (720×350)/600
V' = 252000/600
V' = 420 L
ulius competes in the hammer throw event. The hammer has a mass of 7.26 kg and is 1.215 m long.What is the centripetal force on the hammer when it has a tangential speed of 31.95 m/s
The 6,100 N is the centripetal force on the hammer when it has a tangential speed of 31.95 m/s.
What is centripetal force ?Any force that induces a shift in velocity direction toward the center of a circular motion is referred to as a centripetal force. Centripetal force is caused by the part of the force that is perpendicular to the velocity.
Centripetal force is a force that operates on a body traveling in a circle and is pointed in the direction of the body's center of mass. It is computed using the formula:
F = mv^2/r
where m is the mass, v is the velocity and r is the radius.
F = 7.26(31.95)^2 / (1.215) = 6100 N
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Answer this please.____
Answer:
Explanation:
When a liquid is heated, the particles are given more energy. They start to move faster and further apart. At a certain temperature, the particles break free of one another and the liquid turns to gas. This is the boiling point.
A closed pipe creates a
fundamental frequency of 125 Hz.
What is the next higher frequency
that will create a standing wave in
the pipe?
(Speed of sound = 343 m/s)
(Unit = Hz)
Answer:
375 hz
Explanation:
Trust me
The 6 kg block is then released and accelerates to the right, toward the 5 kg block. The surface is rough and the coefficient of friction between each block and the surface is 0.3 . The two blocks collide, stick together, and move to the right. Remember that the spring is not attached to the 6 kg block. Find the speed of the 6 kg block just before it collides with the 5 kg
Assuming a 6 kg block is coupled to a spring with a 350 N/m spring constant, and that there is 0.5 m between the two blocks.
Solution:Use the formula
U=1/2kx2
U=1/23500.52
U=43.75 J
Utilizing the law of conservation of energy, KE = U - f.d, where f is the frictional force acting on
1/2 mv2 = 43.75 - mgd
1/2 ×6×v²= 43.75-0.3×6×9.8×0.5\s
v= √11.643
The spring constant is k, what is it?The "spring constant," denoted by the letter "k," is a figure that effectively indicates how "stiff" a spring is. A significant value of k indicates that more power is needed to extend it a given distance than would be necessary to stretch a less stiff spring the same distance.
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