Answer:
To find the magnitude of a vector, you can use the Pythagorean theorem. In this case, the magnitude of the vector is given by:
sqrt((-22.2m)^2 + (12.6m)^2)
This simplifies to:
sqrt(486.24 + 159.96)
Which is equal to:
sqrt(646.2)
Which is approximately equal to:
25.4 m
So the magnitude of the vector (-22.2m, 12.6m) is approximately 25.4 m.
Explanation:
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Phillipe is being asked to give testimony. What will this responsibility MOST likely include?
O A. He will donate money to charity.
OB.
O C.
O D.
He will help make peace in his community.
He will take an oath to tell the truth.
He will ignore evidence and say how he feels.
Reset
Next
He will reportedly swear an oath to speak the truth for this obligation, which MOST likely includes.
What types of proof are there?Fingerprints, blood test, DNA, a knife, a pistol, and other tangible things are examples of genuine evidence. Real evidence is often allowed into court because it has the power to support or refute a claim of fact during a trial.
Why is testimony crucial in court?The purpose of evidence is to persuade the jury or judge of the issues involved. Additionally, evidence might be a tangible object or any declarations of fact that were already made at trial to prove the veracity of the subject of the inquiry.
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Consider two points on a graph: (3,6) and (5,11). What is the slope of the line that connects these two points?
Answer:
5/2
Explanation:
Slope = (y2-y1)/(x2-x1)
= (11-6)/((5-3)
= 5/2
Which is the best example of kinetic energy?
• picture of the sun shining on a field of flowers
• an owl
• a dog running
• rocks on grass
A dog running is the best example of Kinetic energy.
In simple terms, Kinetic energy is defined as the energy due to motion. Any object in motion is said to possess kinetic energy.
Kinetic energy is formulated as [tex]E = 1/2 mv^{2}[/tex]
The energy possessed due to the state of rest is Potential Energy. It is represented using the symbol U.
Picture of sun shining on a field of flowers - is not an example of kinetic energy as no motion is involved, The picture is a still object.
An owl - is not an example of kinetic energy as it does not specify whether own is in motion or at rest.
A dog running - is an example of kinetic energy as the dog is in motion.
Rocks on grass - is not an example of kinetic energy as the rocks and grass are in the state of rest thus no motion is involved.
Thus, a dog running is the best example of Kinetic energy.
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Star A has a temperature of 3000K; Star B has a temperature of 5000K; Star C has a temperature of 8000 K. According to Wien's Law, which star would have the shortest maximum wavelength? Star A Star B Star C
Star C will have the shortest maximum wavelength with a wavelength of 3.623 x 10⁻⁷ m
How to calculate wavelength?According to Wien's Law, the maximum wavelength of a star's radiation depends on its temperature. The formula for Wien's Law is:
λ_max = 2.898 x 10⁻³ / T
where λ_max is the maximum wavelength in meters, and T is the temperature in Kelvin.
Plugging in the temperatures for the three stars:
Star A: λ_max = 2.898 x 10^-3 / 3000 = 9.66 x 10⁻⁷ m
Star B: λ_max = 2.898 x 10^-3 / 5000 = 5.796 x 10⁻⁷ m
Star C: λ_max = 2.898 x 10^-3 / 8000 = 3.623 x 10⁻⁷ m
So, Star C would have the shortest maximum wavelength.
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Edwin and cam are playing a golf. Edwin putts his golf ball at a velocity of 3 m/s and it hits Cams golf ball.Both golf balls have a mass of 0.15 kg. Edwin’s golf ball comes to a complete stop after it collides with Cams golf ball. According to the law of conservation of momentum. What should the resulting velocity of cams golf ball be if it was at rest before colliding with Edwin’s golf ball?
A:Equal tot he velocity of Edwin’s golf ball before they collided
B:twice the velocity of Edwin’s golf ball before they collided
C:half the velocity of Edwin’s golf ball before they collided
D:equal to the velocity of Edwin’s golf ball after they collided
Answer: A
Explanation:
Because of the law of conservation of momentum (total momentum of two golf balls must be constant).
What is the scientific definition of energy that reflates it to work? The ability to use the stored potential of an object. The ability to use an applied force to make and object move. The ability to use the change in temperature of an object.
The scientific definition of energy that reflates it to work is: the ability to use the stored potential of an object.
What is energy?In physics, energy is the ability to perform work. It could exist in several different forms, such as potential, kinetic, thermal, electrical, chemical, radioactive, etc.
Additionally, there is heat and work, which is energy being transferred from one body to another. Energy is always assigned based on its nature once it has been transmitted.
So, scientifically energy is the ability to use the stored potential of an object.
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Fundamental Problem 12.28
The car is traveling along the road with a speed of v=(|l2 s) m/s, where s is in meters. (Figure 1)
Part A
Determine the magnitude of its acceleration when s=11 m.
Express your answer to three significant figures and include the appropriate units.
The acceleration of the car in three significant figures is 0.181 m/s².
What is the acceleration of the car?
The acceleration of the car is calculated by applying the following kinematic equation as shown below.
v² = u² + 2as
where;
v is the final velocity of the caru is the initial velocity of the cara is the acceleration of the cars is the distance travelled by the carThe given parameters include the following;
the final velocity of the car = 2 m/s
the distance travelled by the car = 11 m
The acceleration of the car is calculated as follows;
v² = u² + 2as
v² = 0 + 2as
a = v² / 2s
a = ( 2² ) / ( 2 x 11 )
a = 0.181 m/s²
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using f=ma explain why a train is more diffcult to start moving and more difficult to bring to a stop than an average sized car
It is more difficult to start a train moving due its larger mass that will produce a smaller acceleration compared to an average sized car for an equal applied force.
Also is more difficult to bring a train to a stop than an average sized car, because the train exerts a larger force than the average sized car.
What is Newton's first law of motion?
Newton's first law of motion states that an object at rest or uniform motion in a straight line will continue in that path unless an external force acts on the object and the object will move in the direction of the applied force.
Newton's first law of motion is known as inertia because, it depends on the mass of the object.
According to Newton's second law of motion, the force applied to an object is directly proportional to the product of mass and acceleration of the object.
Mathematically, the formula for Newton's second law of motion is given as;
F = ma
where;
m is the mass of the objecta is the acceleration of the objectF is the applied forceThe acceleration of an object is determined from Newton's second law of motion;
a = F / m
Thus, from the equation above, the greater the mass of an object, the smaller the acceleration of the object for a constant force.
Also an object with a large mass such as a train will require large force of friction to be brought to rest since the force exerted by the train will be great due to its large mass.
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Suppose the woman in the figure is 54kg , and the board she is standing on has a 10kg mass. What is the reading on each of the scales?
The reading on each of the scales on the right is 421.4 N.
The reading on each of the scales on the left is 156.8 N.
What is the reading on each scale?The reading on each scale is determined from the distribution of the weight of the woman.
The weight of the board is distributed uniformly and each scale with have equal reading of the weight of the board.
weight of the board = 10 kg x 9.8 m/s² = 98 N
Reading of each due to weight of the board is calculated as;
W₁ = ¹/₂ (98 N) = 24.5 N
The distribution of the weight of the woman on the right scale is calculated as;
W (R) = ( 1.5 m / 2 m) x ( 54 x 9.8 )
W (R) = 396.9 N
The distribution of the weight of the woman on the left scale is calculated as;
W (L) = ( 0.5 m / 2 m) x ( 54 x 9.8 )
W (L) = 132.3 N
Total reading on the scale on the right = 396.9 N + 24.5 N = 421.4 N
Total reading on the scale on the left = 132.3 N + 24.5 N = 156.8 N
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1. Would a cart that has four solid disks for wheels have a final speed that is greater than, less than, or equal to the final speed of a single disc that has the same mass as the cart and
wheels? Explain.
2. Suppose a cart with four wheels and a disk whose mass is equal to the total mass of the cart roll down the ramp. Which, if either, has more gravitational potential energy at the top?
3. Which of those objects has more kinetic energy at the bottom? Why?
4. Imagine the disk just spinning in place instead of rolling, would it have kinetic energy? Why?
5. Why does the cart have more speed at the bottom even though it doesn't have more kinetic energy than the disk?
The final speed would be equal because they don't depend on the mass or the radius.
What variables affect kinetic and potential energy, respectively?The mass, gravitational pull, and height above the earth all affect how much potential energy an item has. This energy is transformed into kinetic or indeed the change in momentum, when you fall the thing. An object's mass and speed affect its kinetic energy.
What three variables determine kinetic energy?The quantity of work performed on an object as well as its velocity following an inertia moment caused by external forces are two aspects that affect the overall kinetic energy about an object. The most crucial variables that affect kinetic energy are the motion calculated in terms of the object's mass and velocity.
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which of the following best describes the strength of coriolis deflection where isobars are very close together?
b) The strength of the apparent deflection varies with speed of Earth's rotation best describes the strength of Coriolis deflection where isobars are very close together.
The Coriolis deflection is a phenomenon of the Earth's rotation that affects the movement of air masses and ocean currents. The strength of the apparent deflection of these air and water masses varies with the speed of the Earth's rotation. Hence, option b is correct.
This is particularly noticeable when isobars, or lines of equal pressure, are very close together. The Coriolis deflection causes the air or water to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
This deflection can result in the formation of cyclonic weather systems and gyres in the ocean.
Although a part of your question is missing, you might be referring to this question:
Which of the following best describes the strength of coriolis deflection where isobars are very close together?
a) Slowly moving objects are deflected more than rapidly moving objects.
b) The strength of the apparent deflection varies with speed of Earth's rotation.
c)Coriolis deflection occurs only along parallels, not meridians.
d) The Coriolis force is zero at the poles, increasing to maximum along the equator.
e)The amount of Coriolis deflection is uniform from equator to poles.
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proton (q 1.6 X10-19 C,m = 1.67 X 10-27 kg) moving with constant velocity enters region containing constant magnetic field that is directed along the z-axis at (x,y) (0,0) as shown The magnetic field extends for distance 0.48 m in the x-direction: The proton leaves the field having velocity vector (5.8 X 105 m/s, 3.2 X 105 m/s).
1) What is the magnitude of the velocity of the proton as it entered the region containing the magnetic field? ______m/s Submit
2) What is R, the radius of curvature of the motion of the proton while it is in the region containing the magnetic field? ______m/s Submit
3) What is h, the co-ordinate of the proton as it leaves the region conating the magnetic field? ______m/s Submit
4)What is Bz, the z-component of the magnetic field? Note that Bz is signed number . ______m/s Submit
5) If the incident velocity were increased_ how would and change if at all? h and would both increase and would both decrease would increase and would decrease would decrease and would increase Neither h nor would change. ______m/s Submit
Magnetic Field:
A magnetic field is the vector field that depicts how the magnetic force is distributed within or around a certain magnetic substance. The magnetic field, which consists of closed loops, travels from the North Pole to the South Pole.
Given Data:
The charge on the proton is:
q = 1.6 × 10⁻¹⁹ C
The mass of the proton is:
m = 1.67 × 10⁻²⁷ Kg
The distance by which the magnetic field extends is:
D = 0.44 m
The velocity of proton in x direction is:
vₓ = 5.1 × 10⁵ m/s
The velocity of proton in y direction is:
v = 2.7 × 10⁵ m/s
Answer and Explanation:
(1):The expression for the resultant velocity when the proton enter the magnetic field is,
[tex]v = \sqrt{v_{x^2} +v_{y^2}}[/tex]
Substitute the values in above expression.
[tex]v = \sqrt({5.1 * 10^{5} m/s} )^{2} + ({2.7 * 10^{5} m/s} )^{2}[/tex]
[tex]v = 5.8 * 10^{5} m/s[/tex]
Thus, the resultant velocity when the proton enter the magnetic field is [tex]v = 5.8 * 10^{5} m/s[/tex]
(2): The expression for the angle of inclination of proton is,
tanΘ = [tex]\frac{v_{x} }{v_{y} }[/tex]
Substitute the values in above expression.
tanΘ = [tex]\frac{2.7 * 10^{5 }m/s }{5.1 * 10^{5} m/s}[/tex]
= tan⁻¹(0.53)
Θ= 27.92°
The expression for the radius of curvature is,
[tex]R = \frac{D}{sin \theta}[/tex]
Substitute the values in above expression.
R= [tex]\frac{0.44 m}{sin 27.92}[/tex]
R≈ 0.94 m
Thus the radius of curvature is 0.94 m
(3): The expression for the y coordinate of proton is,
[tex]h = R -\frac{D}{tan \theta}[/tex]
Substitute the values in above expression.
[tex]h = 0.94 m -\frac{0.44 m}{tan \ 27.92}[/tex]
[tex]h=0.11 m[/tex]
Thus, the y coordinate of proton is 0.11 m
(4): The expression for the z component of the magnetic field is,
[tex]B_{z} =\frac{m*v}{q*R}[/tex]
Substitute the values in above expression.
[tex]B_{z} =\frac{(1.6 * 10^{-27 }kg) *(5.8*10^{5}m/s ) }{1.6*10^{-19} *0.94 m}[/tex]
[tex]B_{z} =6.44 * 10^{-3} kg/C.s[/tex]
Thus, the z component of the magnetic field is [tex]6.44 * 10^{-3} Kg/C.s[/tex]
(5): The radius of curvature would rise by the same amount if the velocity were increased because R varies linearly with v. The angle of incidence also lowers as the radius of curvature increases. The displacement h likewise decreases as the angle narrows.
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Which property of concave mirror is used in telescope?
Answer: reflection
Explanation: the concave mirror will gather light from distant objects outside of the Earth's atmosphere. since these celestial objects are so far, the rays of light are parallel, and the mirror will reflect it at the focus point, and the image displayed depends on how far away the object is.
How many energy levels do the electrons occupy for a neutral Oxygen atom?
Electrons occupy neutral oxygen atom has 8 electrons.
How many electrons are there in a neutral atom of oxygen?Now you can statistic out how many electrons, protons and neutrons Oxygen has: Atomic number which is all the time smaller of the two numbers is 8. Hence 8 protons. Because the atom is impartial, there are also 8 electrons. Oxygen likes to have two extra electrons to make it happy. Each lithium atom provides one.
the first two electrons will inhabit the 1s orbital while the next two electrons will occupy the 2s orbital. The endure four electrons will occupy the 2p orbital. The correct design for a neutral oxygen atom.
So we can conclude that Oxygen is the eighth element with a total of 8 electrons. In writing the electron layout for oxygen the first two electrons will go in the 1s orbital.
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Is the electric field strength in FIGURE increasing, decreasing, or not changing? Explain.
In figure the electric field strength is decreasing.
The electric field strength in FIGURE is not changing.
What is electric field line?
An great approach to see electric fields is with electric field lines.
At one point, a field line is drawn perpendicular to the net. As a result, the direction of the electric field at any place is the same as the tangent to the electric field line. Second, the relative strength (magnitude) of the electric field at a location is correlated with the relative density of the field lines around that point.
In the figure, density of electric field line is same everywhere. Hence, the electric field strength is not changing here.
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Refer to Figure 13-3. Which of the points in the above graph are possible long-run equilibria?
B and D
A and B
A and C
A and D
The points in the above graph that are possible long-run equilibria include B. A and B.
How to explain the equilibrium?A and B are the equilibria. This is because long run equilibrium occurs where the aggregate demand intersects the long run aggregate supply curve. The long run equilibrium will always occur at long-run aggregate supply curve.
The other options are incorrect because they lie at the intersection of short-run aggregate supply curve and aggregate demand curve. They do not lie on long run aggregate supply curves and hence are not long-run equilibrium points.
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suppose a car is accelerating so that its speed in incresing. first describe the line that you would plot on a speed-time graph for the motion of the car. than describe the line that you would plot on a distance-tome graph
On a speed-time graph, the line representing the motion of the car would be a straight line with a positive slope. This is because the speed of the car is increasing, so the line on the graph would slope upwards from left to right.
How to illustrate the information?On a distance-time graph, the line representing the motion of the car would also be a straight line, but with a slope that is greater than that of the line on the speed-time graph.
This is because distance is the product of speed and time, so if the speed of the car is increasing, the distance traveled by the car will also be increasing at an increasing rate. The line on the distance-time graph will therefore have a steeper slope than the line on the speed-time graph.
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if more resistors are added in series to a battery with zero internal resistance, the power supplied by the source______ . group of answer choices decreases does not change increases
If more resistors are added in series to a battery with zero internal resistance, the power supplied by the source decreases.
The reason is that adding more resistors will increase the total resistance and decrease the current through all resistors. The new total resistance is: Rtot = R₁ + R₂ + R₃ + ...
And we know from ohm's law, V/I = R.
From here, we can see that when we add more resistors in series, we have more voltage across each individual part of our circuit, but less current flowing through each part of it. That means our total power supplied by the source decreases because there is less current flowing through the resistors when combined.
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A bus of mass 2500 kg goes round a corner of radius 50 m at a speed of 5 m/s. What force is needed for the bus to go round the corner?
Answer:
force needed for the bus to go round the corner is 50,000 N.
Explanation:
To find the force needed for the bus to go round the corner, we can use the formula for centripetal force:
F = (mv^2)/r
where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
Plugging in the values given in the problem, we get:
F = (2500 kg)(5 m/s)^2 / 50 m
= 50,000 N
So the force needed for the bus to go round the corner is 50,000 N.
A coin has a radius of 1.06 cm and a thickness of 1.1 mm. Find its volume in m3.
Answer:
3.8809144
Since we are looking for volume, we will look at the coin as a cylinder. The volume of a cylinder is pi x r^2 xh. Assuming pi is 3.14 the equation would go 3.14x1.1236x1.1. Which would give you the answer,
A student swings a ball at the end of a string of length R in a vertical circle as shown. The ball moves with the minimum speed necessary to complete a circular path at point 1. Consider the system of the ball. In terms of the mechanical energy of the system, which of the following claims is correct, and why?
In the circular motion, the system is open, because a net force is exerted on the ball as it travels in a circle. Option B
What is the circular motion?We know that the term circular motion would have to do with the kind of motion that is occurring in a circular path. We have to know that the velocity of the object may be constant but the object may still be said to be accelerating.
Given the fact that we know that the acceleration of the ball is not the same at all the points of the circle as we can see it then it follows that the system is an open system as the net force acts on it.
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Using a ring collar the 75-N force can act in the vertical plane at various angles θ.
Determine the magnitude of the moment it produces about point A if θ=36 in N.m
The moment of the force about point A is 66.13 Nm.
What is moment?Moment is the product of a force and its perpendicular distance.
To calculate the magnitude of the moment produce about point A, we use the fornula below.
Formula:
M = Fsin∅d.................. Equation 1Where:
M = moment of the force about A∅ = AngleF = Forced = DistanceFrom the question,
Given:
F = 75 N∅ = 36°d = 1.5 mSubstitute these values into equation 1
M = 75×sin36°×1.5M = 66.13 NmHence, the moment of the force is 66.13 Nm.
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Perform the following mathematical operation, and report the answer rounded to the correct a number of significant figures.
143.6 / 21.2=?
Answer:
6.77
Explanation:
What fraction or percentage of the class do you expect to have
unattached earlobes? What fraction of the class do you expect to have
attached earlobes? What reasoning can you provide to support your
prediction?
Answer in 2-3 complete sentences. Use the data you recorded from
the discussion to support your prediction if available.
Answer:
I expect that approximately half of the class will have unattached earlobes, while the other half will have attached earlobes. This is because the trait for having attached or unattached earlobes is determined by a single gene with two alleles, and these alleles are equally common in the population. Therefore, the probability of an individual having attached earlobes or unattached earlobes is roughly equal. Therefore, I would expect that about half of the class will have each type of earlobe.
What would the speed of an object be if it had a period of 5 seconds and a radius of 2m?
Answer:
2 m/s approximately
Explanation:
We can use linear speed formula to solve this problem as we are given with period and radius:
[tex] \displaystyle{v = \dfrac{2\pi r}{T}}[/tex]
v is velocity, r is radius and T is period. Substitute in known values:
[tex] \displaystyle{v = \dfrac{2\pi \times 2}{5}} \\ \\ \displaystyle{v = \dfrac{4\pi}{5}} \\ \\ \displaystyle{v = \dfrac{4 \times 3.14}{5}} \\ \\ \displaystyle{v = \dfrac{10}{5} } \\ \\ \displaystyle{v = 2 \: \text{m/s}}[/tex]
As for why 4*3.14 becomes 10, it's due to the significant figure rules of multiplication. Since it's 1 significant figure times 3 significant figures, we use the lowest significant figures to determine the answer. Hence, why it's not 12 but 10 instead.
A red blood cell contains 3.0 10^7 free electrons. What is the total charge of these electrons in the red blood cell?
The total charge of these electrons in the red blood cell is 4.8 × 10⁻¹⁰ Coulomb.
What is charge?The physical characteristic of matter that causes it to feel a force when exposed to an electromagnetic field is called electric charge.
The two types of electric charges - protons and electrons.
The red blood cell contains 3.0 × 10⁷ free electrons.
Electric charge of each electron = 1.6 × 10⁻¹⁷ Coulomb.
Hence, the total charge of these electrons in the red blood cell is = total number of electrons × charge of each electrons
= 3.0 × 10⁷ × 1.6 × 10⁻¹⁷ Coulomb.
= 4.8 × 10⁻¹⁰ Coulomb.
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the earth takes approximately 24 hours to complete one rotation on its axis. This unit of time has no direction which makes it a what?
A. Direction
B. Scalar
C. Vector
D. Magnitude
Please have a good explanation
Answer:
scalar
Explanation:
it has only magnitude and no direction (vector has both)
A ball of mass m is fastened to a string. the ball swings at constant speed in a vertical circle of radius r with the other end of the string held fixed. neglecting air resistance, what is the difference between the string's tension at the bottom of the circle and at the top of the circle? (note: a vertical circle means the ball is moving up and down as it goes in a circle - this means that gravity must be considered.)
The difference between the string's tension at the bottom of the circle and at the top of the circle is 2mg.
Given the mass of the ball is m
radius of circle = r and constant speed is maintained = v
At the top of the circle, ΣF = FT + mg = mv^2/r, where F is the force acting on the string, T is tension, m is mass and g is gravitational acceleration.
Here as the ball moves in circle it carries centripetal force = mv^2/r.
Then FT = mv^2/r – mg.
At the bottom of the circle, ΣF = FT – mg = mv^2/r, So
FT = mv^2/r + mg
By comparing these two equations we get:
The difference is (mv^2/r + mg) – (mv^2/r – mg) = 2mg.
Hence the required difference is 2mg.
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There is a 2mg difference in string tension between the circle's bottom and top points.
Calculation:the mass of the ball is m
radius of circle = r and constant speed is maintained = v
At the top of the circle, ΣF = FT + mg = mv^2/r, where F is the force acting on the string, T is tension, m is mass and g is gravitational acceleration.
Here as the ball moves in circle it carries centripetal force = mv^2/r.
Then FT = mv^2/r – mg.
At the bottom of the circle, ΣF = FT – mg = mv^2/r, So
FT = mv^2/r + mg
By comparing these two equations we get:
The difference is (mv^2/r + mg) – (mv^2/r – mg) = 2mg.
Hence the required difference is 2mg.
Why does the top of a circle have zero tension?When the centripetal force and the gravitational force are exactly equal at the peak of the swing, the minimum speed will occur. The tension would then be exactly zero, and the ball would hardly be able to keep rolling in a circle.
Why is the bottom where stress is greatest?The weight of the body operates vertically downward while the centrifugal force acts vertically downward at the lowest position. As a result, the string's tension is at its highest. The weight of the body acts vertically downward and the centrifugal force acts vertically upward at the highest point.
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A wheel of radios 0.5m initialy at rest with a constant angular acceleration and attains a linear speed of 30 m/s in 5 sec. calculate
a) the angular acceleration?
b) the angular velocit's after 4 sec?
c) the number of revolution at a time of 5sec?
Answer:
a.) 12[tex]\frac{rad}{s^2}[/tex]
b.) 48[tex]\frac{rad}{s}[/tex]
c.) 23.87 rev
Explanation:
First, convert linear velocity to angular velocity. The angular velocity can be calculated using the relationship v=rω, where v is the linear velocity, r is the radius, and ω is the angular velocity. Rearrange the equation to solve for ω:
[tex]\omega=\frac{v}{r}[/tex]
For this problem, let v=30[tex]\frac{m}{s}[/tex] and r=0.5m. So,
[tex]\omega=\frac{30\frac{m}{s}}{0.5m}\\\omega=60\frac{rad}{s}[/tex]
Next, to solve for angular acceleration use rotational motion equation #1, [tex]\omega_f=\omega_i+\alpha t[/tex]. For this problem, let
[tex]\omega_i=0.0\frac{rad}{s}\\\omega_f=60\frac{rad}{s}\\t=5s[/tex]
So,
[tex]60\frac{rad}{s}=0.0\frac{rad}{s}+\alpha(5s)\\(\frac{1}{5s})60\frac{rad}{s}=\alpha(5s)(\frac{1}{5s})\\12\frac{rad}{s^2}=\alpha[/tex]
Next, use the angular acceleration and the time given in part b in rotational motion equation #1 to solve for the angular velocity at t=4s:
[tex]\omega_f=\omega_i+\alpha t\\\omega_f=0.0\frac{rad}{s}+(12\frac{rad}{s^2})(4s)\\\omega_f=48\frac{rad}{s}[/tex]
To find the number of revolutions, use rotational motion equation #3, [tex]\theta=v_it+\frac{1}{2}\alpha t^2[/tex], to find the angular displacement at t=5s. So,
[tex]\theta=0.0\frac{m}{s}(5s)+\frac{1}{2}(12.0\frac{rad}{s^2})(5s)^2\\\theta=0.0m+150\ rad\\\theta=150\ rad[/tex]
To convert the angular displacement in radians to revolutions, recall that one revolution equals 2π radians. So,
[tex]150\ rad(\frac{1\ rev}{2\pi\ rad})=\frac{75}{\pi}\ rev\approx23.87\ rev[/tex]
