The unit vector along r(t) will be 3t–4t^2+2
A vector is a quantity with direction and magnitude that is especially useful for locating one location in space in relation to another. A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields weight are a few examples of vectors in nature.
Given the the position of particle as a function of particle of time is given by: r(t)=3tî–4t^2j+2k. Where î & j are unit vector along the x-axis and y-axis respectively.
We have to find the unit vector along r(t)
To find the unit vector along r(t) we have to put the value of (i,j,k) = (1,1,1) in r(t)
So,
r(t) = 3tî–4t^2j+2k
r(t) = 3t(1)–4t^2(1)+2(1)
r(t) = 3t–4t^2+2
Therefore the unit vector along r(t) will be 3t–4t^2+2
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What does the first law of thermodynamics state about energy?
The first law states that the internal energy change of that system is given by Q − W . Since added heat increases the internal energy of a system, Q is positive when added to the system and negative when removed from the system.
Help with this :
What device does not store electric current or charge?
a) Capacitor
b) Transforme
c) vacuum tube
I know a capacitor is a device for storing charge, but it also says from a physical point of view, a capacitor does not store charge or electric current, but simply latent mechanical energy.
So what will be the answer?
Answer:
You are correct, the answer is capacitor
R S ( M ) = 2 G M c 2 , where G is the gravitational constant and c is the speed of light. It is okay if you do not follow the details of the equation; the basic point is that if you put an amount of mass M or larger in a sphere of radius smaller than RS(M)
What equation is this
The provided question's answer is "Schwarzschild radius".
The conversion factor between mass and energy is the speed of light squared.
GM/r stands for gravitational potential energy, also known as energy per unit mass.
GM/rc² then has "mass per unit mass" units. In other words, as mass/mass splits out in a dimensional analysis, "dimensionless per unit."
The derivation yields a formula for time or space coordinate ratios requiring sqrt(1 - 2GM/rc²). This number becomes 0 when r=2GM/c2, or the formula becomes infinite if in the denominator. However, there is no justification for using c² as a conversion factor there. Consider the initial expression sqrt(1 - 2GM/rc²).
Assume that m is used as the test particle's mass instead of 1. Then you have sqrt(m - 2GMm/rc² and mass units. This expression denotes that the rest energy of the test mass m you introduced into the gravitational field is "gone" at that radius.
The 2 would be absent if the gravitational field were Newtonian. However, at the event horizon, Einstein gravity is slightly stronger than Newton gravity, resulting in the factor 2 in qualitative terms.
So, the given equation is of Schwarzschild radius.
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An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a
mass of 3.8x 104 kg, and the force causes its speed to change from 6700 to 4600m/s. (a) What is the work done by the force? (b) If the
asteroid slows down over a distance of 2.4x 10 m determine the magnitude of the force.
The work done by the force is 7. 89 * 10^8 Joules and the magnitude of the force is 3. 3* 10 ^7 Newton
How to determine the work done
a. Work done = force * change in velocity = Impulse
Note that:
Force = mg
mass = 3.8x 104 kg
g = 10m/s²
Substitute into the formula for force
Force = 3.8* 10^4 * 10= 3.8* 10^5 Newton
Change in velocity = 6700 - 4600 = 2100 m/s
Work done = force *change in velocity
Work done = 3.8* 10^5 * 2100
Work done = 7. 89 * 10^8 Joules
b. Magnitude of the force = work done ÷ distance
Force = [tex]\frac{7. 89 * 10^8 }{2.4* 10}[/tex]
Force = 3. 3* 10 ^7 Newton
Therefore, the work done by the force is 7. 89 * 10^8 Joules and the magnitude of the force is 3. 3* 10 ^7 Newton
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Help me ASAP!!!!
If two balls have the same volume, but ball A has twice as much mass as ball B, which one will have the greater density?
A. Ball A
B. Ball B
C. Their Densities are equal.
Answer: A) Ball A
Explanation:
Density = m/v where m is mass and v is volume
This means the greater the mass, the greater the density.
Because of Ball A's greater mass it would have the greater density.
One principle of civil engineering is that when you design a highway you should have traffic flow in
the same direction and avoid interruptions to that flow as much as possible. Exit ramps tend to be
curved so that cars don't have to stop rather than having 90-degree angles that force stops and
starts. This is an application of which Gestalt principle?
The good continuation is an application of the Gestalt principle.
What is good continuation?
According to the Law of Good Continuation, figures with smooth edges are more likely to be perceived as continuous than those with abrupt or sharp angles.
One rule of civil engineering is that while designing a highway, traffic should move in one direction and be as free of interruptions as feasible.
Instead of having 90-degree angles that require stops and starts, exit ramps typically incorporate curves to prevent motorists from having to halt. Applying the Gestalt concept to a good continuation
Hence the good continuation is an application of the Gestalt principle.
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A 63.3 kg wood board is resting on very smooth ice in the middle of a frozen lake. A 35.7 kg boy stands at one end of the board. He walks from one end of the board to the other end with a velocity of 1.47 m/s relative to the ice in the positive direction. What is the velocity of the board relative to the ice?
The velocity of the board relative to the ice is zero, since both are at rest.
What is relative velocity?Relative velocity is the velocity of an object in relation to another reference object or point.
When two objects are travelling or moving with the same velocity in the same direction, the relative velocity one relative to the other is zero.
Also, when two objects are at rest, the relative velocity one relative to the other is zero.
Therefore, the velocity of the board relative to the ice is zero, since both are at rest.
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Given the following specific heat capacities, which material was have the largest change in temperature if 10 grams of each substance absorbs 100 calories of heat?
Substance Heat Capacity - Cal / (g oC)
aluminum 0.22
copper 0.093
lead 0.0305
silver 0.056
Answer:
Explanation:
Comment
You could calculate it out by assuming the same starting temperature for each substance. (You have to assume that the substances do start at the same temperature anyway).
That's like shooting 12 with 2 dice. It can be done, but aiming for a more common number is a better idea.
Same with this question.
You should just develop a rule. The rule will look like this
The greater the heat capacity the (higher or lower) the change in temperature.
The greater the heat capacity the lower the change in temperature
That's not your question. You want to know which substance will have the greatest temperature change given their heat capacities.
Answer
lead. It has the smallest heat capacity and therefore it's temperature change will be the greatest.
Find the relationship
[tex]\\ \rm\Rrightarrow Q=mc\Delta T[/tex]
[tex]\\ \rm\Rrightarrow 100=10c\Delta T[/tex]
[tex]\\ \rm\Rrightarrow 10=c\Delta T[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{10}{c}=\Delta T[/tex]
[tex]\\ \rm\Rrightarrow \Delta T\propto \dfrac{1}{c}[/tex]
So lower the c higher ∆T
Lead has the largest change in T as it has least capacity
find the velocity and acceleration if x=t³ +2t²+4 at a time 2s
Answer:
[tex]\textsf {v = 20 m/s}[/tex]
[tex]\mathsf {a = 16 m/s^2}[/tex]
Explanation:
[tex]\textsf {To find velocity, let's differentatiate x :}[/tex] [tex]\implies \mathsf {v = \frac{dx}{dt} }[/tex]
⇒ [tex]\mathsf {v = \frac{d}{dx}(t^{3}+2t^{2}+4) }[/tex]
⇒ [tex]\mathsf {v = 3t^{2} +4t +0 }[/tex] [tex]\textsf {(By applying law of differentiation)}[/tex]
[tex]\textsf {Substitute t = 2 :}[/tex]
⇒ [tex]\mathsf {v = 3(2)^{2} + 4(2) }[/tex]
⇒ [tex]\textsf {v = 12 + 8}[/tex]
⇒ [tex]\textsf {v = 20 m/s}[/tex]
[tex]\textsf {To find acceleration, let's differentatiate v :}[/tex] [tex]\implies \mathsf {a = \frac{dv}{dt} }[/tex]
⇒ [tex]\mathsf {a = \frac{d}{dx}(3t^{2}+4t) }[/tex]
⇒ [tex]\textsf {a = 6t + 4}[/tex]
[tex]\textsf {Substitute t = 2 :}[/tex]
⇒ [tex]\textsf {a = 6(2) + 4}[/tex]
⇒ [tex]\textsf {a = 12 + 4}[/tex]
⇒ [tex]\mathsf {a = 16 m/s^2}[/tex]
Mark is diving to the bottom of a pool to pick up a penny. Which of the
following describes the fluid pressure on his ears as he dives?
A. The fluid pressure increases as he dives.
B. After he dives, the fluid pressure increases and then decreases as
he dives deeper.
C. The fluid pressure on his ears doesn't change as he dives.
D. The fluid pressure decreases as he dives.
Answer:
A
Explanation:
As you go deeper, the pressure increases because the water is going farther away from the air and atmosphere
A skier is standing on a horizontal patch of snow. She is holding onto a horizontal tow rope, which is about to pull her forward. The skier’s mass is 59 kg, and the coefficient of static friction between the skies and the snow is 0.14. What is the magnitude of the maximum force that the tow rope can apply to the skier without causing her to move?
The magnitude of the maximum force that the tow rope can apply to the skier without causing her to move will be 81.03 N,
What is the friction force?It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N).
It is defined as the product of the coefficient of friction and normal reaction.
On resolving the given force and acceleration. Mathematically aion in the different components and balancing the equation gets. Components in the x-direction.
The normal force is balanced by weight;
N = mg
The magnitude of the maximum force that the tow rope can apply to the skier without causing her to move is;
F = μN
F= μmg
F=0.14 × 59 kg × 9.81 m/s²
F = 81.03 N
Hence, the magnitude of the maximum force will be 81.03 N,
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An athlete is running at a constant velocity with a javelin held in his right hand. The force he is applying on the javelin to carry it is 5.0 newtons. If he covers a distance of 10 meters, what work has he done on the javelin?
Answer:
50J
Explanation:
Work done=Fd
=5×10
=50J
what is the frequency of the photon emitted by a hydrogen atom when its electron drops from the n = 6 to n = 4 energy level?
The frequency of the photon emitted by a hydrogen atom is [tex]26.2*10^-^4 hz[/tex]
What are Photons?A particle representing a quantum of light or other electromagnetic radiation. A photon carries energy proportional to the radiation frequency but has zero rest mass.
In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ:
v = c/λ
Since the wavelength λ is in the bottom of the fraction, the frequency is inversely proportional to the wavelength.
v = c/λ
v= [tex]\frac{3*10^8}{434*10^-^9} = 6.91*10^1^4 Hz[/tex]
By using Rydberg's formula,
1/λ [tex]= Rz^2(\frac{1}{n_1^2} - \frac{1}{n_2^2})[/tex]
1/λ = [tex]109677 *(\frac{1}{4^2} - \frac{1}{6^2}) = 3808.22 cm^-^1[/tex]
λ = [tex]26.2*10^-^4 hz[/tex]
[tex]26.2*10^-^4 hz[/tex] is frequency of the photon emitted by a hydrogen atom.
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A surfer on top of a wave takes 10 seconds to travel a distance of 40 meters. What is the speed of the wave the surfer is riding on?
Select one:
a. 0.25 m/s
b. 4 m/s
c. 40 m/s
d. 400 m/s
Answer:
B. 4 m/sExplanation:
The formula for Speed is distance per time.
Therefore Speed = Distance / TimeData
D = 40 m
T = 10 sec
S = ?
Speed = 40m /10sec
To find the speed , divide the distance by the time.
Note : the unit for Speed is meter /second
Speed = 4 m/sTherefore the speed of the wave, the surfer is riding on is 4 m/s.
Which sentence describes an object that has kinetic energy?
Answer:
Kinetic energy is referred to the energy associated with movement and or motion, thus the only object that is moving would be A boat sailing across the ocean.
Explanation:
For a physics experiment, a solid cube is suspended from a spring scale. The gravitational force exerted on the cube is 0.714 N as measured when the object is suspended from a spring scale. When the suspended cube is submerged in water (ρ = 1000 kg/m3), the scale reads 0.450 N. What is the side of this cube in cm
The side of this cube will be 2.9996 cm. The net force on the solid cube is acting upward.
What is buoyancy force?
A fluid exerts an upward force against the weight of a partly or completely submerged item. The weight of the overlying fluid causes pressure to rise with depth in a column of fluid.
Given data;
Actual weight.W=0.714 N
Apparent weight,W'=0.450 N
The density of water,ρ=1000 kg/m³
The net force on the solid cube is;
Apparent weight = actual weight - buoyancy force
Buoyancy force = Actual weight - apparent weight
F=W-W'
F = 0.714 - 0.450
F= 0.264 N
The buoyancy force(F) is found as;
F = ρgV
0.264 = 1000 × 9.81 × V
V=2.69 × 10⁺⁵
The volume of a cube is found as;
V=a³
2.69 × 10⁺⁵ m³=a³
a=0.02996 m
As we know that 1 m = 100 cm
a=2.996 cm
Hence, the side of this cube will be 2.9996 cm.
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which one of the following is true about Tesite stress
It is defined as the stress that results in the elongation of the material
which of the following is NOT a type of scientist?
A. Geologist
B. Meteorologist
C. Botanist
D. Cryptologist
A cryptologist is not a type of scientist. The correct answer is a cryptologist and the correct option is (D).
Experts in the study of methods for secure communication and data security through encryption and decryption are known as cryptologists.
Even though they are considered scientists in the broadest sense, they are not typically classed with the other natural scientists (geologists, meteorologists, and botanists) stated in the alternatives.
Due to its emphasis on the methods and mathematical principles used in encryption and decryption, cryptology is more intimately related to computer science and mathematics.
Therefore, The correct answer is a cryptologist and the correct option is (D).
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What will be the temperature reading in Fahrenheit scale whe eading is 310 k?
The temperature reading in Fahrenheit scale when reading 310 K is 98.6F
What is temperature?
Temperature is the degree of hotness or coldness of the object.
Given is a temperature in Kelvin scale = 310 K
Temperature on centigrade scale = 310 -273 = 37°C
Temperature conversion from Centigrade to Fahrenheit is
C/5 = F -32/9
Plug the value, we get
37/5 = F-32/9
66.6 = F -32
F = 32+66.6 =
F = 98.6
Thus, the temperature of 310 K in Fahrenheit is 98.6F.
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a person walk at first constant speed 5 m/s then back alone the straight line from B to A at a constant speed 3 m/s a) what is his average speed over the entire trip b) what is his average velocity over the entire trip
Answer:
3.75 m/s
Explanation:
Comment
Let's deal with the second question first. The average velocity is 0 because the displacement (distance between the starting point and ending point) is 0.
The first question is a little harder. You don't seem to have enough information. When that happens, you can just make things up. Now there's an interesting solution. You could do it with algebra, but it is easier to see with numbers.
Givens
d = 150 m. between A and Br1 = rate from A to B = 5 m/sr2 = rate from B to A = 3 m/stime A to B = t1time B to A = t2Formulas
t1 = d / r1
t2 = d/r2
average rate = total distance / total time
Solution
t1 = 150 m / 5 m/s = 30 seconds
t2 = 150 m / 3 m/s = 50 seconds
Total distance = 150 m + 150 m = 300 m
Total time = 30 seconds + 50 seconds = 80 seconds
Average speed = 300 m / 80 s
Answer
Average speed = 3.75 m/s
A small mass of m = 187 g hangs from a string of length l = 1.21 m.
Calculate the initial speed v the mass m should be given at the bottom, so that the string reaches a maximum angle of θ = 36.5°?
The initial speed v, the mass m should be given at the bottom, so that the string reaches a maximum angle is 2.16 m/s.
What is mechanical energy?The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.
M.E = KE +PE
Given is a small mass of m = 187 g hangs from a string of length l = 1.21 m. The string reaches a maximum angle of θ = 36.5. The acceleration due to gravity, g = 9.8 m/s²
The vertical height of the point mass h = l- lcosθ
h = 1.21 - (1.21cos 36.5°)
h = 0.2373 m
The conservation of energy principle states that total mechanical energy remains conserved in all situations where there is no external force acting on the system.
Kinetic energy = Potential energy
1/2 mv²= mgh
Substituting the values, we have
1/2 x v² = 9.8 x 0.2373
v = sqrt [2 x9.8 x 0.2373]
v= 2.16 m/s
Thus, the initial speed v the mass m should be given at the bottom, so that the string reaches a maximum angle is 2.16 m/s.
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Which of the following measurement is most significant?
A. 66.000cm
B. 0.00066cm
C. 6.600cm
D. 6.6cm
Option C. The measurement with the most significant number is 6.600 cm.
What is significant number?
Significant numbers are numbers that have significance or meaning and give more precise details about the value of the entire numbers.
66.000 cm ------> 2 significant numbers0.00066 cm -------> 2 significant numbers6.600 cm ----------> 4 significant numbers6.6 cm ---------------> 2 significant numbersThus, the measurement with the most significant number is 6.600 cm.
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If a cup of coffee is at 90°C and a person with a body temperature of 36°C touches it, how will heat flow between
them?
O from the hand to the cup
from the cup to the hand
from the cup to the surrounding air
from the hand to surrounding air
Mark this and return
Save and Exit
ext
Submit
Answer:
if you pick it up the heat will flow to the hand until the Temperature of both evens out
Psychology is a combination of the Greek words psyche, which means “soul” or “mind,” and logos, which means “the study of.”
Please select the best answer from the choices provided
T
F
Greek terms psyche, which means "soul" or "mind," and logos, which means "the study of," are combined to form the english word psychology. The assertion is true.
What is Psychology?Psychology is the name given to the scientific study of the mind and behavior. Psychologists are actively interested in researching and comprehending how the mind, the brain, and behavior work.
Psychology is a combination of the Greek words psyche, which means “soul” or “mind,” and logos, which means “the study of.”The given statement is corect.
Hence the best answer from the choices provided will be true.
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The three waves shown in the picture below are equal in wavelength, but are travelling at different speeds. Given this information, which wave has the highest frequency?
Select one:
a. 1
b. 2
c. 3
d. Can't tell from the information given.
Wave 3 will have the highest frequency. Option c is correct.
What is the frequency?
Frequency is defined as the number of repititions of a wave occurring waves in 1 second.
Frequency is given by the formula as,
[tex]\rm v = \lambda \times f[/tex]
If the wavelength of the wave is content the velocity of the wave is directly propotional to the frequency.
The velocity of wave 3 is maximum. So that the wave 3 will have the highest frequency.
Hence option c is correct.
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A penny is dropped so that it reaches a terminal velocity of 13.3m/s. If the momentum is measured to be 0.0332kgm/s, what is the mass of the penny
Answer:
2.5 grams
Explanation:
p = mv
m = p/v
m = 0.0332 / 13.3
m = 0.0025kg
0.0025 x 1000 = 2.5
m = 2.5g
There are several ways to model a compound one type of model is shown ?what is the chemical formula for the molecule modeled?
The is organic compound with the correct chemical formula C4H9O2.
What is a model?A model is a representation of reality. A model serves the purpose of prediction as well as explanation.
Looking at the model of the molecule we can see that it is the organic compound with the correct chemical formula C4H9O2. The molecule is shown in the image attached to this answer.
Missing parts:
There are several ways to model a compound. One type of model is shown.
What is the chemical formula for the molecule represented by the model?
CHO
C4H9O2
C4H8O
C3H8O2
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You are standing in an open field near a train track as a train goes by at a constant speed blowing its horn in all directions (except down, into the ground) at a constant frequency. You are first able to hear it when it is approaching you 1 km away. When it is a quarter of a kilometer past you, by how many decibels has the train's sound level intensity shifted?
(options: 6, 12, 58, 105, 108, or 114)
Answer:
108 is the correct answer
Particles q1, 92, and q3 are in a straight line.
Particles q1 = -5.00 x 10-6 C,q2 = +2.50 x 10-6 C,
and q3= -2.50 x 10-6 C. Particles q1 and q2 are
separated by 0.500 m. Particles q and q3 are
separated by 0.250 m. What is the net force on q2?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
-5.00 x 10-6 C
91
0.500 m
+2.50 x 10-6 C
+92
-2.50 x 10-6 C
93
0.250 m
Answer:
-1.35 N
Explanation:
Force due to q1
F = 9 × 10⁹ × 5 × 10⁻⁶ × 2.5 × 10⁻⁶ / 0.5²F = 450 × 10⁻³F = 0.45 N (+)Force due to q2
F = 9 × 10⁹ × 5 × 10⁻⁶ × 2.5 × 10⁻⁶ / 0.25²F = 1800 × 10⁻³F = 1.8 N (-)Net Force
0.45 - 1.8-1.35 NWhat is matter ?
.......................
Answer:
Something which occupies space and have mass.