Answers
Option A from the following options represents the resultant vector r = a-b, therefore the correct answer is option A.
What is a vector quantity?The quantities that contain the magnitude of the quantities along with the direction are known as the vector quantities.
Examples of vector quantities are displacement, velocity acceleration, force, etc.
As given in the problem we have to find out which of the following vector best represents r = a - b,
As per the triangle law of the vector addition, the resultant sum is represented by the closing side of the triangle in regular order.
Thus, the correct answer is option A.
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Related Questions
The driver of a car traveling at 10.0 m/s along a straight road depresses the accelerator and uniformly increases her speed at a rate of 2.00 m/s2. how fast will the car be moving as it passes a parked police cruiser 140 m away?
Answers
Answer:
60m/h
Explanation:
what must the charge (sign and magnitude) of a 1.48-g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 660 n/c ? you may want to review (page) .
Answers
Mass of the particle m=1.48 g=1.48×10−3 kgm=1.48 g=1.48×10−3 kg
Electric field E=670 N/CE=670 N/C directed downwards.
Charge Particle in an Electric FieldThe electric force must act as opposite to the weight of the particle
we know,
qE= mg x qE = mg
q = mgEq= mgE
q= 1.48×10−3 kg × 9.8 m/s 2670 N/C
therefore; q=2.16×10−5 Cq= 2.16×10−5 C
As the force is upwards and an electric field is downwards it means the charge on the particle is negative.
q=−2.16 × 10−5 Cq= −2.16 × 10−5 C
In the second case for a proton
qE= mgqE= mg
E= mgqE= mgq
E= 1.67×10−27 kg × 9.8 m/s21.6×10−19 C
E= 1.023×10−7 N/C
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What are the advantages of using unlicensed frequency bands for rf transmissions? (choose all that apply.)
Answers
B and C. An unlicensed frequency has the main benefits of being open to use by anyone and not requiring a license to transmit on it.
You are still subject to transmission rules and other limitations even though there are no additional expenses. Due to congestion, the fact that anyone can utilize the frequency spectrum is also a drawback.
What group defines the unlicensed frequencies utilized by Wi-Fi?The Wi-Fi Alliance fights for unlicensed spectrum and for preserving the advantages that Wi-Fi offers.
What kind of transmission and reception methods do 802.11 radios employ?802.11ax radios may broadcast and receive data in either the 2.4 GHz or 5 GHz frequency bands, in contrast to 802.11ac, only runs at 5 GHz. 802.11ax technology.
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Complete question:
What are the advantages of using unlicensed frequency bands for rf transmissions? (Choose all that apply.)
A. There are no government regulations.
B. There is no additional financial cost.
C. Anyone can use the frequency band.
D. There are no rules.
A high-mass star near the end of its life undergoes successive cycles of energy generation within its core in which gravitational collapse increases the temperature to the point where a new nuclear fusion cycle generates sufficient energy to stop the collapse. This process does not work beyond the silicon-fusion cycle that produces iron. Why is this?.
Answers
A high mass star will not be able to generate enough energy beyond the silicon fusion cycle to stop its collapse because iron fusion doesn't generate excess energy and gas pressure to prevent the core from collapsing. Instead, it requires additional energy.
Stars get all of their energy through nuclear fusion in the core of the star. The light and heat we get from the sun come from the fusion of nuclei in the core of the sun. Initially, all stars generate energy by fusing the lightest elements, hydrogen and helium at the core of the star. This is the longest phase of nuclear fusion, and stars in this phase are said to be in their main sequence. After the main sequence however, low mass stars become white dwarfs, while high mass stars continue to fuse heavier elements.
Due to the fact that high mass stars are so huge, they have very high temperature and pressure. This high temperature enables elements like helium to fuse and form other heavier nuclei like carbon and oxygen. Other adverse fusions of these heavy elements produce silicon and iron.
After the silicon fusion, no further cycle of energy generation occurs. This is because fusing iron with any other element requires energy and doesn't give out any significant amount of energy. Due to this, the core can't generate enough gas pressure to prevent its core from collapsing, thus, the core collapses and releases a huge amount of energy in an explosion called a supernova.
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what is a universal law?
Answers
Answer:
Universal law is the set of natural, non-man-made, and immutable conditions that determine how reality and consequence operate within the realm that humans exist in.
Explanation:
During car safety crash tests, dummies that don't wear seatbelts fly through the windshield and out of the car. why does this happen? in your answer, be sure to state which of newton's law of motion this pertains to, describe this law, and explain how it causes the dummies to move forward.
Answers
The First Law of Motion of Newton states that an item at rest or in motion will tend to stay at rest or in motion until acted upon by an external force. This means that anybody not wearing a seatbelt will continue to move forward in the initial direction of motion.
What is Newton's First Law of Motion?According to Newton's first law, unless an outside force causes it to change, every item will stay at rest or in uniform motion along a straight path.The link between an object's motion and the forces acting on it is outlined by Newton's laws of motion, which are three fundamental principles of classical mechanics. The following can be used to paraphrase these laws:Unless a force acts on a body, it stays at rest or moves in a straight path at a constant speed.The force acting on a body is equal to the time rate at which its momentum changes.When two bodies interact, forces are generated that are equal in magnitude but directed in different directions.To know more about Newton's First Law of Motion,refer to the following link:
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Small spheres a and b are attached by a 20cm long string. The charges on spheres a and b are 2. 4μc and 3. 6μc, respectively. The tension in the string holding them together is most nearly 0. 019n 0. 019 newton 0. 39n 0. 39 newton 1. 30n 1. 30 newtons 1. 94n 1. 94 newtons 2. 92n
Answers
The electric force or the tension in the string holding the charges together is most nearly to: 1.94 newtons
To solve this exercise the electric force formula and the procedure we will use is:
F = (k * q1 * q2)/r²
Where:
F = electric forcek = coulomb constantq1 = charge 1q2 = charge 2r = separation distance of the chargesInformation about the problem:
q1= 2.4 μcq2= 3.6 μcr = 20 cmF =?k= 9 *10^9 N*m²/C²1μC=1×10−6μCBy converting the the values of the charges (q1) and (q2) from (μC) to (C) we have that:
q1= 2.4 μc * 1×10−6C/ 1 μC
q1= 2.4*10^ -6 C
q2= 3.6 μc * 1×10−6C/ 1 μC
q2= 3.6*10^ -6 C
By converting the the separation distance of the charges from (cm) to (m) we have:
r = 20 cm * 1 m/100 cm
r= 0.20 m
Applying the electric force formula we have:
F = (k * q1 * q2)/r²
F = [(9 *10^9 N*m²/C² * (2.4*10^ -6 C) * (3.6*10^ -6 C)]/ (0.20 m)²
F = 0.07776 N*m² /0.04 m²
F = 1.94 N
What is electric force?In physics the electric force is the force that attracts or repels two charges (q) separated at a distance called (r), this is expressed in the international system of units in Newton.
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Describe how the density of aluminium may be determined using the bar. In your account
() describe the readings to be taken,
(i)
state the instruments used to make the readings,
(ill) describe how the density is calculated from the readings.
Answers
We know that water is denser than air or a piece of paper is denser than rock.
How do we determine density?
Density is determined by measuring it’s mass and then dividing it by it’s volume.
Let us take a solid cube of aluminium.
(i) The readings to be taken are the mass of aluminium and volume of aluminium.
(ii) Instruments used are :
digital weighing scale to measure mass a measuring cylinder to measure volume which is filled with water using pair of tongs we will put the aluminium cube in the water.(iii) We will check the mass of the aluminium cube by simply putting it on the weighing machine. Now we will check the volume by putting that cube into the water. The initial level was x. The water level rises to y after putting the cube into it. To know the volume, we will simply subtract y-x. Hence, we know the volume.
To know the density, divide mass by volume. (Mass / volume)
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Under Problems, who can help me with 1-3? Thank you!!!!
Answers
The current, voltages, resistances of the circuits in problem 1, 2, and 3 are given by Ohm's law as follows;
Questions 1—3 In Problems
The resistance of the hair dryer is 12 OhmsThe current in the light bulb circuit is 0.75 AThe voltage of the battery is 12 VoltsWhat is Ohms law?Ohm's law states that the current, I in a circuit or between two points in a circuit is proportional to the voltage, V, across the circuit or the part of the circuit.
Mathematically, V = I × R
Where;
R = The circuit resistance to current
1. The current in the hair dryer draws from the circuit = 10–A
The voltage of the circuit to which the hair dryer is connected = 120–V
From Ohm's law, we have;
V = I•R
R = V/I
I = 10 A
V = 120 V
Therefore;
R = 120 V/(10 A) = 12 Ohms
The hair dryer resistance is R = 12 Ohms2. The battery resistance = 2 Ohms
The voltage of the battery = 1.5–V
The current in the circuit is therefore found as follows;
R = 2 Ohm
V = 1.5 V
The current, I = V/R
Therefore;
I = (1.5 V)/(2 Ohms) = 0.75 A
The current in the circuit is I = 0.75 A3. The current supplies by the battery, I = 0.25 A
The battery resistance, R = 48 Ohm
The voltage of the battery, V = I × R
Therefore;
V = 0.25 A × 48 Ohm = 12 V
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About 20-25% of the 92 natural elements are known to be essential to life. Which four of these elements make up approximately 96% of living matter?.
Answers
The four elements that make up approximately 96% of living matter are Carbon, Hydrogen, Oxygen, and Nitrogen.
There are approximately 92 naturally occurring elements and most of them occur in living cells.
Of these approximately 20-25% are essential to life.
A pie chart is shown in the adjoining image, which depicts the composition of the elements present inside the living cells.
It is visible from the pie chart that the majority (almost 96-98%) is of 4 elements i.e, carbon, hydrogen, oxygen, nitrogen and the remaining is of calcium and phosphorus.
Thus, the four elements that make up approximately 96% of living matter are Carbon, Hydrogen, Oxygen, and Nitrogen.
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people hoping to travel to other worlds are faced with huge challenges. one of the biggest is the time required for a journey. the nearest star is 4.1×1016m away. suppose you had a spacecraft that could accelerate at 1.1 g for half a year, then continue at a constant speed. (this is far beyond what can be achieved with any known technology.)
Answers
The velocity is v = 3,240,266,666 m/s
How to find the velocity?The question here is about the initial velocity.
If so, the following working equation should be applied:
x = vt + 0.5at²
where
x is the distance
v is the velocity
t is the time
a is the acceleration
The acceleration due to gravity is 1.1g or 1.1(9.81 m/s²) = 10.791 m/s².
There are approximately 3.154×10⁷ seconds in a year.
4.1×10¹⁶ m = v(2/3 yr * 3.154×10⁷ s/yr) + 0.5(10.791m/s²)(2/3 yr * 3.154×10⁷ s/yr)²
Solving for v,
v = 3,240,266,666 m/s
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Two kg of refrigerant 134a undergoes a polytropic process in a piston–cylinder assembly from an initial state of saturated vapor at 2 bar to a final state of 12 bar, 80°c. Determine the work for the process, in kj.
Answers
The work done by polytropic process is -69.88 kJ.
The work for the polytropic process is determined using
P . v^n = constant.
where P is pressure, V is specific volume
As we know that
W = m∫Pdv
W = m(P2v2 - P1v1) / (1 - n)
In order to evaluate this expression, we need to determine the specific volumes and the polytropic exponent, n.
State 1: v1 = vg1 = 0.0993 m3/kg
State 2: at 12 bar, 80oC; v2 = 0.02051 m3/kg
Hence by using polytropic exponent
P1 / P2 = (v2 / v1)^n
n = ln(2/12) / ln(0.02051/0.0993)
n = 1.136
Find the work done
W = m(P2v2 - P1v1) / (1 - n)
W = 2kg(12bar . 0.02051m³/kg - 2 . 0.0993) / (1 - 1.136) x (10⁵ N/m²/1 bar) x (1 kJ / 10³ Nm)
W = -69.88 kJ
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a ball is thrown vertically upward from the ground with an initial velocity of 25 m/s; at the same instant, a ball dropped from rest from a building 15 m high. after how long will the balls be at the same height
Answers
The time at which both the balls will be at the same height is 0.6 s.
The height of the ball that is dropped from a building
= 15 m
The initial velocity of the ball that is thrown vertically upward from the ground = 25 m/s
The height of the ball that is dropped from a building is,
[tex]y _{t} = y _{i} + v _{i}t - \frac{1}{2} \: gt ^{2} [/tex]
[tex] - (15 \: m \: - h) = - \frac{1}{2} \: gt ^{2} [/tex]
[tex] h =15 \: m - \frac{1}{2} \: gt ^{2} [/tex]
The height of the ball that is dropped from a building is
[tex]15 \: m - \frac{1}{2} \: gt ^{2} .[/tex]
The height of the ball that is thrown vertically upward from the ground is,
[tex]y _{t} = y _{i} + v _{i}t - \frac{1}{2} \: gt ^{2} [/tex]
[tex] h =(25 \:) \: t \: - \frac{1}{2} \: gt ^{2} [/tex]
The height of the ball that is thrown vertically upward
[tex]from \: the \: ground \: is \: (25 \:) \: t \: - \frac{1}{2} \: gt ^{2} .[/tex]
The time at which both the balls will be at the same height is,
[tex]15 \: m - \frac{1}{2} \: gt ^{2} =(25 ) \: t \: - \frac{1}{2} \: gt ^{2} [/tex]
[tex]t \: = \frac{15}{25} [/tex]
t = 0.6 seconds
Therefore, the time at which both the balls will be at the same height is 0.6 s.
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Francesca has been feeling very weak. Her doctor asks her about her diet, and it appears that Francesca is not consuming an adequate amount of carbohydrates. What food should Francesca start eating to MOST efficiently increase the amount of carbohydrates in her diet?
A.
eggs
B.
butter
C.
steak
D.
bananas
Answers
Answer:
Banana/Carbohydrate Amount - 27 g
Explanation:
Egg/Carbohydrate Amount - 0.6 g
Banana/Carbohydrate Amount - 27 g
Steak/Carbohydrate Amount - 0 g
Butter/Carbohydrate Amount- 0 g
To win the game, a place kicker must kick
a football from a point 35 m (38.276 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 20 m/s at
an angle of 43.6° from the horizontal.
The acceleration of gravity is 9.8 m/s².
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.
Answers
The vertical distance by which the ball clear the crossbar is
As given in the question,
To win the game, a place kicker must kick a football from a point 35 m (38.276 yd) from the goal,The ball must clear the crossbar, which is 3.05 m high.the ball leaves the ground with a speed of 20 m/s at an angle of 43.6◦.The acceleration of gravity is 9.8 m/s.The distance between two vertical places is known as the vertical separation or vertical distance. There are numerous ways to express vertical position using vertical coordinates, including depth, height, altitude, elevation, etc.
By how much vertical distance does the ball clear the crossbar?
The vertical clearance distance between the crossbar and the ball as stated in the query,
A place kicker must make a football kick from a point 35 meters (38.276 yards) from the goal to win the game.
The 3.05 m-high crossbar must be passed by the ball.
The ball leaves the ground at an angle of 43.6 degrees and a speed of 20 meters per second.
9.8 m/s is the acceleration of gravity.
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what is the relationship between volume anf the amount of madd a boat can hold before sinking??
Answers
Answer:
The volume of water displaced by the boat is equal to the volume occupied by the part of the boat that is below the surfaces of the water. Once the volume of displaced water is greater than the total volume of the boat, it means that the top of the boat will no longer be above the water and the boat will sink.
Explanation:
I did my best on this question. I hope this helps!
Speed calculation
1. Your bus is travelling at an average speed of 25km/hr. How long will it take you to get from your bus stop to the shopping centre that is 4km away?
2. If you are able to run at an average of 8km/hr, how far can you run in 3.4 hours?
Answers
1. The time taken to get to the shopping centre is 0.16 hour
2. The distance you can run in 3.4 hours is 27.2 Km
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
1. How to determine the timeThe time taken to get to the shopping centre can be obtain as follow:
Speed of light = 25 Km/hrDistance = 4 KmTime =?Speed = distance / time
25 = 4 / time
Cross multiply
25 × time = 4
Divide both side by 25
Time = 4 / 25
Time = 0.16 hour
2. How to determine the distance Speed = 8 Km/hrTime = 3.4 hoursDistance =?Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 8 × 3.4
Distance = 27.2 Km
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Which statement best describes an isolated system?
Energy flows into and out of the system but matter is contained.
There is no energy or matter that exists inside an isolated system.
Energy is contained within the system and matter is exchanged.
Neither energy nor matter are exchanged with the surroundings.
Answers
The statement best describes an isolated system is,
(C) Neither energy nor matter are exchanged with the surroundings.
What is Isolated system?Isolated system is a thermodynamic term which we are used to understand the characteristics of the system. An isolated system means that cannot exchange neither energy nor mass outside the boundaries of the system.
How can we conclude that nothing are exchanged with surroundings in isolated system?According to the definition of the isolated system, we know that, Isolated system is a system that is completely bound to its boundary. That means it is closed within its boundary.
But it is not closed system. Because in closed system mass is conserved but energy can be exchanged outside the boundaries of the system.
In the characteristics of isolated system, we know it cannot exchange neither energy nor mass outside the boundaries of the system.
So, from the above discussion we can easily state that, the statement best describes an isolated system is, (C) Neither energy nor matter are exchanged with the surroundings.
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Calculate the volume of copper that has a mass of4.5g and has a density of 8.96g/cm^3
Answers
The volume of the copper having a mass of 4.5 g and a density of 8.96 g/cm³ is 0.502 cm³
Formula for densityThe mathematical representation of the density of a substance can be expressed as
Density = mass / volume
With the above formula, we can obtain the volume. Detail below.
The volume of the copper can be determined as illustrated below:
Mass of copper = 4.5 gDensity of copper = 8.96 g/cm³Volume of copper =?Density = mass / volume
8.96 = 4.5 / volume of copper
Cross multiply
8.96 × volume of copper = 4.5
Divide both sides by 8.96
Volume of copper = 4.5 / 8.96
Volume of copper = 0.502 cm³
Thus, the volume of the copper is 0.502 cm³
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One way to control avalanches is to send explosive charges to key areas on mountain slopes to trigger small avalanches before larger ones can build up. Norway, for instance, uses solar- powered launchers that fire pre-timed charges. Your launcher fires charges at an angle of 70 degrees from the horizontal and a speed of 200 m/s. If you fire a charge and it travels a horizontal distance of 300 m away from you, how high up the slope will it strike?.
Answers
By using uniform motion, the high up the slope will it strike is 730.62 m.
We need to know about uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, we know that
θ = 70⁰
vi = 200 m/s
x = 300 m
Find the initial velocity in x and y axis
vx = vi cosθ = 68.40 m/s
vy = vi sinθ = 187.94 m/s
Find the time taken to reach 300 m
vx = x / t
68.4 = 300 / t
t = 4.39 second
Find the time taken to reach maximum height
vt = vo + a . t
0 = vy - g . t
vy = gt
187.94 = 9.8 . t
t = 19.18 second
The motion of projectile is raising to maximum height, hence
s = vo . t + 1/2 . a . t²
h = vy . t - 1/2 . g . t²
h = 187.94 . 4.39 - 1/2 . 9.8 . 4.39²
h = 730.62 m
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If the magnified cell had a diameter of 40mm on the computer screen using the 10x ocular lens with the 40x objective lens, what would be the actual diameter of the cell in millimeters?.
Answers
The actual diameter of the cell would be 0.1 mm.
We are given that, the magnification due to the ocular lens is 10x and the magnification due to the objective lens is 40x.
Therefore, the total magnification of the whole setup will be 400x.
This means that an object with a diameter of x m will have a magnified diameter of 400x.
In the above situation, the magnified cell has a diameter of 40 mm.
When the actual diameter is x, the magnified diameter is 400x.
Hence 400x = 40 mm
x = 40 mm/400
x = 0.1 mm
Hence, the actual diameter of the cell would be 0.1 mm.
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The actual diameter of the cell would be 0.1 mm.
We are given that, the magnification due to the ocular lens is 10x and the magnification due to the objective lens is 40x.
Therefore, the total magnification of the whole setup will be 400x.
This means that an object with a diameter of x m will have a magnified diameter of 400x.
In the above situation, the magnified cell has a diameter of 40 mm.
When the actual diameter is x, the magnified diameter is 400x.
Hence 400x = 40 mm
x = 40 mm/400
x = 0.1 mm
Hence, the actual diameter of the cell would be 0.1 mm.
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A car moving with a speed of 20m/s has a momentum of 32,000 kg. m/s.
What is the mass of the car
Answers
Answer:
See below
Explanation:
momentum = m * v
so
momentum / v = m = 32 000 kg m/s / 20 m/s = 1600 kg
True or false: defense mechanisms are normal. they help defend and help the ego avoid dealing directly with sexual or aggressive urges and the anxiety they produce.
Answers
Yes, the given statement is true.
Defense mechanisms are normal. they help defend and help the ego avoid dealing directly with sexual or aggressive urges and the anxiety they produce.
In psychoanalytic theory, defense mechanisms are definite psychological strategies that people use to get over difficult feelings, emotions, or thoughts.
It refers to a series of mental abilities that enables the mind to cope with conflicts, and compromises and also strive for their solutions.
Moreover, these mechanisms also protect people from unpleasant and anxious feelings.
To put it simply, defense mechanisms are normal subconscious methods or ways to deal with unexpected feelings, thoughts, or inner conflicts.
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A typical high pressure on a bicycle might have a volume of 365 ml and a pressure of 7. 80 atm at 25oc. Suppose the rider filled the tire with helium to minimize weight. What is the mass of the helium in the tire?.
Answers
By ideal gas approximation, the mass of the helium in the tire is 0.465 grams.
We need to know about the ideal gas theory to solve this problem. The ideal gas is assumed that there is no interaction between particles in a gas. It can be determined by the equation
P . V = n . R . T
where P is pressure, V is volume, n is the number of moles of gas which represents mass, R is the ideal gas constant (0.0821 L.atm/mol.K) and T is temperature.
From the question above, we know that
V = 365 mL = 0.365 L
P = 7.8 atm
T = 25⁰ C = 298 K
Mr = 4
By using the equation of ideal gas, we get the mass
P . V = n . R . T
7.8 . 0.365 = gr / Mr . 0.0821 . 298
7.8 . 0.365 = gr / 4 . 0.0821 . 298
gr = 0.465 grams
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The speed of a projectile when it reaches its maximum height is one-half its speed when it is at half its maximum height. What is the initial projection angle of the projectile?.
Answers
The speed of a projectile when it reaches its maximum height is one-half its speed when it is at half its maximum height. The initial angle of the projectile is 67.8°.
The motion from zero to maximum height is :
Vyi = √2gh
Now the motion from zero to half of the maximum height is :
Vyh = √gh
At maximum height, the speed is Vx = √Vx^2+Vyh^2/2
Vx =√Vx^2+gh/2
by simplifying,
Vx = √gh/3
To find the angle of projection
∅ = tan^-1(Vyi/Vx) = √2gh/√gh/3
∅ = 67.8°
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You are asked to determine the identity of an unknown liquid and can measure only one physical property. You hear the liquid and record that the liquid turns into vapor at 100°C.
Which physical property does this demonstrate?
A. Melting point
B. Boiling point
C. Ability to conduct electricity
D. Meltability
Answers
The answer is The boiling Point as the transition from liquid to gas occurs at the boiling point.
The actuality that it changes from liquid to vapor indicates that you are working with the substance's boiling point.
The material is pure if its temperatures does not change when it turns phases. Since water turns liquid at 100°C in this situation, water is likely the culprit.
The temperature at which a specific liquid will boil is known as its boiling point. For instance, water reaches its boiling point at 1 atm, or 100 degrees Celsius. The temperature of the liquid, the pressure of the atmosphere, and the pressure of the vapor all affect its boiling point.
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I’m having difficulty answering this question. I don’t know how I should draw the graphs.
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The correct answer is dependence of graph remain same. The Speed decreases,
We must first comprehend the difference between distance and displacement in order to understand average speed and average velocity. Distance is a scalar quantity that describes how much space an object has traveled. Displacement, which is a vector quantity, represents the smallest distance between two points. For instance, if a particle moves around a circle, its displacement is 0 but its distance traveled after one rotation is equal to the circle's circumference.
Any object's average speed is calculated by dividing its entire distance traveled by the total amount of time it took to complete that distance. An object's average speed indicates the average speed at which it will travel a given distance.
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9. How did you come up with your answer for #8?
10. If the falling time of an object is doubled, by what factor does the distance increase? Use
the times 2 seconds and 4 seconds to prove your answer. (Hint: x-v4+1/2af²)
a.
b.
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A car travels 20 km north. It then turns around and travels 30 km south. What is the car's displacement? 50 km south 10 km south 10 km north 50 km north
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Answer:
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1. Hooke's law states that the force F in a spring extended by a length x is given by F= -kx . Calculate the dimension of spring constant k.
2. The force between two wires 1,2 length 1 meters separated by a distance d meters and carrying currents I1 AND I2 Amperes is given by :
[tex]F = \frac{kI_1I_2}{d}[/tex] .
find (a.) the units of constant k
(b.) dimension of k
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1. With N = Newtons, m = meters, we have
[tex]F = -kx \iff \mathrm N = -k (\mathrm m) \implies k = \dfrac{\rm N}{\rm m}[/tex]
N itself can be broken down according to Newton's second law,
[tex]F=ma \iff \mathrm N = \mathrm{kg} \, \dfrac{\rm m}{\rm s^2}[/tex]
so the dimension of the force [tex]F[/tex] is
[tex][F] = [M\cdot L\cdot T^{-2}][/tex]
(where M = mass, L = length, T = time) and hence the dimension of [tex]k[/tex] is
[tex][k] = \left[\dfrac{M\cdot L\cdot T^{-2}}{L}\right] = \boxed{[M\cdot T^{-2}]}[/tex]
2.
a. With N = Newtons, A = amperes, and m = meters,
[tex]F = \dfrac{k I_1 I_2}d \iff \mathrm N = \dfrac{k \,\mathrm A\,\mathrm A}{\rm m} \implies k = \boxed{\dfrac{\rm Nm}{\rm A^2}}[/tex]
b. The dimension of [tex]k[/tex] is
[tex][k] = \left[\dfrac{(M\cdot L\cdot T^{-2})\cdot L}{I^2}\right] = \boxed{[M\cdotL^2\cdot T^{-2}\cdot I^{-2}]}[/tex]
(where I = current, with "I" as in capital i)