The density of cheese is 1.33 g/cm³ or 1.33 g/mL.
We need to know about the density to solve this problem. Density is a unit that measures how dense an object is. Density can be measured by dividing mass by volume. It can be written as
ρ = m / V
where ρ is density, m is mass and V is volume
From the question above, we know that
m = 44 g
V = 33 cm³
As we know that 1 cm³ is equal to 1 ml, hence the answer will be the same.
By substituting the following parameters, we get
ρ = m / V
ρ = 44 / 33
ρ = 4/3
ρ = 1.33 g/cm³
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What would be the frequency of a 0.5 kg mass oscillating on a spring with spring constant k = 5 n/m?
The frequency of 0.5 kg mass oscillating on a spring with spring constant k = 5 n/m will be 0.50 Hz.
The oscillation of a spring is governed by the following formulas :
ω = √k/√m
T = 2π/ω = 2π (√m√/k)
f = 1/T = 1/2π(√k/√m)
Here ω represents the angular frequency
T is the time period
And f is the frequency
We can use the third formula to calculate the frequency by putting the given values in it.
f = 1/2π √k/√m
f = 1/2π √5/√0.5
f = 1/2π x √10
f = 1/2 x 3.16/3.14
f = 0.50 Hz
Hence, the frequency of 0.5 kg mass oscillating on a spring with spring constant k = 5 n/m will be 0.50 Hz.
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A watercraft with an initial velocity of 6.4 m/s [e] undergoes an average acceleration of 2.0 m/s2 [s] for 2.5 s. what is the final velocity of the watercraft?
The watercraft with an initial velocity of 6.4 m/s and an average acceleration of 2.0 m/s2 [s] for 2.5 s will have a final velocity of: 11.4 m/s
The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:
vf = vi + (a* t)
Where:
vf = final velocityvi = initial velocityt = timea = accelerationInformation about the problem:
vi= 6.4 m/sa= 2.0 m/s²t = 2.5 svf = ?Applying the final velocity formula, we have:
vf = vi + (a* t)
vf = 6.4 m/s + (2.0 m/s²* 2.5 s)
vf = 6.4 m/s + 5 m/s
vf = 11.4 m/s
What is acceleration?It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2
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At what temperature (degrees fahrenheit) is the fahrenheit scale reading equal to (a) 3 times that of the celsius and (b) 1/6 times that of the celsius?
45.7 °F is the Fahrenheit scale reading equal to 3 times that of the Celsius
-4 °F is 1/6 times that of the Celsius
Evaluating :
The relationship between temperature in degrees Fahrenheit, F, and degrees Celsius, C, is
F = 1.8°C + 32
Part a.
If F = 6°C, then
6°C = 1.8°C + 32
6°C - 1.8°C = 32
4.2°C = 32
C = 7.62
Therefore, F = 6×7.62 = 45.71
= 45.7 °F (nearest tenth)
Part b.
When F = (1/5)C, then
0.2°C = 1.8°C + 32
0.2°C - 1.8°C = 32
-1.6°C = 32
C = - 20
Therefore, F = 0.2 × -20 = -4
= -4 °F
What are Celsius and Fahrenheit scales?
Celsius and Fahrenheit are two scales won't to measure temperature. The temperature within the centigrade scale will be expressed in degrees Celsius. The temperature within the Fahrenheit scale will be expressed in degrees Fahrenheit. The relation between Celsius and Fahrenheit is proportional.
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A __________ was used to probe and find the surfaces of electric potential
a) banana - banana cable
b) voltage sensor
c) digital multimeter
d) meter stick
A voltage sensor was used to probe and find the surfaces of electric potential.
How is the electric potential measured?One of the most widely utilized electrical quantities is electrical potential, which is essential for both storing and releasing electrical energy.
By dividing the potential energy by the total charge, the electric potential of any charge is calculated.
To measure the electrical potential difference between two locations in an electric circuit, a voltmeter is employed.
The electric potential difference between two places is determined using a voltmeter.
The electrical component whose potential difference is being measured is connected in parallel to voltmeters, which have high resistance.
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your friend throws a rock off a cliff straight down with an initial speed of 10.0 m/s using a stopwatch you determine it takes the rock 3.2 s to hit the ground below. how high is the cliff
It it takes the rock a time of 3.2 s with an initial velocity of 10 m / s, the height of the cliff is 82.12 m
s = ut + 1 / 2 at²
s = Height
u = Initial velocity
a = Acceleration due to gravity
t = Time
u = 10 m / s
t = 3.2 s
a = g = 9.8 m / s²
s = ( 10 * 3.2 ) + ( 1 / 2 * 9.8 * 3.2² )
s = 32 + 50.18
s = 82.18 m
The equation used to find the solution is an equation of motion. Equations of motion are discovered to describe the position of an object in motion at any given time.
Therefore, the height of the cliff is 82.12 m
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A tennis ball with a speed of 20.6 m/s is
moving perpendicular to a wall. After striking
the wall, the ball rebounds in the opposite
direction with a speed of 11.948 m/s.
If the ball is in contact with the wall for
0.0082 s, what is the average acceleration of
the ball while it is in contact with the wall?
Take "toward the wall" to be the positive
direction.
Answer in units of m/s².
hig
ate
6
wa
W
ve
The average acceleration of the ball, while it is in contact with the wall, is -3969.27 m/s².
Acceleration is the rate of change of velocity per unit of time. Its S.I. unit is m/s². It is equal to the change in velocity divided by the time taken to change the velocity.
Acceleration a = Change in velocity/ Time taken
Given in the question
Initial Velocity = u = + 20.6 m/s ( towards the wall is positive direction )
Final Velocity = v = - 11.948 m/s (away from the wall is negative direction)
Change in Velocity = Final Velocity - Initial Velocity
= (- 11.948) - ( + 20.6)
= -11.948 - 20.6
= -32.548 m/s
So Change in velocity = 32.548 m/s
Time Taken = Time of contact with the wall
= 0.0082 seconds
Put in the Formula: a = Change in velocity/ Time taken
a = -32.548/0.0082
a = -3969.27 m/s²
Therefore the average acceleration of the ball, while it is in contact with the wall, is -3969.27 m/s².
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The coefficient of sliding friction on concrete is 0.30. what weight of steel can be pulled across a concrete floor by a winch with a capacity of 450 lbs?
The weight of steel can be pulled across a concrete floor by a winch with a capacity of 450 lbs to 1500 lb.
Around 7850 kg/m3, or 7.85 g/cm3, or 490 lbs/ft3, or 13231 lbs/yd3, is the unit weight of steel. The primary usage of the steel bars is as reinforcement to increase the tensile strength of concrete constructions. The weight of steel is typically expressed in kilogrammes, tonnes, and pounds.
Calculate the amount of steel in the slab as 1% of the concrete volume (0.01 x 7850 x 3 = 236kg):
Using the Thumb Rule Given that steel has a density of 7850 kg/m3, the amount of steel needed for an RCC slab should be 1% of the entire volume of concrete, or 236 kg.
The unit weight of structural steel is taken to be 7850 kg/m3 or 78.50 kN/m3 or 7.85 g/cm3 or 490 lbs/ft3 or 13,231 lbs/yd3 according to IS code and Indian standard.
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A 12-n force is applied at the point x=3m, y=1m. find the torque about the origin if the force points in (a) the x direction, (b) the y direction, and (c) the z direction.
The torque about the origin if the force points in (a) the x direction, (b) the y direction, and (c) the z direction are 12; 36; 37.9 respectively
Torque is a twisting force produced by applying a force at a distance from a point. We would need to choose a distance that is perpendicular to the force's direction. We apply the equation to determine torque,
T=Fd
where F is the force and d is the orthogonal distance to a central point.
i. If the force points in the x-direction, we need to use the y-distance to calculate torque.
T=Fxdy
T=12N *1m
T = 12 N.m
ii. If the force points in the y-direction, we need to use the x-distance to calculate torque.
T=Fxdy
T= 12N * 3m
T = 36 N.m
iii. If the force is directed in the z-direction, the straight-line distance from the origin to the point is orthogonal to the force. The magnitude of the distance will be used as the distance value. This may be determined using the equation.
||d||= √ (X2 + Y2)
where X and Y are the x and y coordinates.
T=Fz||d||
T=(12N) (√ (32 + 12)
T = 37.9 N.m
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What is the change in entropy when 2.00 kgof water at is heated to 100 degrees cel form steam at ?
The entropy change when 2.00 kg of water at 100°C is heated to form steam at 100°C is 12.1kJ/K.
Entropy is a metric for a system's unpredictability or disorder. The mass of a system affects the value of entropy. It has units of joules per kelvin and is represented by the letter S. The value of entropy can be either positive or negative.
Total energy change = latent heat of of vapourization × mass
Total energy change = [tex]2.26[/tex] × [tex]10^{6}[/tex] × 2
Total energy change = 4520kJ
Now, entropy change is given as:
Δ[tex]S = \frac{Total energy change}{Temperature}[/tex]
Δ[tex]S = \frac{4520}{273.15+100}[/tex]
Entropy = 12.1kJ/K
Therefore, the entropy change when 2.00 kg of water at 100°C is heated to form steam at 100°C is 12.1kJ/K.
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What was larry's acceleration at take-off? assume a take-off mass of 210 lb (including helium)
Larry's acceleration at take-off is 23.38 m/s.
Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.
Formula for acceleration ->
a= Δu / Δt = [tex]u_{f} - u_{i}[/tex] / Δt
Now, Given
m = 200Lb = 90.71kg
D = 2m / s
[tex]N_{0}[/tex] = 42
volume of balloon = (4/3)π[tex]r^{3}[/tex]
= 4/3 * pi * (1) ^ 3 = 4 . 188 m t ^ 3
Total volume 42 x 4-188 = 175.9 mt3
Buoyancy force = P g x volume of air displaced
= 1.229 * 9.81 * 175 * 9
= 2121N
Force = mass x acceleration
acceleration = F /m = 2121 / 96.71 = 23.38 m/s
Therefore, the required acceleration is 23.38 m/s.
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What is the symbol, atomic number, # of protons, # of electrons, atomic mass, rounded atomic mass, # of neutrons (show work), and period of: carbon
The symbol of the element Carbon is C, its proton number is 6, its atomic mass is 12, its neutron number is 6 and finally carbon belong to period 2 of the periodic table.
What is an Element?This is defined as a substance cannot be further broken down by any chemical reaction and examples include oxygen, nitrogen etc.
Carbon is an element and has an atomic number of 6 with a mass number of 12 and is present in period 2 in the periodic table.
For all atoms with no charge, the atomic number is equal to the number of proton. The number of proton is also equal to the number of electron which is why they all have the same value of 6.
Neutron = atomic mass - atomic number
= 12 - 6 = 6
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The combination of coke and steam produces a mixture called coal gas, which can be used as a fuel or as a starting material for other reactions. the equation for the production of coal gas is:_______
Coal gas is produced by using the following equation: 2C (s) + 2 H,O (g) CH, (g) + CO.
What is coal gas?Coal gas is a mixture of methane and carbon dioxide that is created when coke and steam are combined. Gas from coal can be burned as fuel or employed as a catalyst in other chemical reactions.
How are coal tar, coal gas, and coke produced?When heating coal without the presence of air. It generates gas known as coal gas. It creates a substance known as coal tar. Additionally, coke, a solid residue, is created.
Coal gas is a fuel composed of hydrogen, oxygen, and carbon.
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A 9V battery supplies power to a cordless curling iron with a resistance of 18 ohm how much current is flowing through the curling iron
Answer:
V = IR
V = voltage = 9 volts
I = current
R = resistance = 18 ohms
V = IR
9 = I·18
When pressure is decreased, a substance is more likely to undergo _____ or _____.
When pressure is decreased, a substance is more likely to undergo an expansion process.
What is pressure?The total applied force per unit of area is known as the pressure.
The pressure depends both on externally applied force as well the area on which it is applied.
For constant pressure, the pressure of a substance would decrease with the increase in volume which clearly represents the process of expansion.
Thus, when pressure is decreased, a substance is more likely to undergo an expansion process.
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An atom of a particular element has a volume of 3m^3. what is the volume in nm^3?
The volume of an element in n[tex]m^{3}[/tex] is 3×[tex]10^{27}[/tex] n[tex]m^{3}[/tex].
How are cubic nanometers converted from cubic meters?
When converting cubic meters to cubic nanometers, one must use the following conversion factor:
1 [tex]m^{3}[/tex] = 1×[tex]10^{27}[/tex] n[tex]m^{3}[/tex]
Given that the volume of an element is 3 [tex]m^{3}[/tex]
By using above conversion formula we can now convert as
⇒ 1 [tex]m^{3}[/tex] = 1×[tex]10^{27}[/tex] n[tex]m^{3}[/tex]
⇒ 3 [tex]m^{3}[/tex] = V
V = (3×1×[tex]10^{27}[/tex]) [tex]m^{3}[/tex] n[tex]m^{3}[/tex] / 1 [tex]m^{3}[/tex]
By canceling [tex]m^{3}[/tex] we get,
V = 3×[tex]10^{27}[/tex] n[tex]m^{3}[/tex]
So the volume of an element after conversion is 3×[tex]10^{27}[/tex]n[tex]m^{3}[/tex].
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An object moves at a constant velocity, v, for some distance, x. How long has it been in motion?
A. x/v
B. v/x
C. x∗v
D. v/2x
E. None of the above
Answer:
V = m / s correct units for V
x = V * t = m / s * s = m where x is in meters
Thus t = x / V = m / (m / s) = sec
A) has to be the correct equation
If the average solar constant is 1372 w/m2, what percentage of the solar constant is received at a location if insolation is measured at 343 w/m2?
Percentage of the solar constant is received at a location if insolation is measured at 343 w/m2 is 25%.
The flux density, or measuring mean of solar electromagnetic radiation, is the solar constant, represented by the symbol GSC. It refers to the sun irradiation per square meter.
At Earth's separation from the Sun, the light has an intensity of 1372 W/m2 —this is also known as the solar constant, and the fact that it will not change over the long run.
So it would be 100%
But as mentioned in question Solar Constant is received at a location if insolation is measured at 343
W/m^2
Therefore,
Percentage of the Solar Constant is received = (343 / 1372) × 100
= 25 %
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What is the symbol, atomic number, # of protons, # of electrons, atomic mass, rounded atomic mass, # of neutrons (show work), and period of: aluminum
The properties of aluminum are as follows:
symbol = Alatomic number = 13number of protons = 13number of electrons = 13atomic mass = 26.981539 urounded atomic mass = 27 amunumber of neutrons = 14period : belongs to period 3What are elements?Elements are pure substances which are composed of the same type of atoms.
Elements are the building block of all forms of matter.
Aluminum one of the known 118 elements.
In the period table, aluminum has the following properties:
symbol = Alatomic number = 13number of protons = 13number of electrons = 13atomic mass = 26.981539 urounded atomic mass = 27 amunumber of neutrons = 14period : belongs to period 3In conclusion, aluminum is an element in the periodic table.
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Furthermore, how can it calculate its profit if revenue is in u.s. currency and most of its costs are in canadian currency?
A company can calculate its profit by using the foreign currency exchange rates prevailing in the market. The cost incurred in foreign currency can be converted into domestic currency first. The spot rates prevailing in the market can be used for such conversion. Once the expenses are converted into the domestic currency, the profits can be computed in the normal manner as now both the revenues and the cost are in domestic currency.
What is meant by foreign exchange rate?Foreign Exchange Rate is defined as the cost of the residential currency with regard to another currency. The reason of foreign trade is to compare one currency with another for appearing their relative values.
Foreign exchange rate can also be said to be the rate at which one currency is traded with another or it can be said as the price of one currency that's expressed in terms of another currency.
Exchange rates of a currency can be either fixed or floating. Fixed trade rate is decided by the central bank of the nation whereas the floating rate is decided by the flow of market request and supply.
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Sodium vapor lamps, used for public lighting, emit yellow light of a wavelength of 570 nm. How much energy is emitted by an excited sodium atom when it generates a photon?.
The electromagnetic energy emitted by an excited sodium atom is 3.47 x 10¯¹⁹ joules.
We need to know about electromagnetic energy to solve the problem. The electromagnetic energy of radiated photons can be calculated by wavelength. It can be determined as
E = h . c / λ
where E is energy, h is Max Planck's constant (6.6 x 10¯³⁴ Js), c is the speed of light (3 x 10⁸ m/s) and λ is the wavelength.
From the question above, the given parameter is
λ = 570 nm = 570 x 10¯⁹ m
By using the equation, we can calculate the energy generated from an sodium atom
E = h . c / λ
E = 6.6 x 10¯³⁴ . 3 x 10⁸ / 570 x 10¯⁹
E = 3.47 x 10¯¹⁹ joules
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During a baseball game, a batter hits a high
pop-up.
If the ball remains in the air for 5.86 s, how
high above the point where it hits the bat
does it rise? Assume when it hits the ground
it hits at exactly the level of the bat. The
acceleration of gravity is 9.8 m/s².
Answer in units of m
Answer:
Доброе утро, ответ 5+5="4
Explanation:
A 60.0-cm long string with a mass 8.00 g has a tension 200 n. what is the fundamental frequency of this string?
The fundamental frequency is 102.06 Hz m/s.
We need to know about the fundamental resonant frequency to solve this problem. When the string is vibrating at its lowest resonant frequency, it should follow the rule
λ = 2L
where λ is wavelength and L is the length of string
The transverse waves on a string also can be defined as
v = √(F . l/m)
where v is velocity, F is string tension, l is the length of string and m is mass
From the question above, we know that
l = 60 cm = 0.6 m
m = 8 g = 8 x 10¯³ kg
F = 200 N
By substituting the following equation, we can calculate the wavelength
λ = 2L
λ = 2 . 0.6
λ = 1.2 m
Find the speed of the wave
v = √(F . l/m)
v = √(200 . 0.6/(8 x 10¯³))
v = 122.47 m/s
Find the frequency
v = λ . f
122.47 = 1.2 . f
f = 102.06 Hz
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J. J. Thomson created an apparatus composed of a sealed glass tube with electrodes of different polarities fixed at each end. By passing a high voltage through gas in the sealed tube, he was able to create a cathode ray. What did thompson call the particles that make up a cathode ray?.
J. J. Thompson created an apparatus composed of a sealed glass tube with electrodes of different polarities fixed at each end. By passing a high voltage through the gas in the sealed tube, he was able to create a cathode ray. J.J. Thompson called the particles that makeup cathode rays as negatively charged particles.
In the experiment, the flow of particles was from the negative terminal (cathode) to the positive terminal (anode). He also placed two plates of opposite charges around the cathode rays. The cathode rays were deflected towards the positive place.
J.J Thompson concluded that the cathode rays were composed of negatively charged particles.
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PLEASE HELP ME WITH THIS!!
starting from one shore you row a boat across a narrow river to the other shore. the river is 30.0 m wide as u row the river current moves your boat down the river a distance of 15.0 m what is the resultant displacement of your boat? express your answer in components, and then determine the magnitude
The magnitude of the resultant displacement of your boat will be 33.5 m
What is Displacement ?Displacement is the distance travelled in a specific direction. It is a vector quantity and it is measured in meter.
If starting from one shore you row a boat across a narrow river to the other shore. the river is 30.0 m wide as u row the river current moves your boat down the river a distance of 15.0 m
The resultant displacement of your boat can be calculated by using Pythagoras theorem.
The horizontal component = 15 m, while the vertical component = 30 m
The magnitude of the resultant displacement D = √(x² + y²)
D = √(15² + 30²)
D = √(225 + 900)
D = √1125
D = 33.5 m
Therefore, the magnitude of the resultant displacement of your boat will be 33.5 m
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The coal has 50 J of potential energy and no kinetic energy. It is burned in the power plant to produce electrical energy, but only 20 J of electrical energy is produced.
Which of the following may account for this?
Some of the coal's energy was destroyed by the fire.
Some of the coal's energy was turned into other forms.
The fire was used to create the electrical energy from scratch.
Some of the coal's energy was turned into other forms of energy.
What is conversion of energy?According to the first law of thermodynamics, energy can neither be created nor destroyed but is converted from one form to another. We know that from the first law of thermodynamics, the energy that originally in the coal does not vanish into thin air but undergoes a conversion.
Thus, want to find out what accounts for the energy of the coal. Thus, we could say that some of the coal's energy was turned into other forms as this is in consonance with the first la of thermodynamics.
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in a slap shot, a hockey player accelerates the puck from a velocity of 11 m/s to 50 m/s in the same direction. if this takes 3.33x10^-2 s, calculate the distance over which the puck accelerates
The distance traveled by the puck is 0.203 m.
What is distance?This can be defined as the length between two points.
To calculate the distance which the puck accelerate, we use the formula below.
Formula:
S = (v+u)t/2.......... Equation 1Where:
S = Distancev = Final velocityu = Initial velocityt = TimeFrom the question,
Given:
v = 50 m/su = 11 m/st = 3.33×10⁻³ sSubstitute these values into equation 1
S = (50+11)3.33×10⁻³ /2S = 0.203 mHence, the distance traveled by the puck is 0.203 m.
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A diode hasiso=10 fa and a built-in voltage of 0.8 v. what isisfor a reverse biasof 10 v?
A diode that has the iso=10 fa and a built-in voltage of 0.8 v, its reverse basis for 10v is 36.7fA
What does a diode do?As rectifiers, signal limiters, voltage regulators, switches, signal modulators, signal mixers, signal demodulators, and oscillators, diodes are a versatile electrical component.
A diode’s propensity to transmit electric current solely in one direction is its fundamental characteristic.
What are diodes and their types?An electrical device with two terminals is a diode. A semiconductor, most frequently silicon but occasionally germanium, is used to create diodes.
There are many different kinds of diodes, but the ones being addressed here include the silicon-controlled rectifier, TRIAC, transient voltage suppressor, Zener, rectifier, and Schottky diodes.
What is the diode’s operating principle?A diode’s most frequent use is to permit an electric current to flow in one direction while blocking it in another. This is known as the diode’s forward direction.
It is provided that
Vr = 10V
ϕj = 0.8 V
Iso = 10fA
The reverse current Is
Is = Iso sqrt [1 + Vr/ϕj] → 1
Substituting all the values provided in question to equation 1, we have
Is = 10fA sqrt (1+10/0.8)
=(10fA) sqrt (13.5)
= 36.7fA
Thus Is = 36.7fA
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Doubling only the mass of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?
Produces no change in the energy because total energy is independent of the mass.
Mechanical energy = [tex]\frac{1}{2} \times K V^2[/tex]
K = Spring constant
A = Amplitude of oscillation
what is mechanical energy?Mechanical energy is the sum of kinetic energy and potential energy in an object that's utilized to do a specific work. In other words, it describes the energy of an object since of its movement or position, or both. mechanical energy, sum of the kinetic energy.
Mechanical energy is the energy of either an object in movement or the energy that's put away in objects by their position.
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At what pressure will 1.00 mole of ch4 be in a 10.0 l container at 298 k assuming ch4 is a real gas. (van der waals constants for ch4 are a = 2.253 l2 atm mol-2, b = 0.04278 l mol-1)
The pressure is 2.43456 atm.
An atom or molecule has electrons all over it. Additionally, electrons are always traveling. Uneven electron distributions are possible at any time. The result is the creation of a transient dipole. Another transient dipole may develop in an atom next to this one as a result of this dipole. It causes a cascade of transient dipoles, which causes the atoms or molecules to attract one another. It's referred as Vander wall force.
We have van der waals equation and values given
use R = 0.0821 l atm/mol/k
[tex][P+an^2/V^2][v-nb] = nRT[/tex]
[tex][P+an^2/V^2] = nRT/[V-nb][/tex]
[tex][P+an^2/V^2] = 1\times0.0821 l atm/mol/k\times298 K/[10 L ^{- 1}\times 0.04278 Lmol^{-1}][/tex]
[tex][P+an^2/V^2] = 24.4658/9.95722 = 2.45709[/tex]
[tex][P +2.253\times 1^2/(10)^2] = 2.45709[/tex]
P+ 0.02253 = 2.45709
P = 2.45709-0.02253 = 2.43456 atm
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A particle is executing accelerated motion. The acceleration is constant in magnitude but
not in direction. Predict the path followed by the particle. How will you find the speed of the
(2)
particle?
When the magnitude remains came and the direction changes the particle is moving in a circular motion. Speed is equal to the arc length traveled (S) divided by the change in time (Δ),
A particle travels in a uniform circular motion while maintaining a constant speed. The radius R of the circle sweeps out the angle, and the particle's velocity vector v in the illustration has a constant magnitude but changes direction as it advances from location B to position C.
The isosceles triangles OBC and DEF are identical because OB and OC are perpendicular to the velocity vectors, and as a result, the ratio of the chord BC to the radius R is the same as the ratio of the magnitudes of v to v. The chord BC and the arc BC approach one another as approaches zero, and the chord can be replaced by the arc in the ratio.
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