Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:

a. it has the same linear (tangential) acceleration as car A.
b. it has the same centripetal acceleration as car A.
c. it has traveled farther than car A since starting.
d. it has the same total acceleration as car A.
e. it is passing car A.

Two forces f1=(8i+3j)N and f2=(4i+6j) are acting on 5kg object then  the magnitude of the resultant force is 15 N and the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

The acceleration of the object in the x-component (\(a_x\)) is 2.4  \(m/s^{2}\), and the acceleration in the y-component (\(a_y\)) is 1.8  \(m/s^{2}\).

The magnitude of the acceleration of the object is 3  \(m/s^{2}\).

To find the magnitude and direction of the resultant force, we need to add the two given forces together.

Given:

f1 = (8i + 3j) N

f2 = (4i + 6j) N

To find the resultant force (\(F_res\)), we simply add the corresponding components:

\(F_res\) = f1 + f2

= (8i + 3j) + (4i + 6j)

= (8 + 4)i + (3 + 6)j

= 12i + 9j

The magnitude of the resultant force (\(|F_res|\)) can be found using the Pythagorean theorem:

\(|F_res|\)= \(\sqrt{(12^2) + (9^2)}\)

= \(\sqrt{144 + 81}\)

= \(\sqrt{225}\)

= 15 N

So, the magnitude of the resultant force is 15 N.

To find the direction of the resultant force, we can use trigonometry. The direction can be represented by the angle θ between the positive x-axis and the resultant force vector. We can calculate θ using the inverse tangent function:

θ = arctan(9/12)

= arctan(3/4)

≈ 36.87 degrees

Therefore, the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

Now let's calculate the acceleration of the object in the x and y components. We know that force (F) is related to acceleration (a) through Newton's second law:

F = ma

For the x-component:

\(F_x\)= 12 N

m = 5 kg

Using  \(F_x\)= \(ma_x\), we can solve for \(a_x\):

12 N = 5 kg * \(a_x\)

\(a_x\)= 12 N / 5 kg

\(a_x\) = 2.4 \(m/s^{2}\)

For the y-component:

\(F_y\) = 9 N

m = 5 kg

Using \(F_y\) = \(ma_y\), we can solve for \(a_y\):

9 N = 5 kg * \(a_y\)

\(a_y\) = 9 N / 5 kg

\(a_y\)= 1.8  \(m/s^{2}\)

So, the acceleration of the object in the x-component (\(a_x\)) is 2.4  \(m/s^{2}\), and the acceleration in the y-component (\(a_y\)) is 1.8  \(m/s^{2}\).

To find the magnitude of the acceleration (|a|), we can use the Pythagorean theorem:

|a| = \(\sqrt{(a_x^2) + (a_y^2)}\)

= \(\sqrt{(2.4^2) + (1.8^2}\)

= \(\sqrt{5.76 + 3.24}\)

= \(\sqrt{9}\)

= 3  \(m/s^{2}\)

Therefore, the magnitude of the acceleration of the object is 3  \(m/s^{2}\)

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If A box of mass 210 kg is pulled from rest with a string of tension 1300n inclined at 35° to the horizontal. if the box moved with a speed of 10m/s and the frictional force between the box and surface is 100 n, Then the distance covered by the box is 10.89 meters.

To calculate the distance covered by the box, we need to analyze the forces acting on it and apply the work-energy principle.

Given:

Mass of the box, m = 210 kg

Tension in the string, T = 1300 N

The angle of inclination, θ = 35°

Frictional force, f = 100 N

Initial speed, u = 0 m/s

Final speed, v = 10 m/s

First, let's resolve the tension force into components parallel and perpendicular to the incline. The parallel component of the tension force can be calculated as:

T_parallel = T * cos(θ)

Next, let's calculate the net force acting on the box along the incline. The net force is given by:

Net force = T_parallel - f

Now, using Newton's second law, we can calculate the acceleration (a) of the box:

Net force = m * a

From the given information, we have the final velocity (v), initial velocity (u), and acceleration (a). We can use the following kinematic equation to calculate the distance covered (s):

v^2 = u^2 + 2as

Rearranging the equation, we get:

s = (v^2 - u^2) / (2a)

Now, let's plug in the given values and calculate the distance covered:

T_parallel = 1300 N * cos(35°) ≈ 1067.35 N

Net force = 1067.35 N - 100 N = 967.35 N

a = (967.35 N) / (210 kg) ≈ 4.61 m/s^2

s = (10 m/s)^2 - (0 m/s)^2 / (2 * 4.61 m/s^2) ≈ 10.89 m

Therefore, the distance covered by the box is approximately 10.89 meters.

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The speed of the rocket would be  1,607.6 m/s.

Let's start by calculating the mass of the rocket at any given time t:

m(t) = 5,000 kg - (200 kg/s) t

The net force on the rocket is given by:

F = (u - v(t)) dm/dt

where v(t) is the velocity of the rocket at time t, and u is the velocity of the ejected gas relative to the rocket.

At the moment when the rocket reaches the ejection velocity of the gas, the net force is zero. So we can set F to zero and solve for v(t):

0 = (2,000 kg/s - v(t)) (200 kg/s)

v(t) = 2,000 kg/s

Now we can use Newton's second law of motion to relate the net force on the rocket to its acceleration:

F = m(t) a(t)

a(t) = F / m(t)

At the moment when the rocket reaches the ejection velocity of the gas, the acceleration of the rocket is:

a(t) = (2,000 kg/s) / (5,000 kg - (200 kg/s) t)

We can integrate this expression with respect to time to find the velocity of the rocket as a function of time:

v(t) = (2,000 m/s) ln(5,000 kg / (5,000 kg - (200 kg/s) t)) + C

where C is a constant of integration that we can determine from the initial condition v(0) = 0:

0 = (2,000 m/s) ln(5,000 kg / 5,000 kg) + C

C = 0

Therefore, the velocity of the rocket as a function of time is:

v(t) = (2,000 m/s) ln(5,000 kg / (5,000 kg - (200 kg/s) t))

We can now find the velocity of the rocket after 20 seconds:

v(20) = (2,000 m/s) ln(5,000 kg / (5,000 kg - (200 kg/s) (20 s)))

v(20) ≈ 1,607.6 m/s

So the speed of the rocket after 20 seconds of launching is approximately 1,607.6 m/s.

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1. The force between the two charges is 1.78 × 10⁻⁵ pounds, with opposite signs indicating attraction between the charges.

2. The resistance of 10 gauge aluminum wire over a 40 ft distance would be 0.506 ohms.

3. The cost of electricity from the automobile battery is 38.6 cents per kWh.

4. The current that would be carried through the body is 0.8 mA if dry.

1. The force between two point charges can be calculated using Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Using the values given, the force can be calculated as F = (k * q1 * q2) / r², where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. Plugging in the values, the force can be calculated as 1.78 × 10⁻⁵ pounds, with opposite signs indicating attraction between the charges.

2. The resistance of a wire is determined by its length, cross-sectional area, and resistivity. The resistivity of aluminum is higher than that of copper, so a larger cross-sectional area is required to achieve the same resistance. Using the gauge size conversion chart, 10 gauge aluminum wire has a cross-sectional area of 5.26 mm², which is approximately 83% of the cross-sectional area of 12 gauge copper wire.

Thus, the resistance of 10 gauge aluminum wire over a 40 ft distance can be calculated as R = (rho * L) / A, where rho is the resistivity of aluminum, L is the length, and A is the cross-sectional area. Plugging in the values, the resistance can be calculated as 0.506 ohms.

3. To calculate the cost of electricity per kWh, the total cost and the total amount of energy supplied must be known. Since the battery supplies 12 V and 51 A for one hour, the total energy supplied can be calculated as E = V * I * t, where V is the voltage, I is the current, and t is the time.

Plugging in the values, the total energy supplied can be calculated as 612 watt-hours (Wh). Since one kWh is equal to 1000 Wh, the total energy supplied can be converted to 0.612 kWh. Dividing the total cost by the total energy supplied gives the cost per kWh, which is 38.6 cents.

4. The current through the body can be calculated using Ohm's law, which states that current is equal to voltage divided by resistance. Using the values given, the resistance can be either 100,000 ohms or 300 ohms depending on whether the skin is dry or wet.

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At x = 2π/3 and 4π/3, the local maximum value is 3/2, and at x = π/3 and 5π/3, the local lowest value is -3/2.

To find the intervals of increasing and decreasing for f(x), we need to find the first derivative of f(x) and check its sign. f'(x) = -2cosx - 2cos2x Now we need to determine the sign of f'(x) in the interval (0, 2π).f'(x) < 0 when 0 < x < π/3, 2π/3 < x < 4π/3, and 5π/3 < x < 2π.f'(x) > 0 when π/3 < x < 2π/3 and 4π/3 < x < 5π/3.

Therefore, f(x) is decreasing on the intervals (0, π/3), (2π/3, 4π/3), and (5π/3, 2π), and increasing on the intervals (π/3, 2π/3) and (4π/3, 5π/3).To find the local maximum and minimum values of f(x), we need to find the critical points of f(x) by setting f'(x) = 0.f'(x) = -2cosx - 2cos2x = 0Solving this equation is not easy, so we will use an approximation method or graphing calculator to find the critical points. We get x ≈ 0.465, 2.677, and 4.777.

Now we need to evaluate f(x) at these critical points and the endpoints of the interval.f(0) = -2sin0 = 0f(π/3) = cos2(π/3) - 2sin(π/3) = -3/2f(2π/3) = cos2(2π/3) - 2sin(2π/3) = 3/2f(4π/3) = cos2(4π/3) - 2sin(4π/3) = 3/2f(5π/3) = cos2(5π/3) - 2sin(5π/3) = -3/2f(2π) = -2sin(2π) = 0Therefore, the local maximum values are 3/2 at x = 2π/3 and 4π/3, and the local minimum value is -3/2 at x = π/3 and 5π/3.

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Answer:

The magnitude of the resultant vector is 22.66 cm and it has a direction of 29.33°

Explanation:

To find the resultant vector, you first calculate x and y components of the two vectors M and N. The components of the vectors are calculated by using cos and sin function.

For M vector you obtain:

\(M=M_x\hat{i}+M_y\hat{j}\\\\M=15.0cm\ cos(20\°)\hat{i}+15.0cm\ sin(20\°)\hat{j}\\\\M=14.09cm\ \hat{i}+5.13\ \hat{j}\)

For N vector:

\(N=N_x\hat{i}+N_y\hat{j}\\\\N=8.0cm\ cos(40\°)\hat{i}+8.0cm\ sin(40\°)\hat{j}\\\\N=6.12cm\ \hat{i}+5.142\ \hat{j}\)

The resultant vector is the sum of the components of M and N:

\(F=(M_x+N_x)\hat{i}+(M_y+N_y)\hat{j}\\\\F=(14.09+6.12)cm\ \hat{i}+(5.13+5.142)cm\ \hat{j}\\\\F=20.21cm\ \hat{i}+10.27cm\ \hat{j}\)

The magnitude of the resultant vector is:

\(|F|=\sqrt{(20.21)^2+(10.27)^2}cm=22.66cm\)

And the direction of the vector is:

\(\theta=tan^{-1}(\frac{10.27}{20.21})=29.93\°\)

hence, the magnitude of the resultant vector is 22.66 cm and it has a direction of 29.33°

No, because covering uniform distance in uniform units of time ( which the graph one represents) is constant speed, and not uniform speed (as represented in the second graph).

What is a graph?

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According to Ohms law, the resistance in a circuit is the ratio of its voltage to the current across the circuit. The resistance of the circuit with 12 v and 3.5 A current is 3.4 ohms.

Ohm's law is one of the fundamental law in physics. It states that, the voltage over a circuit is the product of the resistance and current through the circuit.

hence, V = IR

Therefore, the voltage through a circuit is directly proportional to the current and resistance through the circuit. As the resistance increases, current through the circuit decreases.

The voltage in the cell = 12 V

current I = 3.5 A.

then internal resistance R = V/I

R = 12/3.5 = 3.4 Ω

Therefore, the resistance in the cell is 3.4 ohms.

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The speed with which the egg pass the point from which it was thrown is √(-216) m/s.

The speed with which the egg pass the point from which it was thrown is calculated by using the following kinematic equation.

Since the only acceleration acting on the egg is gravity (g = 9.8 m/s²), we have:

v² = u² + 2gh

where:

Solving for v, the final velocity

v² = 6.00² + 2(-9.8) (13.0)

v²  = 36 + (-252)

v²  = -216

v = √(-216)

The square root of a negative number is not a real number, so this answer is not physically meaningful. This means that the egg will not pass the point from which it was thrown. The egg will instead reach its highest point and then fall back down to the ground.

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The gravitational force on planet X is one-eight (¹/₈) of the magnitude of gravitational force on planet Y.

The gravitational force on each planet is directly proportional to the product of mass of the planet and the tennis ball and inversely proportional to the square of the radius of the planets.

F = GmM/r²

where;

The gravitational force on planet X is written as;

F_X = Gm(mt) / r²

where;

The gravitational force on planet Y is written as;

F_y = G(½m)(mt) / (¼r)²

F_y = ½(Gm(mt) / (¹/₁₆ r²)

F_y = (16 Gm mt)/(2r²)

F_y = 8(G m(mt) ) / r²

F_y = 8(F_X)

F_X = ¹/₈(F_Y)

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Answer:

calcium chloride

Explanation:

an inorganic compound,a salt with the chemical formula CaCl2

Answer:analize a afirmacao a seguir e tudo que envolve o gerenciamento da marca e que ultrapassa as acoes com objetivos economicos e refere se a cultura principios e valores

Explanation:

Answer:

so you have a question

Explanation:

either way, have a nice day

SeaWorld is a chain of theme parks and oceanariums that showcase marine life through educational exhibits, live shows, and thrilling rides. While it has faced criticism for its treatment of animals, SeaWorld has made changes to prioritize conservation and phased out its orca breeding program.

SeaWorld is a chain of theme parks and oceanariums that primarily focuses on marine life and entertainment. The company operates various parks across the United States, including SeaWorld parks in Orlando, San Diego, and San Antonio, as well as Busch Gardens parks in Tampa and Williamsburg. SeaWorld offers a combination of educational exhibits, live shows, and thrilling rides, with a special emphasis on marine animals such as dolphins, whales, sea lions, penguins, and sharks.

SeaWorld parks provide visitors with opportunities to observe and interact with marine creatures up close, while also offering educational programs that aim to raise awareness about marine conservation and preservation. The parks feature captivating shows featuring trained animals, where they perform impressive behaviors and stunts, showcasing their intelligence and natural abilities.

Over the years, SeaWorld has faced criticism from animal rights activists and environmentalists, who argue that the captivity and use of marine animals for entertainment purposes is unethical and harmful to the animals' well-being. These concerns have led to significant changes in the company's practices, including the phasing out of its orca breeding program and the introduction of more educational and conservation-focused initiatives.

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Answer: -18

Explanation:

Answer:

its -18

Explanation:

Khan Academy

The speed of the running shaft driving the machine, given that the main shaft to drive the machine has a pulley of diameter 140 mm is 111.4 rev/min

First, we shall list out the given parameters from the question. Details below:

The speed of the running shaft can be obtain as shown below:

S₁D₁ = S₂D₂

183 × 140 = S₂ × 230

183 × 140 = S₂ × 230

25620 = S₂ × 230

Divide both sides by 230

S₂ = 25620 / 230

S₂ = 111.4 rev/min

Thus, we can conclude that the speed of the running shaft driving the machine is 111.4 rev/min

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Answer: So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). When the distance between the 2 objects is halved, the gravitational force between the 2 objects is doubled. when the distance between the 2 objects is doubled then the gravitational force doubles

Hope this helps

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Please find attached photograph for your answer.

The displacement of the object is 2 meters.

To determine the displacement of the object, we need to consider the change in position from the initial position to the final position.

Given:

Initial position = 0 meters

Final position = 2 meters

Calculate the displacement:

Displacement = Final position - Initial position

Displacement = 2 meters - 0 meters

Displacement = 2 meters

Therefore, the displacement of the object is 2 meters.

Explanation:

The position-time graph shows the position of an object over a specific time interval. In this case, the graph shows that the object starts at a position of 0 meters and ends at a position of 2 meters. The displacement of the object is the change in position from the initial point to the final point.

In this context, the displacement of 2 meters indicates that the object has moved 2 meters to the right or in the positive direction from its initial position. The negative and positive signs on the graph indicate the direction of motion, where positive values represent motion in one direction and negative values represent motion in the opposite direction.

The time interval is not directly related to the displacement calculation. It simply represents the duration of the object's motion. To determine the displacement, we only need to consider the initial and final positions, which in this case result in a displacement of 2 meters.

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Answer:

Depends on position

Explanation:

Rest:

A body is said to be at rest, if it does not change its position with respect to its surroundings.

Motion:

A body is said to be in motion, if it changes its position with respect to its surroundings.

The state of rest and motion is relative

First, let's calculate the equivalent resistance of the three parallel resistors, using the formula below:

Now, let's add this resistance with the one resistance in series:

To find the total current, let's divide the voltage by the total resistance:

Therefore the correct option is b.

Answer:

CRISTO

Explanation:

UWU

Answer:

The Eucharist

Explanation:

In The Catechism of the Catholic Church (1324-1327), it states that The Eucharist is the source and summit of the whole Christian Life.

Convert to m/s

\(\\ \sf\longmapsto v=20\times 5/18=5.5m/s\)

We know

\(\boxed{\sf \omega=\dfrac{rv}{|r|^2}}\)

\(\\ \sf\longmapsto \omega=\dfrac{0.5(5.5)}{|0.5|^2}\)

\(\\ \sf\longmapsto \omega=\dfrac{2.75}{0.25}\)

\(\\ \sf\longmapsto \omega=11rad/s\)

When the acceleration is three times as large, the mass of the new block will be one-third the initial mass.

The acceleration of the block is the rate of change of velocity of the block with time.

The magnitude of the acceleration of each block can be obtained by applying Newton's second law of motion as follows;

F = ma

m = F/a

where;

When the acceleration is three times as large, the mass of the new block is calculated as;

m = F/3a

m = 1/3 (F/a)

new mass = one-third the initial mass

Thus, we can conclude that when the acceleration is three times as large, the mass of the new block will be one-third the initial mass.

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The equivalent resistance of the circuit is 8.6 Ω.

Resistance can be defined as the opposition to current flow in an electric circuit. The S.I unit of resistance is ohms.

To calculate the equivalent resistance, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, The equivalent resistance of the circuit is 8.6 Ω
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Two factors that determine the amount of electricity that can be generated by an individual hydroelectric power plants - It depends on the vertical distance through which the water falls and the flow rate, or amount of water that flows past a certain point per unit time, The greater the distance that the water falls, the more potential energy it had and the more electricity is generated the more kinetic energy it has and the more .

Impoundment, diversion, and pumped storage facilities are the three different types of hydroelectric facilities. Hydropower plants vary in their utilisation of dams. Despite the fact that not all dams were constructed for hydropower, they have been successful in supplying vast amounts of renewable energy to the grid. As of 2020, fewer than 2,300 of the more than 90,000 dams in the United States were producing electricity. The other dams are utilised for water supply, irrigation, flood control, stock/farm ponds, and recreation. Hydropower facilities come in a variety of sizes, from modest initiatives providing electricity for a single house or community to massive undertakings. 

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The near point of a human eye is about a distance of 25 cm.

The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.

This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.

The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.

In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.

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Answer:

(a) \(\vec F_{\parallel} = -\frac{102}{13}\,i-\frac{103}{13}\,j\) , (b) \(\vec F_{\perp} = \frac{102}{13}\,i -\frac{68}{13}\,j\), (c) \(W = -51\)

Explanation:

The statement is incomplete:

The force on an object is \(\vec F = -17\,j\). For the vector \(\vec v = 2\,i +3\,j\). Find: (a) The component of \(\vec F\) parallel to \(\vec v\), (b) The component of \(\vec F\) perpendicular to \(\vec v\), and (c) The work \(W\), done by force \(\vec F\) through displacement \(\vec v\).

(a) The component of \(\vec F\) parallel to \(\vec v\) is determined by the following expression:

\(\vec F_{\parallel} = (\vec F \bullet \hat {v} )\cdot \hat{v}\)

Where \(\hat{v}\) is the unit vector of \(\vec v\), which is determined by the following expression:

\(\hat{v} = \frac{\vec v}{\|\vec v \|}\)

Where \(\|\vec v\|\) is the norm of \(\vec v\), whose value can be found by Pythagorean Theorem.

Then, if \(\vec F = -17\,j\) and \(\vec v = 2\,i +3\,j\), then:

\(\|\vec v\| =\sqrt{2^{2}+3^{3}}\)

\(\|\vec v\|=\sqrt{13}\)

\(\hat{v} = \frac{1}{\sqrt{13}} \cdot(2\,i + 3\,j)\)

\(\hat{v} = \frac{2}{\sqrt{13}}\,i+ \frac{3}{\sqrt{13}}\,j\)

\(\vec F \bullet \hat{v} = (0)\cdot \left(\frac{2}{\sqrt{13}} \right)+(-17)\cdot \left(\frac{3}{\sqrt{13}} \right)\)

\(\vec F \bullet \hat{v} = -\frac{51}{\sqrt{13}}\)

\(\vec F_{\parallel} = \left(-\frac{51}{\sqrt{13}} \right)\cdot \left(\frac{2}{\sqrt{13}}\,i+\frac{3}{\sqrt{13}}\,j \right)\)

\(\vec F_{\parallel} = -\frac{102}{13}\,i-\frac{153}{13}\,j\)

(b) Parallel and perpendicular components are orthogonal to each other and the perpendicular component can be found by using the following vectorial subtraction:

\(\vec F_{\perp} = \vec F - \vec F_{\parallel}\)

Given that \(\vec F = -17\,j\) and \(\vec F_{\parallel} = -\frac{102}{13}\,i-\frac{153}{13}\,j\), the component of \(\vec F\) perpendicular to \(\vec v\) is:

\(\vec F_{\perp} = -17\,j -\left(-\frac{102}{13}\,i-\frac{153}{13}\,j \right)\)

\(\vec F_{\perp} = \frac{102}{13}\,i + \left(\frac{153}{13}-17 \right)\,j\)

\(\vec F_{\perp} = \frac{102}{13}\,i -\frac{68}{13}\,j\)

(c) The work done by  \(\vec F\) through displacement \(\vec v\) is:

\(W = \vec F \bullet \vec v\)

\(W = (0)\cdot (2)+(-17)\cdot (3)\)

\(W = -51\)

Answer:

\(V=9.2565m/s\)

Explanation:

From the question we are told that:

Force \(F = 34 N\)  

Time \(t = 0.6 s\)

Length of pedal \(l_p=16.5cm \approx0.165m\)

Radius of wheel \(r = 33 cm = 0.33 m\)

Moment of inertia, \(I = 1200 kgcm2 = 0.12 kg.m2\)

Generally the equation for Torque on pedal \(\mu\) is mathematically given by

\(\mu=F*L\\\mu=34*0.165\)

\(\mu=5.61N.m\)

Generally the equation for  angular acceleration \(\alpha\) is mathematically given by

 \(\alpha=\frac{\mu}{l}\)

 \(\alpha=\frac{5.61}{0.12}\)

 \(\alpha=46.75\)

Therefore Angular speed is \omega

\(\omega=\alpha*t\)

\(\omega=(46.75)*(0.6)\)

\(\omega=28.05rad/s\)

Generally the equation for  Tangential velocity V is mathematically given by

\(V=r\omega\)

\(V=(0.33)(28.05)\)

\(V=9.2565m/s\)