An electron is moving in the xy-plane. If at time t a magnetic field B = 0.200 T in the +z direction exerts a force on the electron equal to F = 5.5*10^-18 N in the -y-direction, what is the velocity (magnitude and direction) of the electron at this instant?

The magnitude of the third force is 7.93 N and South west direction.

Force \( F_{1}\) = 6 N in east direction

Force \( F_{2}\) = 3 N 60 degrees in northeast direction

Three forces are acting on the body. For a body to be in equilibrium the sum of all three forces must be zero.

Net force = \( F_{1}\) + \( F_{2}\) + \( F_{3}\)

Resolving the forces in x and y directions,

\( F_{1x}\) = 6N

\( F_{1x}\) = 0N

\( F_{2y}\) = 3cos(60) = 1.5 N

\( F_{2y}\) = 3sin(60) = 2.59 N

Hence calculating the third force magnitude

\( F_{3x}\) = net F - \( F_{1x}\) - \( F_{2x}\)

\( F_{3x}\) = 0-6-1.5

\( F_{3x}\) = -7.5 N

Similarly

\( F_{3y}\) = net F - \( F_{1y}\) - \( F_{2y}\)

\( F_{3y}\) = 0-0-2.59

\( F_{3y}\) = -2.59 N

Magnitude of resultant

\( F_{3} = \sqrt[ 2 ] {{F_{3x}}^{2} +{F_{3y}}^{2} }\)

\( F_{3} = \sqrt{ { - 7.5}^{2} + { - 2.59}^{2} } \)

\( F_{3}\) = 7.93 N

Since the resultant is the closing vector the direction is south west.

Hence the magnitude and direction if Third force are 7.39 N and Southwest respectively.

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Answer:

Explanation:

As per the question, both the stones will meet after

3

sec

.

Let, total height of the building be

H

and the distance covered by dropped and thrown stone be

H

1

and

H

2

respectively, we have

H

=

H

1

+

H

2

So, from equation of motion we have

s

=

u

t

+

1

2

a

t

2

⇒

H

1

=

0

(

3

)

+

1

2

×

10

×

(

3

)

2

⇒

H

1

=

45

m

also,

H

2

=

(

20

)

(

3

)

−

1

2

×

10

×

(

3

)

2

⇒

H

2

=

15

m

Hence, total height of the building is

H

=

45

+

15

=

60

m

Answer:

Let's assume that the acceleration due to gravity is `g = 9.8 m/s²` and that the building is tall enough that the stones do not reach the ground during the time period we are considering. Let `h1(t)` be the height of the first stone (the one dropped freely) at time `t`, and let `h2(t)` be the height of the second stone (the one thrown upward) at time `t`. Since the first stone is dropped freely, its height at time `t` is given by the equation `h1(t) = 100 - (1/2)gt²`. Since the second stone is thrown upward with an initial velocity of `20 m/s`, its height at time `t` is given by the equation `h2(t) = 100 + 20t - (1/2)gt²`.

The stones will meet each other when their heights are equal, i.e., when `h1(t) = h2(t)`. Substituting the expressions for `h1(t)` and `h2(t)` into this equation, we get:

`100 - (1/2)gt² = 100 + 20t - (1/2)gt²`

Solving this equation for `t`, we find that `t = 5 s`. Substituting this value of `t` into either of the equations for `h1(t)` or `h2(t)`, we find that the height at which the stones meet is `h1(5) = h2(5) = 100 + 20(5) - (1/2)(9.8)(5)² ≈ 50 m`.

Therefore, **the two stones will meet each other at a height of 50 meters above the ground, 5 seconds after they are released**.

The slope of a velocity-time graph gives the acceleration of the object.

A - The part A shows that there is no increase in the velocity of the object. That means the object is at rest.

B - In the part B of the graph, it is shown that the velocity of the object is increasing linearly. That means, the velocity is changing, thus the object has an acceleration in the positive direction.

C - In the part C of the graph, it is shown that there is no change in the velocity of the object, but it is moving with a non-zero velocity. Therefore, we can say that the object is moving with a constant speed.

D - In the part D of the graph, it is shown that the velocity of the object is decreasing linearly. That means the object is having a negative acceleration, but in the positive direction.

E - In the part E of the graph, it is shown that the velocity of the object is again increasing from zero, but in the opposite direction.

F - In the part C of the graph, it is shown that the object is moving with a constant velocity, but in the opposite direction.

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Answer:

See below

Explanation:

You didn't show the e-magnet construction diagram....but:

If the e-magnet is built properly and has current flowing through the coils, it will affect the compass.....also note that a compass is a magnet, so if the e-magnet is ferrous (iron-containng)  material it will affect the compass ....current flowing or not !

Answer:

The horizontal component of the force, \(F_x= 34.24 \ N\)

The  vertical component of the force, \(F_y=7.28 \ N\)

Explanation:

Given;

Force on the rope, F = 35 N

angle between the rope and the horizontal = 12 °

The horizontal component of the force is given by;

\(F_x = Fcos \theta\\\\F_x = 35cos(12^0)\\\\F_x = 34.24 \ N\)

The vertical component of the force is given by;

\(F_y = Fsin\theta\\\\F_y = 35sin(12^0)\\\\F_y = 7.28 \ N\)

Given the following information:Mass of the system, m = 20 kg.Damping coefficient, b = 6 Ns/m.Force, F = 90 N.Frequency of applied force, f = ?Applied force angular frequency, w = 6 rad/s.Forced vibration equation:F(t) = F0 sin(wt)where F0 = 90 N and w = 6 rad/s.Under the action of the force F, the mass m will oscillate.The equation of motion for the mass-spring-damper system is given by:$$\mathrm{m\frac{d^{2}x}{dt^{2}}} + \mathrm{b\frac{dx}{dt}} + \mathrm{kx = F_{0}sin(\omega t)}$$where k is the spring constant.x(0) = 0 and x'(0) = 0.As we have the damping coefficient (b), we can calculate the damping ratio (ζ) and natural frequency (ωn) of the system.Damping ratio:$$\mathrm{\zeta = \frac{b}{2\sqrt{km}}}$$where k is the spring constant and m is the mass of the system.Natural frequency:$$\mathrm{\omega_{n} = \sqrt{\frac{k}{m}}}$$where k is the spring constant and m is the mass of the system.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$At resonance, the amplitude of the system will be maximum when forced by a sinusoidal force of frequency equal to the resonant frequency.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$$$\mathrm{\omega_{d} = \sqrt{(6.57)^{2}-(-2.88)^{2}} = 6.98 rad/s}$$Hence, the frequency of applied force at which resonance will occur is 6.98 rad/s.

The frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.

To determine the frequency of the applied force at which resonance will occur, resonance happens when the frequency of the applied force matches the natural frequency of the system. The natural frequency can be determined using the formula:

ωn = √(K / M),

where ωn is the natural frequency, K is the spring constant, and M is the mass of the system.

Substituting the given values of K = 400 N/m and M = 20 kg into the equation, we can calculate the natural frequency ωn.

ωn = √(400 N/m / 20 kg) = √(20 rad/s²) = 2√5 rad/s.

Therefore, the frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.

The correct question is given as,

M= 20kg

Fo = 90 N

ω = 6 rad/s

K = 400 N/m

C = 125 Ns/m

Determine the frequency of applied force at which resonance will occur?

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Answer:

C. 1.42 s

Explanation:

Givens:

length = 0.5m

gravity = 9.807 m/s

Solve:

T = 2π√(L/g)

T = 2π√(0.5/9.807)

T = 2π√(0.0509)

T = 2π * 0.22579

T = 6.28318 * 0.22579

T = 1.418 ≈ 1.42s

Answer:

Ke²

Explanation:

So,

q1 = e

q2 = e

r = 1m

By coulumb's law,

F = K (q1q2/r²)

F = K (e)(e)/(1)²  

F = Ke²  

Option(a)

The astronaut's height, as measured from the space station, will appear contracted due to relativistic effects. Due to relativistic length contraction, the astronaut's height, as measured from the space station, appears to be approximately 3.52 meters.

According to the theory of special relativity, objects in motion relative to an observer will experience length contraction along the direction of motion. In this case, the spaceship is moving at a speed of 0.9 times the speed of light (0.9 c) relative to the space station.

The length contraction factor, denoted by γ, can be calculated using the Lorentz factor:

γ = 1 / √(1 - v²/c²)

Where v is the velocity of the spaceship and c is the speed of light. Plugging in the values, we have:

γ = 1 / √(1 - 0.9²)

γ ≈ 1.92

To determine the astronaut's height as measured from the space station, we multiply her actual height by the length contraction factor:

Height (as measured from the space station) = Actual height × γ

Height (as measured from the space station) = 1.83 m × 1.92

Height (as measured from the space station) ≈ 3.52 m

Therefore, due to relativistic length contraction, the astronaut's height, as measured from the space station, appears to be approximately 3.52 meters.

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The average force exerted as the displacement from 0 to x changes is 12kx. W = 12kx² is the work done when stretching or compressing a spring a distance x from its equilibrium position.

The Hooke's Law Calculator employs the formula Fs = -kx, where F is the spring's restoring force, k is the spring constant, and x is the displacement, or distance the spring is stretched. Hooke's Law states that when a spring is stretched, the force exerted is proportional to the increase in length from the equilibrium length. The spring constant can be calculated as follows: k = -F/x, where k is the spring constant. The Young's modulus (E) is a material property that indicates how easily it can stretch and deform. It is defined as the ratio of tensile stress () to tensile strain ().

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a. The shift of the LM curve to the left occurs due to a decrease in the money supply or an increase in the demand for money.

b. Two reasons for a steep IS curve are High Investment Demand and Inflexibility in Investment.

The LM curve shows the various combinations of interest rates and income that bring about the equality of the supply and demand for money.

Below are three reasons for the leftward shift of the LM curve:

1. Decrease in Money Supply: The leftward shift of the LM curve can occur if the money supply decreases. This causes the interest rates to rise because the demand for money is greater than the supply.

2. Increase in Money Demand: An increase in the demand for money can lead to a leftward shift of the LM curve. This happens when people want to hold more money than is available in the economy, and the interest rate rises as a result.

3. Increase in Prices: An increase in prices causes a leftward shift of the LM curve. This is because, at higher prices, people need more money to conduct their transactions, and an increase in the money supply is required to keep the interest rate constant.

Now, moving on to the steep IS curve:

1. High Investment Demand: A steep IS curve may occur if there is high investment demand. This happens when businesses are optimistic about the future and invest more, causing the demand for credit to increase and the interest rates to rise.

2. Inflexibility in Investment: A steep IS curve can also be caused by inflexibility in investment. This occurs when businesses are unwilling to change their level of investment due to economic conditions, and any changes in the interest rates have a significant effect on investment and output levels.

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Therefore the value of t is sin⁻¹√(m/100k(m+100k))

The motion of a particle connected to a spring can be described by the following equation;

x = 10 sin(πt)

Given that the spring is elastic, we can use this equation to determine the potential energy and kinetic energy.

Potential Energy; Potential energy is the energy an object has because of its position or state. It is stored energy that can be converted into kinetic energy. In this case, the potential energy can be determined as follows;

Let m be the mass of the particle and k be the spring constant.

The potential energy of a spring is given by;

P.E = (1/2)kx²

Substituting the given values we have;

P.E = (1/2)k[10 sin(πt)]²

P.E = (1/2)k100sin²(πt)

At the point where potential energy is equal to kinetic energy, then;

P.E = K.E

Therefore; P.E = K.E(1/2)k100sin²(πt)

= (1/2)mv²

Kinetic Energy; Kinetic energy is the energy an object possesses due to its motion. It is defined as one-half the mass of an object times its velocity squared.

K.E = (1/2)mv²

Substituting the given values we have;

(1/2)k100sin²(πt) = (1/2)m(πx)²1/2 is a constant that appears on both sides of the equation.

It can be cancelled out, thus leaving us with;

k100sin²(πt) = m(πx)²k(10sin(πt))²

= m(πx)²100k(sin²(πt))

= mπ²cos²(πt)100k(sin²(πt))

= m(1 - sin²(πt))100ksin²(πt)

= m - msin²(πt)msin²(πt) + 100ksin²(πt)

= mmsin²(πt)(1 + 100k/m)

= m

Solving for t;

t = sin⁻¹√(m/100k(m+100k))

The answer is the value of t obtained from the above equation.

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When you change the thickness of the wire in a circuit, option B. the resistance (R) and current (I) will also change, but the voltage (V) will remain constant.

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area (thickness). As the thickness of the wire changes, the cross-sectional area changes, which in turn affects the resistance. Thicker wires have a larger cross-sectional area, resulting in lower resistance, while thinner wires have a smaller cross-sectional area, resulting in higher resistance. Therefore, changing the thickness of the wire will cause a change in resistance.

According to Ohm's Law (V = IR), the voltage (V) in a circuit is equal to the product of the current (I) and the resistance (R). If the voltage is kept constant, and the resistance changes due to the thickness of the wire, the current will also change to maintain the relationship defined by Ohm's Law. When the resistance increases, the current decreases, and vice versa.

However, it's important to note that changing the thickness of the wire will not directly affect the voltage. The voltage in a circuit is determined by the power source or the potential difference applied across the circuit and is independent of the wire thickness. As long as the voltage source remains constant, the voltage across the circuit will remain constant regardless of the wire thickness. Therefore, the correct answer is option B.

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Answer: when water flows on the earths surface

Explanation:

Answer:

\(the \: net \: force = \: 50 - 15 = 35.\)

Answer:

Net force is going to be GREATER FORCE - LESS FORCE if they are working in opposite direction

so,

         50N - 15N = 35N

pushed to the right = 300 newtons

pushed to the left = 400 newtons

\(400-300=100\)

\(\fbox{100 Newtons to the left}\)

Gases such as carbon dioxide (CO2) play a crucial role in climate and weather patterns.Carbon dioxide, along with other greenhouse gases like methane and water vapor, helps trap heat in the Earth's atmosphere, leading to the greenhouse effect.

This effect is essential for maintaining a habitable temperature on Earth. Without greenhouse gases, the planet would be too cold to support life.

However, the increased concentration of greenhouse gases, primarily due to human activities like burning fossil fuels, has led to an enhanced greenhouse effect, resulting in global warming. The rise in CO2 levels has been directly linked to the increase in average global temperatures and climate change.

Moreover, changes in CO2 levels can affect weather patterns and climate systems. The absorption and release of heat by the atmosphere, influenced by greenhouse gases, contribute to the formation of weather systems such as storms, precipitation patterns, and wind patterns.

Therefore, gases like carbon dioxide are indeed important factors in climate and weather, and their concentrations and effects are subjects of significant scientific study and concern.

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One of the best ways to protect yourself from excessive exposure to radiation is to avoid unnecessary exposure. If possible, avoid getting X-rays or other types of radiation when they are not medically necessary. However, if you do need to get an X-ray, make sure it is done by a licensed professional who will take the necessary precautions to limit your exposure.

Radiation can be harmful to the human body, and exposure to excessive radiation can lead to serious health problems such as cancer and radiation sickness. Therefore, it is essential to protect yourself from excessive exposure to radiation.

Finally, increasing your distance from the source of radiation can also help protect you from excessive exposure. The further away you are from the source of radiation, the less exposure you will receive. Therefore, if you work in an environment where you are exposed to radiation, try to keep as much distance between yourself and the source as possible.

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Explanation:

1) left ⬅️

2) into the page

3) upward ⬆️

4) right ➡️

5) downward ⬇️

To determine the acceleration field for a three-dimensional flow, we need to calculate the acceleration vectors at each point in the flow. This can be done by taking the derivatives of the velocity components with respect to time.

In a three-dimensional flow, the velocity of the fluid at any point can be described by three components: u, v, and w, representing the velocities in the x, y, and z directions, respectively. The acceleration field represents how the velocity is changing with time at each point in the flow. To determine the acceleration field, we need to calculate the time derivatives of the velocity components. Mathematically, this can be expressed as:

\(\[\frac{{du}}{{dt}} = \frac{{\partial u}}{{\partial t}} + u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial y}} + w\frac{{\partial u}}{{\partial z}}\]\[\frac{{dv}}{{dt}} = \frac{{\partial v}}{{\partial t}} + u\frac{{\partial v}}{{\partial x}} + v\frac{{\partial v}}{{\partial y}} + w\frac{{\partial v}}{{\partial z}}\]\)

\(\[\frac{{dw}}{{dt}} = \frac{{\partial w}}{{\partial t}} + u\frac{{\partial w}}{{\partial x}} + v\frac{{\partial w}}{{\partial y}} + w\frac{{\partial w}}{{\partial z}}\]\)

where \(\(\frac{{\partial}}{{\partial t}}\)\) represents the partial derivative with respect to time, and \(\(\frac{{\partial}}{{\partial x}}\), \(\frac{{\partial}}{{\partial y}}\), and \(\frac{{\partial}}{{\partial z}}\)\) represent the partial derivatives with respect to the spatial coordinates. By evaluating these derivatives at each point in the flow, we can obtain the acceleration vectors \((\(\frac{{du}}{{dt}}\), \(\frac{{dv}}{{dt}}\), \(\frac{{dw}}{{dt}}\))\) that define the acceleration field. These vectors indicate how the velocity is changing with time in the x, y, and z directions at each point in the flow, providing a comprehensive description of the three-dimensional acceleration field.

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70 degrees

90 - 20 since angle of incidence is the complement of the angle it strikes with.

The deceleration experienced by the 1075 N sky diver as he opened his parachute is 13.39 m/s²

Force = mass × acceleration

We know that deceleration is the acceleration of stopping objects. Thus,

Force (F) = mass (m) × deceleration (a)

Thus, we can obtain the deceleration of the sky diver as follow:

Force = mass (m) × deceleration (a)

1469 = 109.69 × a

Divide both sides by 109.69

a = 1469 / 109.69

a = 13.39 m/s²

Thus, the deceleration is 13.39 m/s²

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Answer:

Volt divided by ampere

Explanation:

V = IR

V/I = R

The unit of resistance from ohms law is volt / ampere. Thus, option A is correct.

Ohm's law states that the applied voltage is directly proportional to the current flow in the conductor. It is written as V ∝ I. It remains constant at room temperature.

V is defined as  potential difference or voltage. The SI unit of voltage is volt(V). I is defined as the current flowing in the circuit. The SI unit of current is ampere (A).

Generally, ohm's law equals to V = IR. R represents resistance of a material which oppose the current flow in the conductor. The unit of resistance is ohm(Ω).

When the potential difference(V) is constant, Resistance is inversely proportional to current. Current increases with decrease of resistance and current decreases with increase of resistance.

To find  equivalent unit of resistance, the ohm's law is :

V = IR

R = V / I

  = volt / ampere.

Hence, the unit of resistance from ohm's law is volt / ampere. The SI unit of resistance is ohm(Ω). Thus, option A is correct.

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The new boiling point of water, when 0.125 kg of NaCl solute is added to 750 g of water, is predicted to be approximately 101.45 °C.

To calculate the new boiling point, we can use the formula:

ΔTb = Kb * m

where ΔTb is the boiling point elevation, Kb is the molal boiling point elevation constant for the solvent (water), and m is the molality of the solute (NaCl).

First, we need to calculate the molality of the NaCl solution:

molality (m) = moles of solute / mass of solvent (in kg)

The moles of NaCl can be calculated using its molar mass (58.44 g/mol) and the given mass of NaCl (0.125 kg). Similarly, the mass of the water is given as 750 g, which is 0.75 kg.

Once we have the molality, we can use the molal boiling point elevation constant for water (Kb = 0.51 °C/m) to calculate the boiling point elevation (ΔTb).

Finally, the new boiling point is obtained by adding the boiling point elevation to the boiling point of pure water, which is 100 °C at standard atmospheric pressure.

Therefore, the predicted new boiling point of water is approximately 101.45 °C.

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Complete question here:

Predict what the new boiling point of water will be if you add 0.125 kg of |NaCl solute to 750 g of water (Kb of water = 0.51°C/m). ?

101.45°C ?

98.55°C ?

102.91°C

197.09°C

It can be determined that  Kinetic energy at point A is 2.16 J and Speed at point B is 4.16 m/s and Total work done on the object from A to B = 5.84 J, found using work-energy theorem.

(a) Kinetic energy at point A can be calculated using the formula:

Kinetic energy = (1/2) * mass * speed²

Kinetic energy at point A = (1/2) * 0.48 kg * (3.0 m/s)²

= 2.16 J

Therefore, the kinetic energy of the object at point A is 2.16 J.

(b) The speed of the object at point B can be calculated using the formula:

Kinetic energy = (1/2) * mass * speed²

speed² = (2 * Kinetic energy) / mass

speed = \sqrt{[(2 * 8.0 J) / 0.48 kg]}

= 4.16 m/s

Therefore, the speed of the object at point B is 4.16 m/s.

(c) The total work done on the particle as it moves from A to B is equal to the change in kinetic energy of the object, which can be calculated as:

Work done = Kinetic energy at point B - Kinetic energy at point A

= 8.0 J - 2.16 J

= 5.84 J

Therefore, the total work done on the particle as it moves from A to B is 5.84 J.

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The term that describes the impact of thick walls and ceilings on radio wave signals is attenuation. Attenuation refers to the loss of signal strength or energy as it travels through a medium, such as a wall or ceiling.

The thicker the material, the higher the level of attenuation, resulting in weaker radio wave signals on the other side of the barrier.

Attenuation refers to the reduction in the strength or intensity of a signal as it travels through a medium or encounters obstacles. In the context of radio wave signals, thick walls and ceilings can act as barriers or obstacles that obstruct the transmission of radio waves. As radio waves encounter these physical barriers, they can be absorbed, reflected, or refracted, leading to a decrease in signal strength.

Thick walls and ceilings tend to be denser and more opaque to radio waves compared to open spaces or thinner materials. This increased density and opacity result in greater attenuation of the radio waves passing through them. The higher the attenuation, the weaker the signal becomes after passing through the barriers.

The extent of attenuation depends on factors such as the thickness and composition of the walls and ceilings, the frequency of the radio waves, and the distance between the transmitter and receiver. In some cases, the attenuation caused by thick walls and ceilings may require the use of additional signal amplification or the installation of repeaters or signal boosters to maintain an adequate signal strength.

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Answer:

2.5 m/s^2

Explanation:

the equation to find acceleration is \(\frac{v - v_{0} }{t}\) where \(v_{0}\) is the initial velocity, v is the current velocity, and t is the total time

so plug in your values: \(\frac{20 - 0}{8}\)

that turns into 20 ÷ 8

this equals 2.5 m/s^2

They found out that their vectors did not point in the same direction because the two students observed the vector's motion from opposite direction.

Vector addition is the operation of adding two or more vectors together into a vector sum. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

When the two students added a vector for a moving object’s position at t=2s to a motion diagram. They found out that their vectors did not point in the same direction because the two students observed the vector's motion from opposite direction.

Thus, they found out that their vectors did not point in the same direction because the two students observed the vector's motion from opposite direction.

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