The coordinate of a particle in meters is given by x(t)=1 6t- 3.0t , where the time tis in seconds. The
particle is momentarily at rest at t is:
Select one:
a. 9.3s
b. 1.3s
C. 0.75s
d.5.3s
e. 7.3s

Answers

Answer 1

Complete question:

The coordinate of a particle in meters is given by x(t)=1 6t- 3.0t³ , where the time tis in seconds. The

particle is momentarily at rest at t is:

Select one:

a. 9.3s

b. 1.3s

C. 0.75s

d.5.3s

e. 7.3s

Answer:

b. 1.3 s

Explanation:

Given;

position of the particle, x(t)=1 6t- 3.0t³

when the particle is at rest, the velocity is zero.

velocity = dx/dt

dx /dt = 16 - 9t²

16 - 9t² = 0

9t² = 16

t² = 16 /9

t = √(16 / 9)

t = 4/3

t = 1.3 s

Therefore, the particle is momentarily at rest at t = 1.3 s


Related Questions

What is the best description of the function of stars?


Stars are the recycling centers of the universe.
Stars are the light bulbs of the universe.
Stars are the batteries of the universe.
Stars are the motors of the universe.

Answers

Answer:

Stars are the light bulbs of the universe.

Answer:

Stars are the recycling centers of the universe

Explanation:

I just did on edge C

A 1 kg rock is sitting at the edge of a cliff 100 meters high. What is the rock's gravitational potential energy?

Answers

Answer:

000.83

Explanation:

i dont know how to explain it bt i did something on paper for it

Frequency= Wavelength = 502 km Speed= 100 m/s​

Answers

Answer:

Explanation:

Wavelength = 100m. Speed = V. 2.) Frequency = 20 Hz. Wavelength = 200 m. Speed = ... 2=1.7m. F=Y/2 f=2×10. 5.) Wavelength = 502 km. Speed= 100 m/s.

menstruation occurs in females when ?

Answers

Answer:

when they hit puberty

Explanation:

.

have a good day

Answer:

Their inner lining of uterus sheds

Explanation:

this occurs typically in females between 9-15

A park ranger driving on a back country road suddenly sees a deer in his headlights 20m ahead. The ranger, who is driving at 11.4 m/s, immediately applies the brakes andslows down with an acceleration of 3.80 m/s2. How much distance is required for theranger's vehicle to come to rest? Only enter the number, not the units,

Answers

Given data

*The speed of the ranger who is driving at 11.4 m/s

*The given acceleration is a = -3.80 m/s^2

The formula for the distance covered by the ranger's vehicle is given by the kinematic equation of motion as

\(\Delta x=\frac{v^2-v^2_0}{2a}\)

*Here v = 0 m/s is the initial speed of the ranger's vehicle

Substitute the values in the above expression as

\(\begin{gathered} \Delta x=\frac{0^2-(11.4)^2}{2\times(3.80)} \\ =17.1\text{ m} \end{gathered}\)

The distance is required for the ranger's vehicle to come to rest is calculated as

\(\begin{gathered} D=20-17.1 \\ =2.9\text{ m} \end{gathered}\)

The stopping time is calculated as

\(v=v_0+at\)

Substitute the values in the above expression as

\(\begin{gathered} 0=11.4+(-3.80)(t) \\ t=3.00\text{ s} \end{gathered}\)

-0,32 m - 4.2 At the instant the marble leaves the canon, the canon starts moving backwards (recoils) at a constant velocity. 4.1 State the principle of conservation of linear momentum in words. that is stationary canon is placed 0,32 m from a fixed bare After firing, the canon takes 0,33 s to collide with a barrier at a distance of 0,32 m. Calculate the speed the: W< 1 >E S 4.2.1 Canon collides with the barrier​

Answers

The cannon will completely stop when it collides with the barrier.

To calculate the speed at which the cannon collides with the barrier, we can follow these step-by-step calculations:

Determine the initial momentum of the system.

Since the cannon is initially stationary, the initial momentum is zero.

Apply the conservation of linear momentum.

According to the principle of conservation of linear momentum, the initial momentum of the system (zero) is equal to the final momentum of the system. The final momentum is the momentum of the cannon after firing.

Calculate the final momentum of the system.

Let's assume the mass of the cannon is represented by 'm' and the final velocity of the cannon is represented by 'v'. The final momentum of the system is given by: final momentum = m × v.

Set up the equation.

Since the initial momentum is zero, we have: 0 = m × v.

Solve for the final velocity of the cannon.

Dividing both sides of the equation by 'm', we get: v = 0.

Interpret the result.

The calculation shows that the final velocity of the cannon is zero. This means that the cannon comes to a complete stop when it collides with the barrier.

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2. You are traveling along a highway at night at a speed of 100 km/h when you spot an object directly in front of you in the road at the limit of your headlights. (10 Marks)

a) If the maximum braking deceleration that your car can provide is 7 m/s2, and if your headlights extend out to a range of 30 m, will you hit the object before coming to a stop?

b) How long will it take to stop?

Answers

a) To determine if the car will hit the object before coming to a stop, we need to calculate the distance required to stop the car, assuming maximum braking deceleration. We can use the following formula:

d = (v^2) / (2a)

where:

d = distance required to stop

v = initial velocity

a = acceleration/deceleration

In this case, v = 100 km/h = 27.78 m/s (converted from km/h to m/s)

a = -7 m/s^2 (negative sign indicates deceleration)

We know that the car's headlights extend out to a range of 30 m, so if the distance required to stop the car is greater than 30 m, the car will hit the object before coming to a stop.

Plugging in the values to the formula, we get:

d = (27.78^2) / (2 x -7) = 108.61 m

Since 108.61 m is greater than 30 m, the car will hit the object before coming to a stop.

b) To calculate the time required to stop, we can use the following formula:

t = v / a

where:

t = time required to stop

v = initial velocity

a = acceleration/deceleration

Plugging in the values, we get:

t = 27.78 / 7 = 3.97 s

Therefore, it will take 3.97 seconds to stop the car.

why is sun considered the center of the solar system​

Answers

Answer: All the planets in our solar system rotate around it without the sun itself moving therefore all the planets make a cicular shape and the sun is in the middle

Explanation:

A baseball is popped straight up into the air and has a hang-time of 6.25 S.
Determine the height to which the ball rises before it reaches its peak. (Hint: the
time to rise to the peak is one-half the total hang-time.)

A baseball is popped straight up into the air and has a hang-time of 6.25 S.Determine the height to which

Answers

Answer:

To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.

The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.

The height to which the ball rises can be calculated using the formula:

height = v * t - (1/2) * g * t^2

Substituting in the values we know, we get:

height = v * 3.125 s - (1/2) * g * (3.125 s)^2

To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.

Explanation:

Answer:

Approximately \(47.9\; {\rm m}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\) and that air resistance on the baseball is negligible.)

Explanation:

If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly \((1/2)\) the time it is in the air. In this example, that will be \(t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}\).

When the baseball is at maximum height, the velocity of the baseball will be \(0\). Let \(v_{f}\) denote the velocity of the baseball after a period of \(t\). After \(t = 3.125\; {\rm s}\), the baseball would reach maximum height with a velocity of \(v_{f} = 0\; {\rm m\cdot s^{-1}}\).

Since air resistance is negligible, the acceleration on the baseball will be constantly \(a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})\).

Let \(v_{i}\) denote the initial velocity of this baseball. The SUVAT equation \(v_{f} = v_{i} + a\, t\) relates these quantities. Rearrange this equation and solve for initial velocity \(v_{i}\):

\(\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}\).

The displacement of an object is the change in the position. Let \(x\) denote the displacement of the baseball when its velocity changed from \(v_{i} = 0\; {\rm m\cdot s^{-1}}\) (at starting point) to \(v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}\) (at max height) in \(t = 3.125\; {\rm s}\). Apply the equation \(x = (1/2)\, (v_{i} + v_{t}) \, t\) to find the displacement of this baseball:

\(\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}\).

In other words, the position of the baseball changed by approximately \(47.9\; {\rm m}\) from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately \(47.9\; {\rm m}\!\).

A new band sensation is playing a concert and recording it for a live album to be released this summer. The band asks the sound mixer if he can autotune
the singer who has a habit of singing slightly lower than the note.
What would the mixer need to do to the sound wave? How would it affect the characteristics of the wave?

Answers

The sound mixer will need to increase the amplitude of the sound wave produced by the singer which will increase the loudness of the sound.

Amplitude of sound wave

The amplitude of a sound wave is the maximum vertical displacement of the sound wave.

The sound mixer will need to increase the amplitude of the sound wave produced by the singer.

The increase in the amplitude of the sound wave produced by the lower tune singer will result in increased loudness of the sound.

Thus, the sound mixer will need to increase the amplitude of the sound wave produced by the singer which will increase the loudness of the sound.

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When a low-pressure gas of hydrogen atoms is placed in a tube and a large voltage is applied to the end of the tube, the alors will emit electromagnetic radiation and visible light can be observed. If this light passes through a diffraction grating, the resulting spectrum appears as a pattern of four isolated, sharp parallel lines, called spectral lines. Each spectral line corresponds lo one specific wavelength that is present in the light emitted by the source. Such a discrete spectrum is referred to as a line spectrum
By the early 19th century, it was found that discrete spectra were produced by every chemical element in its gaseous slale. Even though these spectra were found to share the common feature of appearing as a set of isolated lines, it was observed that each element produces its own unique pattern of lines. This indicated that the light emitted by each element contains a specific set of wavelengths that is characteristic of that element.
part A What is the wavelength of the line corresponding to n =4 in the Balmer series? Express your answer in nanometers to three significant figures.
Part B What is the wavelength of the line corresponding to t=5 in the Balmer series? Express your answer in nanometers to three significant figures.

Answers

Answer:

A)  λ = 4.88 10² nm,  B)   λ = 4.08 10² nm

Explanation:

The spectrum of hydrogen is correctly explained by the Bohr model, where the energy of each level is

          Eₙ = -13.606 /n²       [eV]

the transition generally occurs from a given level to a lower state nf <no, so a transition is

          ΔE = E_f -Eₙ = -13,606 ( \(\frac{1}{n_f^2} - \frac{1}{n_o^2}\) )

to find the wavelength let's use the planck relation

          ΔE = h f

the speed of light is

          c = λ f

we substitute

          ΔE = h c /λ

          λ = \(\frac{h \ c}{ \Delta \lambda}\)

       

let's apply this equation to our case

the Balmer series has as final state the level n_f = 2

A) initial state n₀ = 4, final state n_f = 2

         ΔE = -13.606 ( \(\frac{1}{2^2} - \frac{1}{4^2}\) )

         ΔE = 2.55 eV

let's reduce to SI units

         ΔE = 2.55 eV (1.6 10⁻¹⁹ J / 1 eV) = 4.08 10⁻¹⁹ J

     

we calculate

         λ = 6.63 10⁻³⁴ 3 10⁸ / 4.08 10⁻¹⁹

         λ = 4.875 10⁻⁻⁷ m

we reduce to nm

         λ = 4.875 10⁻⁷ m (10⁹ nm / 1m)

         λ = 487.5 nm

we reduce to three significant figures

         λ = 4.88 10² nm

B) initial state n₀ = 5

          ΔE = -13,606 ( \(\frac{1}{2^2} - \frac{1}{5^2}\) )

          ΔE = 2,857 eV

we repeat the process of the previous point

         ΔE= 2,857 1.6 10⁺¹⁹ = 4.286 10⁻¹⁹J

we look for the wavelength

           λ = 6.63 10⁻³⁴ 3 10⁸ / 4.88 10⁻¹⁹

           λ = 4.0758 10⁻⁷ m

we reduce to nm

           λ = 4.0758 10² nm

ignificant numbers

           λ = 4.08 10² nm

..
David rides his bike with a
constant speed of 10 km/h.
How far can he travel in 1 1/2
hours?
T

Answers

im not sure i wanna say 2 miles

a race car goes around a circular track of radius 150 m at speed of 10.0 m/s. How long does it take to complete one lap?

Answers

Answer:

94.25 seconds

Explanation:

Solve for period (T) using: v=(2*pi*r)/T

rearrange: vT=2*pi*r

rearrange: T=(2*pi*r)/v

Plug in values.

T=(2*pi*150)/10

T=94.25 seconds

If a race car goes around a circular track of a radius of 150 m at speed of 10.0 m/s ,then the time taken to complete the one lap would be 94.25 seconds.

What is speed?

The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.

As given in the problem a race car goes around a circular track of radius 150 m at speed of 10.0 m/s.

vT = 2 × π × r

T = (2 × π × r)/ v

T = (2 × π× 150)/10

T = 94.25 seconds

Thus, the time taken to complete the one lap would be 94.25 seconds.

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Can someone please explain why the answer to this net torque question is +115 Nm

Can someone please explain why the answer to this net torque question is +115 Nm

Answers

Answer:

Net torque in positive direction:

Fz = -450 * cos 30 deg * 1.5 = -585 N-M

Fz = 200 * 3.5 = 700 N-M

Net F = 115 N-M

Torque is generally defined as L = R X F

X cross Y = Z     normal coordinate system

Note that Z will be out of the page giving the positive value for the torque.

a car is moving eastward and speeding up The momentum of the car is

Answers

There is no change in an object's momentum because momentum is still a conserved quantity. Direct correlation exists between an object's momentum and speed.

In real life, what is momentum?

The definition of momentum is pretty much any motion-related activity. In physics, it is a fundamental idea. Momentum is a term frequently used in sports. For instance, if a team is moving and needs to be stopped, it has momentum and will need some work.

Why does momentum differ from motivation?

Motivation is the feeling that propels you into the uncertainty of making a change by ejecting you from the security of passivity. Your forward motion is sustained by momentum. Though it is an emotion, motivation.

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An electron enters a magnetic field of with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path

Answers

Answer:

A) 2.1 × 1010 Hz

Explanation:

I think this is the answer you're looking for but it may change depending on mass and charge of electron. Hope this helps :)

While passing a slower car on the highway, you accelerate uniformly from 20.1 m/s to 33.2 m/s in a time of 10.6 s. How far do you travel during this time?

Answers

Answer:

282 m

Explanation:

Given:

v₀ = 20.1 m/s

v = 33.2 m/s

t = 10.6 s

Find: Δx

Δx = ½ (v + v₀) t

Δx = ½ (33.2 m/s + 20.1 m/s) (10.6 s)

Δx ≈ 282 m

There are 9,000 houses in Elizabeth's town. Last summer, 7,020 of the houses were for sale. What percentage of the houses in the town were for sale last summer?

Answers

78% of the houses in Elizabeth's town were for sale last summer.

To find the percentage of houses that were for sale last summer in Elizabeth's town, we need to divide the number of houses for sale by the total number of houses and then multiply by 100.

The total number of houses in Elizabeth's town is given as 9,000. Last summer, 7,020 houses were for sale. To calculate the percentage, we divide 7,020 by 9,000:

Percentage = (7,020 / 9,000) * 100

Simplifying the calculation:

Percentage = 0.780 * 100

Percentage = 78.0%

To explain further, we take the number of houses for sale (7,020) and divide it by the total number of houses (9,000) to get the ratio of houses for sale to the total. Multiplying this ratio by 100 gives us the percentage. In this case, 78.0% indicates that a significant portion of the houses in Elizabeth's town were available for sale during the summer.

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A student walks downstairs to class. Which statement correctly describes the types of energy the student has at the top of the stairs and as she walks down the
stairs?
A kinetic energy at the top of the stairs, kinetic energy as she walks down
B. potential energy at the top of the stairs, potential energy as she walks down
OC kinetic energy at the top of the stairs, potential energy as she walks down
OD potential energy at the top of the stairs, kinetic energy as she walks down

Answers

Answer:

D potential energy at the top of the stairs, kinetic energy as she walks down

Explanation:

The potential energy of a body is the energy due to the position of the body.

At the top of the stair case, the student is at a significant height.

Kinetic energy is the energy due to the motion of the body.

As the student descends, the potential energy is changed to kinetic energy.

 To find the potential energy;

          P.E  = mgH

 m is the mass

 g is the acceleration due to gravity

 H is the height of the body

 To find the kinetic energy;

         K.E  = \(\frac{1}{2}\) m v²

   m is the mass

   v is the velocity

A uniform rod with a mass of m = 1.94 kg and a length of l = 2.10 m is attached to a horizontal surface with a hi=nge. The rod can rotate without friction. (See figure.)
Initially the rod is held at rest at an angle of Θ = 70.4 with respect to the horizontal surface. Then the rod is released.
What is the angular speed of the rod, when it lands on the horizontal surface?

What is the angular acceleration of the rod, just before it touches the horizontal surface?

A uniform rod with a mass of m = 1.94 kg and a length of l = 2.10 m is attached to a horizontal surface

Answers

(a) The angular speed of the rod, when it lands on the horizontal surface is 1.61 rad/s.

(b) The the angular acceleration of the rod, just before it touches the horizontal surface is 1.06 rad/s² .

Angular acceleration of the rod

The angular acceleration of the rod is calculated as follows;

Apply the principle of conservation of angular momentum;

τ = Iα

where;

τ is torqueI is moment of inertial of the rodα is the angular acceleration

τ = Fr = mg(L/2) cosθ

I = mL²/3

mg(L/2) cosθ =  mL²/3(α)

g(1/2) cosθ =  L/3(α)

(³/₂)g cosθ  = L(α)

(³/₂ L)g cosθ  = α

1.5Lg cosθ  = α

1.5(2.1) cos (70.4) = α

1.06 rad/s² = α

Angular speed of the rod

ωf² = ω₁² + 2αθ

ωf² = 0 + 2(1.06)(70.4π/180)

ωf² = 2.605

ωf = √2.605

ωf = 1.61 rad/s

Thus, the angular speed of the rod, when it lands on the horizontal surface is 1.61 rad/s.

The the angular acceleration of the rod, just before it touches the horizontal surface is 1.06 rad/s² .

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The beam is constructed from four pieces of wood, glued together as shown. If M = 10 kip ft, determine the maximum bending stress in the beam. Sketch a three-dimensional view of the stress distribution acting over the cross section.

Answers

The maximum bending stress in the beam is 1.46 ksi.

What is bending stress?

All of the sections of a beam will experience a bending moment when it is loaded externally.

The internal stresses in the beam fight against the bending that the bending moment at a section tends to cause in the beam.

Bending stress is the term used to describe the resistance provided by internal stresses to bending.

In other words, bending stresses are the internal resistance to an external force that bends a member.

The symbol for it is.

N/mm2 will serve as its unit.

\($ I =\frac{1}{12}^{b'h'3} - \frac{1}{12}^{bh3}\)

\($ I = \frac{1}{12} \times 8 \times 10^3 - \frac{1}{12} \times 6 \times 8^3\)

I = 410.667 inch

Depth of neutral axis

d = 10/2 = 5 inch

Maximum bending stress (σmax) = md/I

σmax = md/I

          \($ =\frac{ (10 \times 12)\times 5}{410.667}\)

          = 1.46 ksi

Thus, the maximum bending stress in the beam is 1.46 ksi.

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The beam is constructed from four pieces of wood, glued together as shown. If M = 10 kip ft, determine

Which force requires contact?

A.
The force of attraction between two masses

B.
The force exerted by air as an object moves through it

C.
The force produced by interactions between electrically charged objects

D.
The force produced by interactions between magnetic objects

Answers

Answer:

the force produced between magnetic objects

Answer:D: The force produced by interactions between magnetic objects

Explanation:

Write a hypothesis about how the mass of the cylinder affects the temperature of the water. Use the "if . . . then . . . because . . .” format and be sure to answer the lesson question: "How is potential energy converted to thermal energy in a system?”

Answers

Hypothesis, If the mass of the cylinder increases, then the temperature of the water will also increase because an increase in mass leads to greater potential energy, which is converted to thermal energy in the system.

According to the principle of conservation of energy, energy cannot be created or destroyed but can be transformed from one form to another. In this case, potential energy from the mass of the cylinder can be converted into thermal energy in the system. When the cylinder is lifted and submerged in the water, it possesses gravitational potential energy due to its elevated position.

As the cylinder is released and descends into the water, this potential energy is converted into kinetic energy, causing the water molecules to move and collide with higher energy. These collisions generate heat and increase the overall temperature of the water. By increasing the mass of the cylinder, more potential energy is stored.

As a result, there is a greater amount of energy available to be converted into thermal energy when the cylinder is released into the water. Thus, the temperature of the water is expected to increase as the mass of the cylinder increases.

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choose inertial frames. check all that apply. choose inertial frames.check all that apply. a carousel rotates at a constant speed. a vertically tossed ball is at the highest point of its trajectory. a plane moves at a constant speed of 254 m/s . at the instant the traffic light turns green, a bus starts from rest

Answers

The highest point in a ball's trajectory is when it is thrown vertically. The average speed of a plane is 254 m/s/s. A carousel rotates continuously.

What is the unit for speed?

seconds per metre Miles per hour (mph), kilometres per hour (km/h), and metres per second (m/s) are the three most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed equals distance x time is the speed equation.

Who defined speed?

Galileo Galilei, an Italian physicist, is typically attributed with being the first to quantify speed by taking into account the distance travelled and the time required. Galileo defined speed as the amount of distance travelled in a given amount of time.

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41
Adam is pushing his box of baseball
equipment with a force of 10 N and
the box is pushing back towards
Adam with a force of 6 N. What is the
total net force? What will happen to the motion of
the box? Explain.
The Magnolia loh
deneaker notes

41Adam is pushing his box of baseballequipment with a force of 10 N andthe box is pushing back towardsAdam

Answers

Answer:

16

Explanation:

6+10=16

the box will go forward but it will be a little harder.


What amount of force is required to accelerate a 1,264 kg car at a rate of 13 m/s²?
(Round you answer to the nearest whole number. Do not use units or decimals in your answer.)

Answers

16432 N force is required  to accelerate a 1,264 kg car at a rate of 13 m/s²

What is force?

Force is an external agent that may change the condition of rest or motion of a body. It has a magnitude as well as a direction. The direction of the force is the place where force is applied, and the application of force is the location where force is applied. Newton (N) is the SI unit of force.

Given that,

Mass of the car (m) = 1264 kg

Acceleration (a) = 13 m/s²

Now calculate how much force (F) is required,

F = m × a

F = 1264 × 13 kg m/s²

F = 16432 N

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How do I measure the drag of a paper airplane?

Answers

Answer:

hmmmmm ill get back later

Explanation:

Select ALL of the factors that influence the gravitational potential energy of an object.
movement
height
mass
compression

Answers

Answer:

I think it is movement height and mass.  Let me know if I am wrong.

Explanation:

The factors affecting the gravitation potential energy of an object are given as follows,

The mass of the object .

The height attained by the object.

What is mechanical energy?

Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.

ME= PE+KE

As given in the problem we have to select all of the factors that influence the gravitational potential energy of an object,

The gravitational potential energy acquired by any object is given by the expression,

PE = mgh

where m is the mass, g is the gravity and h is the height

Thus, the gravitational potential energy depends upon the mass of the object as well as the height attained by the object.

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Please help me with the attached image.

Please help me with the attached image.

Answers

a. The two cars are moving at the same speed at t = 3.88 seconds.

b. The two autos are moving at a speed of 4.18 cm/s at that moment.

c. The cars pass each other at time t = 1.05 s and t = 2.54 s, respectively.

d. At t = 1.05 seconds, the first car is located at 12.15 cm, and the second car is located at 16.55 cm. At t = 2.54 seconds, the first car is located at 10.69 cm, and the second car is located at 17.39 cm.

What is the speed of the two cars?

The speed of the cars is derived using the formula for linear velocity.

The velocity of the first car is calculated as follows:

v = v₀ + at

where;

v₀ is the initial velocity,a is the acceleration, andt is the time elapsed.

The velocity of the second car can be calculated as:

v = v₀

where;

v₀ is the initial velocity since there is no acceleration.

We equate the two velocities of the two cars and solve for time:

-4.40 + 2.70t = 6.10

2.70t = 10.50

t = 3.88 seconds

b. To find the speeds of the cars at time t, we can substitute t = 3.88 seconds in the velocity equation for the first car:

For the first car:

v = -4.40 + 2.70 * 3.88

v = 4.18 cm/s

c. Solving for the time when the positions of the cars are equal allows us to determine when they pass one another.

The position of the first car will be:

x = x₀ + v₀t + 1/2 at²

where x₀ is the initial position.

The position of the second car will be:

x = x₀ + v₀t

equating the two positions equal and solving for time:

13.5 - 4.40t + 1/2 * 2.70t² = 10.5 + 6.10t

1.35t² + 1.70t + 3.00 = 0

Solving the quadratic equation, we get two times:

t = 1.05 s and t = 2.54 s

d. We can re-insert the time values into the position equation for each car to determine where the automobiles were at the times indicated in (c).

For t = 1.05 seconds:

First car:

x = 13.5 - 4.40 * 1.05 + 1/2 * 2.70 * 1.05²

x = 12.15 cm

Second car:

x = 10.5 + 6.10 * 1.05

x = 16.55 cm

For t = 2.54 seconds:

First car:

x = 13.5 - 4.40 * 2.54 + 1/2 * 2.70 * 2.54²

x = 10.69 cm

Second car:

x = 10.5 + 6.10 * 2.54

x = 17.39 cm

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an object with an initial velocity of 5m/s has a constant acceleration of 2m/s2 when it is speed is 15m/s how far has us travelled​

Answers

An object with an initial velocity of 5m/s has a constant acceleration of \(2m/s^2\) .The object has traveled a distance of 50 meters when it is speed is 15m/s how far has us travelled​

To find the distance traveled by the object, we can use the equation:

\(v^2 = u^2 + 2as\)

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.

Given:

Initial velocity (u) = 5 m/s

Acceleration (a) = 2\(m/s^2\)

Final velocity (v) = 15 m/s

We need to solve for s.

Rearranging the equation, we have:

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

Substituting the given values, we get:

s = \((15^2 - 5^2)\)/ (2 * 2)

s = (225 - 25) / 4

s = 200 / 4

s = 50 m

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