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## For a mass hanging from a spring, the maximum displacement the spring is stretched or compressed from its equilibrium position is the system’s a. amplitude. c. frequency. b. period. d. acceleration

For a mass hanging from a spring, the maximum displacement the spring is stretched or compressed from its equilibrium position is the system’s a. amplitude. c. frequency. b. period. d. acceleration

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## A student used a yardstick to model the displacement of rock at a fault during an earthquake. The student bent the yardstick without breaking it and then let it go. What process did the student show? A. A moment magnitude vibration B. Elastic rebound C. Isostasy D. The formation of a new fault

I think the correct answer would be B. The process of elastic rebound is being shown by the student. It is a theory that is used to explain earthquakes. It focuses on how energy is being spread in times of earthquakes. As the rocks on the fault experiences shift and force, these rocks would be accumulating energy causing it to deform reaching the internal strength and eventually exceeding it. At that moment, a rapid motion would happen along the fault, which releases the energy, then the rocks would go back to its original shape or the undeformed state. This theory is the first theory that sufficiently was able to explain earthquakes.

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## If you travel 40 miles east and then turn around and drive 12 miles west, the displacement is?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## A boat moves 60 kilometers east from point A to point B. There, it reverses direction and travels another 45 kilometers toward point A. What are the total distance and total displacement of the boat?

The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

Categories

## The table below represents the displacement of a horse from its barn as a function of time: Time(hours) x. 0 1 2 3 4 Displacement from barn (feet) y 8 58 108 158 208 part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?

The polinomials only can have positive whole exponents, that is: 1, 2, 3, 4, 5, 6, … (you can include 0 also, because it iis the independent term).

So, if you are told that one term of the polynomial is 9 x ^ (negative something), it is necessary that the number after the negative sign be negative, given that negative times negative is positive.

Therefore, the only possible option from the answer choices is the option 3) -9.

Categories

## The table below represents the displacement of a horse from its barn as a function of time: Time(hours) x. 0 1 2 3 4 Displacement from barn (feet) y 8 58 108 158 208 part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn? PLEASE HELP!! WILL RATE BRAINLIEST!!

A. The
y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the
given table,

y – intercept
= 8

Since at
time zero the displacement is 8 ft, this means that the horse was already
outside the barn initially.

B. The
average rate of change of the function represents the slope of the linear
equation (m). This can be calculated using the formula:

average rate
of change = m = (y2 – y1) / (x2 – x1)

m = (158 –
58) / (3 – 1)

m = 50

C.  Since we have determine the y-intercept and
the slope, we can formulate the linear equation:

y = m x + b

y = 50 x + 8

The domain
is the value of x. When y = 508, x is equivalent to

508 = 50 x +
8

x = 10 hrs

Categories

## A motorist drives along a straight road at a constant speed of 15.0 m/s. Just as she passes a parked motorcycle police offi cer, the offi cer starts to accelerate at 2.00 m/s2 to overtake her. Assuming that the offi cer maintains this acceleration, (a) determine the time interval required for the police offi cer to reach the motorist. Find (b) the speed and (c) the total displacement of the offi cer as he overtakes the motorist.

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

Categories

## Let theta denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the Bob is m, then the tension in string is

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

Categories

## An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 degrees north of west, then 50 steps due south.Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut. …?

Setting the coordinate system: positive x points to the east and positive y points to the north. This can be solved by vector addition.

A = <40cos(45), 40sin(45)>
B = <-60cos(60), 60sin(60)>
C = <0, -50>

R = A + B + C = <-1.72, 80.25>

The displacement that needs to return him is by the vector -R.

Therefore, <1.72, -80.25>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

## Related Questions

Posted in Mathematics

Match the inequality to the graph of its solution. a. n/4 ≤ -1 b. -10 ≥ -100 c. 5x ≥ 20

Part (a):
The given inequality is:
n/4 ≤ -1
we need to isolate the n on one side of the inequality. To do this, we will multiply both sides by 4 as follows:
n/4 x 4 ≤ -1 x 4
The inequality now is:
n ≤ -4
The correct graph representing this is graph (b)

Part (b):
The given inequality is:

-10 ≥ -100
So, we will just search for the graph the shows that -10 is greater than the -100
The correct graph representing this is graph (a)

Part (c):
The given inequality is:

5x ≥ 20
we need to isolate the x on one side of the inequality. To do this, we will divide both sides by 5 as follows:
5x/5 ≥ 20/5
The inequality now is:
x ≥ 4
The correct graph representing this is graph (c)

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Posted in Mathematics

Find angle A if mDE is equal to 53° and mBC is equal to 8°

So here is how we are going to answer this:
Remember that if two secants intersect in the exterior of a circle,
then the measure of the angle formed is one half the difference
of the measures of the intercepted arcs. So, our equation would be A = (1/2)(mDE-mBC). Now let us plug in the values.
A= 1/2(53-8)
a= 1/2(45)
A = 22.5
Therefore, the measure of angle A is 22.5 degrees.
Hope this is the answer that you are looking for.

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Posted in Mathematics

A sailboat race course consists of four legs, defined by the displacement vectors A, B, C, and D as the drawing indicates. The magnitudes of the first three vectors are A=6.4 km , B=5.10 km, and C=4.80 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find the distance of the fourth leg and the angle theta.

The first step is to solve the horizontal component using the given values from the problem and the illustration,
horizontal component = 6.4sin(40°) + 5.1sin(35°) – 4.8sin(23°)Then the vertical component is determined,
vertical component = 6.4cos(40°) – 5.1cos(35°) – 4.8cos(23°)

The distance of the fourth leg is calculated using the Pythagorean Theorem,
distance = (h²+v²)^1/2 = 6.35 km

Finally, the angle is computed by applying the inverse tangent function,
theta = tan^-1(v/-h) = 54.42°

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Posted in Mathematics

If the roots of the equation (a2+b2)x2-2(ac+bd)x+(c2+d2)=0 are equal, prove that a/b=c/d …?

Roots are real only when the discriminant d is positive or 0.

Since d = -4(ad – bc)^2, then roots are real only when ad – bc = 0, ie, ad = bc.

Now, using the quadratic formula we get just one root = -(ac + bd)/(a^2 + b^2).

—————————————…

You can also check:

(x + (ac + bd)/(a^2 + b^2))^2 = x^2 + 2(ac + bd)/(a^2 + b^2)x + (ac + bd)^2/(a^2 + b^2)^2 and note

(ac + bd)^2 = a^2c^2 + 2abcd + b^2d^2 = a^2c^2 + abcd + abcd + b^2d^2 = a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2 = (a^2 + b^2)(c^2 + d^2).

So x^2 + 2(ac + bd)/(a^2 + b^2)x + (ac + bd)^2/(a^2 + b^2)^2 = x^2 + 2(ac + bd)/(a^2 + b^2)x + (c^2 + d^2)/(a^2 + b^2)

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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Posted in Mathematics

A function takes in values of the ____________________ variable, called inputs, and gives back values of the ____________________ variable, called outputs. A function takes in values of the ____________________ variable, called inputs, and gives back values of the ____________________ variable, called outputs.

The answers the would best complete the given statement above would be independent and dependent, respectively. Here is the complete statement. A function takes in values of the independent variable, called inputs, and gives back values of the dependent variable, called outputs. Hope this answer helps.

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#### Literature

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#### Finance

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#### Law

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#### Nursing

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#### Sociology

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## A girl delivering newspapers covers her route by traveling 2.00 blocks west, 3.00 blocks north, and then 7.00 blocks east. (a) What is her resultant displacement? ____blocks at ____° north of east (b) What is the total distance she travels? ____blocks …?

She travels 2+3+7 blocks for a total of 12 blocks  (B part)
So she travels √(5^2+3^2) = √34 blocks part(A)

## Related Questions

Posted in Physics

The train accelerates from 30 km/h to 45 km/h in 15 secs. a. find its acceleration. b. distance it travels during this time …?

(a) The acceleration is,

(b) Distance it travels during this time is, 156.225 m

Solution for part (a) :

Formula used :

where,

a = acceleration

v = final velocity =

u = initial velocity =

t = time = 15 s

Now put all the given values in the above formula, we get

Therefore, the acceleration is,

Solution for part (b) :

Formula used :

where,

s = distance traveled

Now put all the given values in this formula, we get

Therefore, the distance it travels during this time is, 156.225 m

Posted in Physics

Is it possible to travel a great distance without any displacement? Prove your answer.

Explanation: The definition of displacement is the change on the position, So if i start in my home, then i go to the mall, and after that i return home, the total displacement over that period of time is 0, because i started in my house and ended in my house. But in that proces i traveled the distance between my house and the mall two times. So is possible to travel great distances without any displacement, only if the endpoint of the travel is the same as the start point.

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Posted in Physics

a uniform rope of length l is pulled by a constant force F.what is the tension in the rope at a distance l from the end, where it is applied? …?

Imagine the rope tied to a hook on the ceiling. And then attach a weight to the rope. You have your situation exactly as described. The tension is equal all along the rope and will be the amount of the weight of the rope plus the weight of your load. You may ignore the weight of the rope if it is small compared to the load. If you are considering a horizontal suspension then the result is still the same at any point on the rope. The rope conforms to a curve known as a Catenary. Which is a class of curves that are all hyperbolic. If you have the formula for the curve you can figure out the forces. and they will all be uniform along the suspending cable. Look up Catenary

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Posted in Physics

Present at least one example that illustrates acceleration. Is this a scalar or vector quantity? Explain why. …?

Vector

Explanation:

Acceleration is defined as the rate of change of velocity. As velocity is a vector quantity, so acceleration is also a vector quantity.

If a car starts from rest and attains some velocity after some time, then car is accelerating and the firection of acceleration is same as the direction of velocity.

If a car is moving and after applying the brakes it come to rest it means the motion of car has negative acceleration which means the direction of velocity and the direction of acceleration is opposite to each other.

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Posted in Physics

A rock dropped from a cliff covers one-third of its total distance to the ground in the last second of its fall. Air resistance is negligible. How high is the cliff?

So lets say that the total height the object falls from is expressed as:
h = 0.5gt₁²———->(1)

Here, t₁ represents the TOTAL time the object takes to fall through h.
Now the distance it falls through from rest until it has 1.00s to fall is:

h – 0.33h = 0.5gt₂²
0.667h = 0.5gt₂²———–>(2)
Now that we know that it takes 1.00s to fall part of h, we can express it as:
t₁ – t₂ = 1.00s
t₂ = t₁ – 1.00s——>(3)

We can eliminate t₂ by subbing (1) and (3) into (2):
0.667(0.5gt₁²) = 0.5g(t₁ – 1.00s)²
0.3335gt₁² = 0.5gt₁² – gt₁+ 0.5g

This is a quadratic equation, in standard form:
0.1665gt₁² – gt₁+ 0.5g = 0
0.1665(-9.80m/s²)t₁² – (-9.80m/s²)t₁+ 0.5(-9.80m/s²) = 0
(-1.6317m/s²)t₁² + (9.80m/s²)t₁- 4.90m/s² = 0
t₁ = -b ± √[b² – 4ac] / 2a
= -(9.80) ±√[(9.80)² – 4(-1.6317)(-4.90)] / 2(-1.6317)
t₁ = 0.55s or t₁ = 5.456s

Lets plug them both individually into (3) and if one value for t₂is negative, choose the other:
t₂ = t₁ – 1.00s
= 0.55s – 1.00s
= -0.45s

So:
t₂= 5.456s – 1.00s
= 4.46s

The distance fallen is easy, as you only need put the total time t₁ into (1):

h = 0.5gt₁²
= 0.5(9.80m/s²)(4.46s)²
= 97.5m

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#### Sociology

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## A reaction that absorbs heat from the surroundings is known as a(n) A) exothermic reaction. B) endothermic reaction. C) displacement reaction. D) decomposition reaction

What we’re looking for here is the gas sample’s molar mass given its mass, pressure, volume, and temperature. Recalling the gas law, we have

or

where R is 0.08206 L atm / mol K, P is the given pressure, T is the temperature, and V is the volume.

Before applying the values given, it is important to make sure that they are to be converted to have consistent units with that of R.
Thus, we have

P = 736/ 729 = 0.968 atm
T = 28 + 273.15 = 301.15 K
V = 250/1000 = 0.250 L

Now, applying these converted values into the gas law, we have

Given that the mass of the sample is 0.430 g, we have

Thus, the gas sample has a molar mass of 43.9 g/mol.