Interpreting Graphics
6. Figure 1.9 shows position-time graphs of the straight-line movement of
two brown bears in a wildlife preserve. Which bear has the greater aver-
age velocity over the entire period? Which bear has the greater velocity
at t = 8.0 min? Is the velocity of bear A always positive? Is the velocity of
bear B ever negative?

The calculated angle is 305° and if v=a,b is the position vector, then |v|=a²+b² is the calculated magnitude.

If v=a,b is the position vector, then |v|=a²+b² will give the magnitude. Depending on the application, the direction is equal to the angle made with the x-axis or the y-axis. The formula tan=(ba)=tan1 determines the direction of a position vector (ba), We may say that the vector must be inclined in the fourth quadrant in this case because the vector's x and y components are both positive.

Consequently, the angle must be greater than 270 degrees and less than 360 degrees.

Now, in order to determine the value, we can say that

tanθ=opposite side/adjacent side

=8.6/6.1

=tan⁻¹1.41

=54.65, which indicates that it is inclined at an angle above with the X axis in the fourth quadrant (360-54.65 = 305.6°).

Consequently, the proper response will be 305° degrees if the angle is measured counterclockwise.

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The maximum speed at which a car could go around this curve without slipping is6.12m/s

To solve this it is necessary to take concepts related to Centripetal Force and Friction Force.

In the case of the centripetal force,

Fc = mv²/r      ....1

Where,

m=mass

v= velocity

r= Radius

In the case of the Force of Friction we have to,

F= [tex]\mu[/tex]mg      ......1.

Where,

[tex]\mu[/tex] = Friction Constant

m= mass

g= gravity

the centripetal equal to the friction force to stay on the road, in this way

mv²/r  = [tex]\mu[/tex]mg      

v² = mgr

v = √([tex]\mu[/tex]gr)

The coefficient of friction between the cars' tires and the track

 [tex]\mu[/tex] = 0.50

radius = 800m

g = 9.8 m/s²

using above values we get

v = [tex]\sqrt[]{800*9.8*0.5}[/tex]

V = 6.12m/s

The maximum speed at which a car could go around this curve without slipping is6.12m/s

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According to the given question, mBg- mAg = a(mA + mB)  is the equation that will be used to determine acceleration.  

The gravitational constant, represented by the capital G, is an empirical physical constant used in the calculation of gravitational effects in both Albert Einstein's theory of general relativity and Sir Isaac Newton's law of universal gravitation.

It is the proportionality constant in Newton's law that links the gravitational force between two bodies to the sum of their respective masses and the square root of their distance. It quantifies the relationship between the energy-momentum tensor and the spacetime geometry in the Einstein field equations.

The measured value of the constant is known to four significant digits with some certainty. Its value is approximately 6.674×10−11 m3⋅kg−1⋅s−2 in SI units.

Given in the qusetion

T -  WA = mAa         --------------1

WB - T = mBa            --------------2

We know that, WA = mAg and WB = mBg

T = mAa + WA

T = mAa + mAg           --------------3

Similarly, T = WB - mBa

T = mBg- mBa            --------------4

From equation 3 and 4

mAa + mAg = mBg- mBa

mAa + mBa = mBg- mAg

a(mA + mB) =  mBg- mAg

So, mBg- mAg = a(mA + mB)  is the equation that will be used to determine the acceleration.  

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Your question is incomplete. Please check the full content below.
The Universal Gravitational constant converts the ratio of mass and distance to Newton

gives the mass and distance a value

converts the ratio of mass and distance to kilograms

gives the mass and value a direction

The following equations are for two connected objects in the axis of motion

T-WA=mAa

WB-T=mBa

Which of the following equations would be used to determine the acceleration

T+mBg-mAg=(mA+mB)a

-T+mBg-mAg=(mA+mB)a

mBg-mAg=(mA+mB)a

mBg-mAg=mAa

The length of the skid marks is 136m.

Speed is the time charge at which an object is moving alongside a path, whilst pace is the price and direction of an item's movement. The rate of change of role of an item in any route. speed is measured because of the ratio of distance to the time in which the space changed into included.

calculation,

mass of car = 1900kg

speed = 14 m/s

F = ma

a = F(friction) / m

F(friction) = mu F(normal)

F(friction) = mu g m

a = mu g m / m

a = mu g

a = 0.6 * 9.81m/s²

a = 5.886 m/s²

v² = 2 a x

x = v² / 2 a

x = (40m/s)²/ 2 * 5.886m/s²

x = 136m

Speed is a way of measuring how quickly something is shifting or being executed, or something moving rapidly. Speed is described because of the charge of trade of distance with time. It has the dimension of distance by time. therefore, the SI unit of pace is given as the aggregate of the simple unit of distance and the primary unit of Time. for this reason, the SI unit of velocity is a meter in step 2d. the rate of a body is converting with appreciation to time it's far shifting with a non-uniform velocity.

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Soil erosion is the wearing down of soil. The trend that the map shows is that soil erosion rates vary across the united states.

Hence, option (D) is correct.

What is Soil Erosion?

As shown on the map, soil erosion vary across the United States.

Therefore, option (D) is correct.

Soil erosion is a slow method that happens while the impact of water or wind detaches and gets rid of soil particles, inflicting the soil to go to pot. Soil deterioration and low water excellent because of erosion and surface runoff have turn out to be intense troubles international.

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Answer:

t = 10/9.81 = 1.02s

Explanation:

the ball will be up in the air for 1.02 seconds

Option D. continental shelf

Continental shelf is a part of a continent that is submerged under an area of ​​relatively shallow water known as a shelf sea.

It is given in the question, that the shelf of undersea land reaches 200 meters and it also extends out from the shoreline. This condition is only possible when a structure is submerged, and such submerged region can only be called as continental shelf.

On the other hand guyots is a underwater volcanic mountain and deep-sea trenches are the the long narrow lowerings in the ocean floor with the depth upto 6000 meters. And abyssal plains are the underwater ocean floors which cannot be found at the depth of 200 meters.

Therefore continental shelf is used to described as a shelf of undersea land reaching a depth of about 200 meters (656 feet) and extending out from the shoreline.

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Answer:

[tex]1.0*10^{-5} N[/tex]

Explanation:

To answer this question we can use the formula: [tex]P=\frac{F}{A}[/tex]

Pressure (Pascals) = Force (Newtons) divided by Area (Square Meters)

We are given pressure and area in the question and are trying to find force so we can rearrange the equation to suit our needs by multiplying both sides by Area:

[tex]P(A) = \frac{F}{A} (A)\\ \\F =PA[/tex]

The next step is to ensure all given information is in the correct units. Because we are given pressure in the units [tex]N/m^{2}[/tex], we need to convert 0.0025[tex]cm^{2}[/tex] into [tex]m^{2}[/tex].

There are 10,000 [tex]cm^{2}[/tex] in 1 [tex]m^{2}[/tex], therefore to convert between them, we need to divide 0.0025 by 10,000.

[tex]0.0025/10000 = 0.00000025m^{2}[/tex]

OR [tex]2.5*10^{-7} m^{2}[/tex]

Now we just need to multiply them together to get force:

[tex]F=PA\\F=40*2.5*10^{-7}\\F=1.0*10^{-5} N[/tex]

Hope this helped!

The magnitude of the change in velocity is determined as 408.94 km/h.

The change in direction of the velocity is 64.4⁰ north of west.

The magnitude of the average acceleration during the trip is 0.0105 m/s².

The magnitude of change in velocity is the resultant velocity of the plane.

v² = a² + b² - 2ab cosθ

where;

v² = (192²) + (250²) - 2(192 x 250) cos(135)

v² = 167,236

v = √167,236

v = 408.94 km/h

vyi = 192 km/h

vy2 = 250 x sin(45) = 176.77 km/h

vy(total) = 192 km/h + 176.77 km/h = 368.77 km/h

vxi = 0

vx2 = - 250 km/h x cos(45) = -176.77 km/h

θ = arc tan (Vy/Vx)

θ = arc tan(368.77 / -176.77)

θ = -64.4 ⁰

θ = 64.4⁰ north of west.

a = v/t

v = 408.94 km/h = 113.6 m/s

h = 3 h = 10,800 seconds

a = (113.6 m/s) / ( 10,800 s)

a = 0.0105 m/s²

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The time has taken the ball to hit the ground is (t)= 5.11 Seconds.

The best example that would help us understand and know what time are the clock and the calendar. This clock gives us the exact hour, minutes and seconds. The calendar tells us the exact day, month and year.

To calculate the time has taken the ball to hit the ground, we are using the formula,

S=ut+(1/2)gt²

Here we are given,

u= The initial velocity of the ball= 0 m/s

g= The acceleration due to gravity is= 9.8 m/s²

S= The height of the cliff = 128m.

We have to calculate the time has taken the ball to hit the ground = t

Now, we put the known values in the above equation we get,

S=ut+(1/2)gt²

Or, 128=0*t+(1/2)*9.8*t²

Or, t= √((2*128)/9.8)

Or, t=5.11 Seconds

Thus from the above calculation we can conclude that, the time has taken the ball to hit the ground is (t)= 5.11 Seconds

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The radius of the disc will be 0.496 meters.

The pace at which an object rotates or revolves around an axis is known as its angular velocity. The Greek letter omega stands for angular velocity. Because it is expressed as an angle per unit of time, angular velocity in the SI is measured in radians per second. [[tex]M^{0}L^{0}T^{-1}[/tex]] is the dimensional formula for angular velocity.

According to the question, the given values are :

Acceleration, a=4.9 m/s² and,

Period of rotation, T=2.0 seconds

So, angular velocity (ω) of disc =2π/T

⇒2π/2

= π rad/sec.

Acceleration= rω²

4.9= r×π²

r=0.496 meters.

Hence, the radius of the disc will be 0.496 meters.

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Answer: Vx= 86.6 m/s & Vy= 50 m/s

Explanation:

Vx= 100*cos30° = 86.6 m/s

Vy= 100*sin30° = 50 m/s

Answer:

Explanation:

We find the difference in speeds between the 2 animals

106 - 75.6 = 29.4 km/h

then we convert it to m/s by dividing it with 3.6

29.4 / 3.6 = 8.2 m/s

distance divided by speed equals time

63.4 / 8.2 = 7.7 seconds

You are traveling up on an elevator to the 95th floor of the Hancock tower. As it nears the 95th floor, your weight appears to be lighter.

Here is an exercise in thought. Consider a container with internally completely reflecting surfaces that is partially filled with light and located at sea level on Earth. The light will be somewhat gravitationally redshifted as it ascends, which will cause it to reflect at the top of the container with a little less momentum. Similar to how it will be blue shifted when travelling downward and give the container's bottom greater momentum. Weight is a quality of something that is subject to gravity. Light is drawn to objects with mass by gravity because it has energy. Since two photons (separate "pieces" of light, in a broad sense) have energy, I imagine they would be attracted to one another gravitationally. However, it would be really little.

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The correct answer is 54.6 min.

Running speed of Ilya and Anya is v_r=7.50 mi/hr

Walking speed of Ilya and Anya is v_w=3.50 mi/hr

Total length of the route is d=5.00 miles.

Total time taken by Anya to cover the distance is

[tex]t_A= d/2/v_r+ d/2/v_w[/tex]

[tex]t_A= d/2v_r + d/2v_w[/tex]

[tex]t_A=d/2 \times1/v_r +1/v_w[/tex]

[tex]t_A= d/2 \times v_r+v_w / v_rv_w[/tex]

[tex]t_A[/tex]= 5.00/2 × 7.50+3.50/7.50 × 3.50 hr

[tex]t_A[/tex]= 5.00/2 × 11/26.25 hr

[tex]t_A[/tex]= 55/52.5 hr

[tex]t_A[/tex]=1.05 hr

Therefore Anya will take 1.05 hr to cover the distance.

Average speed of Anya is

[tex]v_{avg} = d/t_A[/tex]

[tex]v_{avg}[/tex]= 5.00/1.05 mi/hr

[tex]v_{avg}[/tex] = 4.76 mi/hr

Therefore Anya's average speed is 4.76 mi/hr.

If total time taken by Ilya to cover the distance is t , then

([tex]v_r[/tex] × t/2+(v_w × t/2=d))

t/2 × ([tex]v_r+v_w[/tex])=d

t × ([tex]v_r+v_w[/tex])=2d

t = 2d/([tex]v_r+v_w[/tex])

t = 2 × 5.00/7.50+3.50

t = 10/11 hr

t = 0.91 × 60 min

t = 54.6 min

Therefore total time taken by Ilya to cover the distance is 54.6 min.

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Answer:

the size, length, or amount of something, as established by measuring.

A car is traveling due north at 23.6 m>s.

Find the velocity of the car after 7.10 s if its

acceleration is

The acceleration is known to be: a(t) = 1.7 m/s2.

We must integrate over time to obtain the velocity function, and the results are:

v(t) = (1.7m/s^2)

*t + v0

If we suppose that we begin at 23.6 m/s, then the initial velocity is: v0 = 23.6 m/s, where v0 is the beginning velocity.

The velocity formula is then: v(t) = (1.7m/s2).

*t + 23.6 m/s

We now seek to determine the value of t such that v(t) = 27.8 m/s.

Consequently, v(t) = 27.8 m/s = (1.7 m/s2)

*t + 23.6 m/s = (1.7 m/s2) 27.8 m/s - 23.6 m/s

t = 2.5 seconds when *t 4.2 m/s = (1.7 m/s/2)

At such acceleration, 2.5 seconds are required.

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When the length of the pendulum in pendulum clock increases by 0.1 % , then the error in time per day is c) 43.2s

Let the pendulum = L

The time in a day will be: = 60 × 60 × 24

When the length is increased, the new length will be:

= L + 0.001L

New time period will be:

T =✓0.001s

Now, the error in a day will be:

= ✓0.001 × 60 × 60 × 24 - 1 × 60 × 60 × 24.

= 60 × 60 × 24(✓1.001 - 1)

= 43.2 seconds.

Therefore, the correct option is C.

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The resultant velocity of the man is 12.5 m/s N of E.

Velocity of the man, Vm = 7.5 m/s

Velocity of Ship, Vs= 10 m/s

Since, velocity is a vector quantity, it will have both the magnitude and the direction.

So the magnitude for the resultant vector can be calculated by using the formula

[tex]\sqrt{x^{2} +y^{2} }[/tex] ; where x is the magnitude of the x-axis component and y is the magnitude of the y-axis component

i.e.

= [tex]\sqrt{Vm^{2} +Vs^{2} }[/tex]

= [tex]\sqrt{7.5^{2} + 10^{2} }[/tex]

= [tex]\sqrt{156.25}[/tex]

= 12.5 m/s

Also the direction can be calculated by Tan[tex]\alpha[/tex]

Tan[tex]\alpha[/tex] = [tex]\frac{10}{7.5}[/tex]

= Tan⁻(1.33)

= 58.9°

The angle between the resultant velocity and the horizontal axis is 58.9°.

Therefore the resultant velocity of the man relative to the water is 12.5 m/s towards NORTH-EAST direction.

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Time taken by the tennis ball to reach the ground is 1.23 second, if the initial velocity is  10.0 m/s.

Velocity is the time price at which an object is transferring alongside a route, even as the pace is the fee and path of an item's motion. put some other manner, velocity is a scalar price, at the same time as velocity is a vector.

Speed is the speed at which something moves in a particular direction. for instance as the rate of a car traveling north on a motorway, or the rate a rocket travels after launching. In a scalar way, absolutely the value magnitude of the velocity vector is continually the velocity of the motion.

Speed is a vector expression of the displacement that an item or particle undergoes with appreciation to time. the standard unit of speed magnitude (also known as velocity ) is the meter consistent with 2nd (m/s).

The top of a water tower lands 20.0 m

initial velocity = 10.0 m/s

time required to reach the ground  =

S = ut + 1/2 at²

20 = 10t + 5t²

t = 1.23 second

The water is at a height of 20 m.

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When using association to store and remember information, you are also encoding.

When trying to store and remember information, the following stages take place in order:

Storing a memory trace is called as encoding. Perception leaves representation in memory. It is the conversion of information for storage purposes.

Therefore, when using association to store and remember information, you are also encoding.

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A. Magnitude that the winner calculates for the displacement to find the keys to the Porsche is 38.83m.

B. The direction that the winner calculates for the displacement to find the key to the Porsche is 72.38° East of North.

When a particle moves from position A to point B, its displacement cannot be expressed using scalars. Always represented as a vector.

If an object's beginning and final positions are the same, its displacement is zero. That is, if a person begins a voyage at one location, walks some distance, and then returns to that location, his mobility will be zero.

The distance to the item will be 0 in this situation. Furthermore, there is no direction of zero displacements.

Given,

S1 = 90.9m, 30.0° west of north

S1 = 90.9 sin 30°( - î) + cos 30° j

∴ S1 = -45.45î + 78.72j

S2 = 15.5 m straight north

S2= 15.5 j

S3 = 80.9m, 45° south of east

S3 = 80.9 cos 45° î + 80.9 sin 45° j

S3 = 57.21 î - 57.21 j

Now,

Total displacement, S = S1 + S2 + S3

S = (-45.45î + 78.72j) + ( 15.5 j) + (57.21 î - 57.21 j)

  = ( -45.45 + 57.21) î + ( 78.72 + 15.5 -57.21) j

S  = 11.76 î + 37.01 j

|S| = 38.38m

tan α = y / x

tan α = 37.01 / 11.76

tan α = 3.15

α = 72.38°   from East of North

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Answer:

1 Newton (N) 1 kg*m/s²

Acceleration is measured in m/s², so combine your starting figures in such a way as to get m/s² (you have to divide away the kg):

9N/2kg = 4.5 m/s²

Explanation:

Kenny’s ideas and their acceptance were due to open-mindedness because she led to the use of hot baths and exercise to treat polio victims.

Elizabeth Kenny was a world-renowned nurse from Australia who develop a treatment for poliomyelitis, a very serious viral disease caused by poliovirus.

Elizabeth Kenny's ideas were controversial because they may be considered to be against conventional medical treatments.

In conclusion, Kenny’s ideas and their acceptance were due to open-mindedness because she led to the use of hot baths and exercise to treat polio victims.

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Answer:

The ball accelerates because of gravity which is constant. So we can apply one of the equations of uniformly accelerated motion to solve the problem.

[tex]Vf^2=Vo^2+2aS\\[/tex] is compatible since [tex]S, Vo, a[/tex] are given enabling us to calculate [tex]Vf[/tex] .

[tex]Vf^2=(0m/s)^2+2*10m/s^2*37m\\Vf^2=20m/s^2*37m\\Vf^2=740m^2/s^2\\Vf=\sqrt{740} m/s\\ Vf=27.202941017 m/s\\[/tex]