A roller coaster car is traveling at a constant 3 m/s when it reaches a downward slope. On the slope, the car accelerates at a constant rate of 4.5 m/s 2 . The length of the slope is 45 meters. A) Find the velocity of the car at the bottom of the hill. B) Find the time of travel.
Answer:
Velocity of the car at the bottom of the slope: approximately \(20.3\; \rm m \cdot s^{-2}\).
It would take approximately \(3.9\; \rm s\) for the car to travel from the top of the slope to the bottom.
Explanation:
The time of the travel needs to be found. Hence, make use of the SUVAT equation that does not include time.
Let \(v\) denote the final velocity of the car. Let \(u\) denote the initial velocity of the car.Let \(a\) denote the acceleration of the car. Let \(x\) denote the distance that this car travelled.\(v^2 - u^2 = 2\, a\cdot x\).
Given:
\(u = 3\; \rm m \cdot s^{-1}\).\(a = 4.5\; \rm m \cdot s^{-2}\).\(x = 45\; \rm m\).Rearrange the equation \(v^2 - u^2 = 2\, a\cdot x\) and solve for \(v\):
\(\begin{aligned}v &= \sqrt{2\, a \cdot x + u^2} \\ &= \sqrt{2 \times 4.5\; \rm m \cdot s^{-2} \times 45\; \rm m + \left(3\; \rm m \cdot s^{-1}\right)^{2}} \\ &\approx 20.3\; \rm m \cdot s^{-1}\end{aligned}\).
Calculate the time required for reaching this speed from \(u = 3\; \rm m \cdot s^{-1}\) at \(a = 4.5\; \rm m \cdot s^{-2}\):
\(\begin{aligned}t &= \frac{v - u}{a} \\ &\approx \frac{20.3\; \rm m \cdot s^{-1} - 3\; \rm m \cdot s^{-1}}{4.5\; \rm m \cdot s^{-2}} \approx 3.9\; \rm m \cdot s^{-1}\end{aligned}\).
A fish swimming in a horizontal plane has velocity v with arrowi = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r with arrowi = (14.0 î − 2.80 ĵ) m. After the fish swims with constant acceleration for 19.0 s, its velocity is v with arrow = (23.0 î − 1.00 ĵ) m/s.
(a) What are the components of the acceleration of the fish?
ax =
m/s2
ay =
m/s2
(b) What is the direction of its acceleration with respect to unit vector î?
° counterclockwise from the +x-axis
(c) If the fish maintains constant acceleration, where is it at t = 26.0 s?
x =
m
y =
m
In what direction is it moving?
° counterclockwise from the +x-axis
(a) We can find the components of the acceleration of the fish by using the following kinematic equation:
v = u + at
where u is the initial velocity, v is the final velocity, a is the acceleration, and t is the time interval.
Let's find the acceleration of the fish in the x-direction first:
v_x = u_x + a_xt
where v_x is the x-component of the final velocity, u_x is the x-component of the initial velocity, a_x is the x-component of the acceleration, and t is the time interval.
Substituting the given values, we get:
23.0 = 4.00 + a_x * 19.0
Solving for a_x, we get:
a_x = (23.0 - 4.00) / 19.0 = 0.895 m/s^2
Similarly, we can find the acceleration of the fish in the y-direction:
v_y = u_y + a_yt
where v_y is the y-component of the final velocity, u_y is the y-component of the initial velocity, a_y is the y-component of the acceleration, and t is the time interval.
Substituting the given values, we get:
-1.00 = 1.00 + a_y * 19.0
Solving for a_y, we get:
a_y = (-1.00 - 1.00) / 19.0 = -0.105 m/s^2
Therefore, the components of the acceleration of the fish are:
a_x = 0.895 m/s²
a_y = -0.105 m/s²
What is acceleration?The rate of change of velocity of an object over the course of time is defined as acceleration. It is a vector quantity, that also means it has magnitude as well as direction. Acceleration occurs when an object changes its velocity, either by increasing or decreasing its speed or by changing its direction of motion. The following formula may be utilized to calculate an object's acceleration:
a = (v_f - v_i) / t
(b) To find the direction of the acceleration with respect to unit vector î, we can use the following formula:
θ = tan⁻¹(a_y / a_x)
Substituting the values we just found, we get:
θ = tan⁻¹(-0.105 / 0.895) = -6.84°
Therefore, the direction of the acceleration with respect to unit vector î is 6.84° clockwise from the +x-axis.
(c) To find the position of the fish at t = 26.0 s, we can use the following kinematic equations:
x = u_xt + 0.5 a_xt²
y = u_yt + 0.5 a_yt²
where x is the position in the x-direction, y is the position in the y-direction, u_x is the initial velocity in the x-direction, u_y is the initial velocity in the y-direction, a_x is the acceleration in the x-direction, a_y is the acceleration in the y-direction, and t is the time interval.
Let's first find the position of the fish in the x-direction:
x = u_xt + 0.5 a_xt²
Substituting the given values, we get:
x = 14.0 + 0.5 * 0.895 * (26.0 - 19.0)² = 37.4 m
Similarly, we can find the position of the fish in the y-direction:
y = u_yt + 0.5 a_yt²
Substituting the given values, we get:
y = -2.80 + 0.5 * (-0.105) * (26.0 - 19.0)²= -3.17 m
Therefore, the fish is at the position (37.4 m, -3.17 m) at t = 26.0 s.
To know more about velocity, visit:
https://brainly.com/question/17127206
#SPJ1
Net force acting on a 100 kg man standing in an elevator accelerating downward with a = 9. 8m/s^2 comes out to be:(a) 980N(b) 580N(c) 1380N(d) zero
Answer:
(d) zero
Explanation:
Net acceleration = (a - g)
a is downward so it is positive
F(net) = ma(net)
F = 100 x (9.8 - 9.8)
F = 0
The correct option is (d).
What is the average speed of an object that travels 510 meters in 17 days?
a . 30 meters/day
b. 493 meters/day
c . 527 meters/day
d . 8670 meters/day
e . none of the above
How long will it take for a basketball spinning on someone’s finger to stop if it undergoes and angular acceleration of -0.15 rad/s and is traveling at 27 rad/s initially? How many revolutions will it make?
The basketball's angular velocity ω at time t is
ω = 27 rad/s + (-0.15 rad/s²) t
It comes to a stop when ω = 0, which happens for
0 = 27 rad/s - (0.15 rad/s²) t
t = (27 rad/s) / (0.15 rad/s²)
t = 180 s
In this time, the ball would undergoes an angular displacement θ of
θ = (27 rad/s) t + 1/2 (-0.15 rad/s²) t ²
Plug in t = 180 s and solve for θ :
θ = (27 rad/s) (180 s) - 1/2 (0.15 rad/s²) (180 s)² = 2430 rad
One complete revolution corresponds to a turn of 2π rad, so the ball makes
(2430 rad) / (2π rad/rev) ≈ 386.747 rev
or about 387 revolutions as it slows down.
Which of the following best describes the condition where a signal sent on one wire is received on another wire within the same connector? a. Split pair b. Impedance c. NEXT d. Attenuation e. FEXT
The condition where a signal sent on one wire is received on another wire within the same connector is best described as NEXT (Near-End Crosstalk).
Near-End Crosstalk refers to the phenomenon where a transmitted signal from one wire interferes with the signal on an adjacent wire within a connector or cable. This interference occurs when the electromagnetic fields generated by one wire induce undesired voltages in nearby wires. In the context of data transmission, NEXT can lead to signal degradation and loss of data integrity. To mitigate NEXT, proper cable shielding, proper spacing between wires, and effective connector design are implemented. By reducing the crosstalk between adjacent wires, the quality and reliability of the transmitted signals can be improved. In summary, the condition described in the question is known as Near-End Crosstalk (NEXT).
To learn more about signal
https://brainly.com/question/30130156
#SPJ11
a heater 60w evaporates 6×10–3kg of boiling water in 60s.what is the specific latent heat of vaporisation of water in jkg–1
Your question doesn't look right, so lemme assume you meant this.
A heater marked 60w evaporate 6x 10^-³kg of boiling water in 60 seconds. What is the specific latent heat of vaporization of water in jkg?
so you can understand it better..
Latent heat of evaporation is the heat required required to change water to vapor at the same temperature.(100°C)
eg. water boils at 100°C and in presence of more heat it turns to vapor at that Same temperature.
This heat is know as latent heat of Vaporization.
it's give by H=mL
where L is the specific latent heat of vaporization.
The specific latent heat of vaporization of water is 6×10⁵ Joule/kg.
What is latent heat?The heat or energy that is absorbed or released during a substance's phase change is known as latent heat. It might go from a solid to a liquid or from a liquid to a gas, or vice versa. Enthalpy, a characteristic of heat, is connected to latent heat.
Given parameters:
Mass of the water = 6 × 10⁻³ kg.
Power of the heater = 60 watts.
Time taken = 60 second.
Hence, total heat absorbed by the water = 60×60 joule = 3600 joule.
Hence, specific latent heat of vaporization of water =
total heat absorbed /mass of the water
= 3600/6 × 10⁻³ J/kg
= 6×10⁵ Joule/kg.
Learn more about latent heat here:
https://brainly.com/question/28044951
#SPJ2
a weightless spring scale is attached to two equal weights as shown below. the reading on the scale will be
When a weightless spring scale is attached to two equal weights, the reading on the scale will be zero. This is because the weights on both sides are balanced, resulting in no net force acting on the scale.
The reason for this is Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, when one weight exerts a downward force on the spring scale, the other weight exerts an upward force of the same magnitude on the scale.
These opposing forces cancel each other out, resulting in a net force of zero. As a result, the spring scale does not experience any deformation and the reading remains at zero.
It is important to note that this only applies when the two weights are equal. If the weights were different, there would be an imbalance in the forces, causing the spring scale to register a non-zero reading.
In summary, when a weightless spring scale is attached to two equal weights, the reading on the scale will be zero due to the balanced forces acting on it.
For more question force
https://brainly.com/question/17927930
#SPJ8
A 25 kg mass is accelerated by a force at a rate of 5 m/s2. What is the magnitude of the force that accelerates the man?
y UD Eda
NF-22
11. A race car traveling at +44 m/s is uniformly accelerated to a velocity of +22 m/s over an
11-s interval. What is its displacement during this time?
a
We have to find acceleration first.
Initial velocity=u=44m/sFinal velocity=v=22m/sTime=11s=t\(\boxed{\sf Acceleration=\dfrac{v-u}{t}}\)
\(\\ \sf\longmapsto Acceleration=\dfrac{22-44}{11}\)
\(\\ \sf\longmapsto Acceleration=\dfrac{-22}{11}\)
\(\\ \sf\longmapsto Acceleration=-2m/s^2\)
Now Distance=sUsing second equation of kinematics
\(\boxed{\sf s=ut+\dfrac{1}{2}at^2}\)
\(\\ \sf\longmapsto s=44(11)+\dfrac{1}{2}(-2)(11)^2\)
\(\\ \sf\longmapsto s=484+(-1)(121)\)
\(\\ \sf\longmapsto s=484-(121)\)
\(\\ \sf\longmapsto s=363m\)
Explanation:
\(we \: want \: to \: find \: displacement \\ we \: can \: use \: newtons \: laws \: of \: motion \\ s = ut + \frac{1}{2} a {t}^{2}....(1) \\here \: 44 = u \: (initial) \\ v = 22(final) \\ t = 11 \\ then \: \\ s = 44 \times 11 + \frac{1}{2} (\frac{22 - 44}{11} ) {11}^{2} \\ s = 484 + \frac{1}{2} \times \frac{ - 22}{11} \times 11 \times 11 \\ s = 484 - 121 \\ s = 363m \\ thank \: you\)
What is Socio historical context
Answer:
It is the combination of social and historical factors.
(x – 2)² = 5(y + 1), where x and y are measured in centimeters. You need to place a new light bulb in your flashlight. How far away from the vertex of the parabolic mirror should you place the bulb to ensure a perfect beam of light? The bulb should be placed .
Answer:
The coordinates of the point the bulb should be placed is (2, 0.25)
Explanation:
The given equation of a parabola is presented as follows;
(x - 2)² = 5·(y + 1)
The point the bulb should be placed is the focus of the parabolic mirror to ensure a perfect (straight) beam
The general form of the equation of a parabola is (x - h)² = 4·p·(y - k)
The coordinates of the focus of the parabola for p > 0 f = (h, k + p)
By comparison, h = 2, k = -1, and p = 5/4
∴ The coordinates of the focus of the parabola, f = (2, -1 + 5/4) = (2, 0.25)
The coordinates of the point the bulb should be placed is at the focus, f = (2, 0.25).
PLEASE HELP ME ON QUESTION 27 ILL GIVE YOU BRAINLIEST!!
Answer:
question 22, the third answer is correct
Explanation:
you sent question 22 not 27
Which wave is carrying the most energy?
Li Wei loves cardio and finds it very easy to fit into his schedule. Because he knows it is important to diversify his exercise routine, sometimes he runs and other days he rides his bike. What else should Li Wei consider regarding his routine?
OPTIONS:
A.
He should add some strength training.
B.
He needs to add one more form of cardio.
C.
He has too much cardio and should cut half of it.
D.
His program works for him, so he should not change it.
PLEASE NO LINKS
Answer:
D.
Explanation:
Li Wei loves cardio and finds it very easy to fit into his schedule. Li Wei should consider his routine is his program works for him, so he should not change it. The correct option is D.
What is cardio?Any form of exercise that raises your heart rate and keeps it there for a long time is considered cardio. As you start to breathe more quickly and deeply, your respiratory system will start to work harder.
The four components of a fitness program are flexibility, cardio, strength, and power.
The physical exercise that increases muscular strength and fitness is referred to as strength.The capacity to produce the most muscle contractions possible during a movement is referred to as power.Cardio refers to the capacity to handle various circumstances of various lengths.Flexibility is the characteristic that is linked to the range of motion offered by a particular joint.Therefore, the correct option is D. His program works for him, so he should not change it.
To learn more about cardio, refer to the link:
https://brainly.com/question/24985980
#SPJ2
what is the physical significance of the nusselt number n u? how does the reynolds number affect it?
a. Nusselt number (Nu) represents the ratio of convective to conductive heat transfer, indicating the efficiency of convective heat transfer.
b. The Reynolds number (Re) influences the Nusselt number by determining the flow regime, with higher Reynolds numbers corresponding to higher Nusselt numbers and more efficient convective heat transfer.
a. The physical significance of the Nusselt number is that it provides information about the efficiency of convective heat transfer. A higher Nusselt number indicates that convective heat transfer is more dominant compared to conductive heat transfer. It is commonly used to analyze heat transfer in fluid flows, such as in pipes, channels, or heat exchangers.
b. The Reynolds number influences the Nusselt number because it affects the flow regime and flow behavior. In forced convection heat transfer, the Reynolds number determines whether the flow is laminar or turbulent. The transition from laminar to turbulent flow is characterized by a critical Reynolds number.
Learn more about Nusselt Number at
https://brainly.com/question/32614506
#SPJ4
Newton's 2nd law of Motion
what are some objects that have a little mass but a large amount of acceleration and therefore produce a large Force upon impact with something else.
aka..
what are some objects that have less mass but a larger acceleration
to break cardboard?
A bullet and a base ball
What objects has a small mass but produce large acceleration?Objects with a small mass can produce a large acceleration if they experience a large force. This is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass.
It's important to note that while these objects can produce a large acceleration, they can also cause significant damage or harm if not handled properly. It's important to always take appropriate safety precautions when working with objects that have the potential to produce large forces and accelerations.
Learn more about acceleration:https://brainly.com/question/12550364
#SPJ1
a planet's moon travels in an approximately circular orbit of radius 5.4 107 m with a period of 6 h 7 min. calculate the mass of the planet from this information.
The mass of the planet from this information. 3.56×10²⁶ Kg. A planet's gravitational pull on other bodies determines its weight (or mass).
Every piece of matter in the cosmos is drawn to one another by a gravitational force that is proportionate to its mass, according to Newton's Law of Gravitation. A balance is what you would use to measure mass. A triple beam balance or an electronic balance may be used in the lab to measure mass, but the traditional balance shown below could help you understand what mass is. This is significant because a planet's atmosphere has a direct impact on its climate. The mass of the planet in issue will consequently affect where the "habitable zone" surrounding a star is located.
Learn more about gravitational here-
https://brainly.com/question/3009841
#SPJ4
The higher the density, the
_____ compact the particles are within the object.
Answer:
more
Explanation:
the higher the density the more closely/tighter the particles in the object will be
13. Who named out seventh month?
Answer:
it was the gods of war.....
Answer:
juliest and august cesar
Explanation:
number of passengers in a PUJ? what type of variable and classification.
Answer:
QUANTITATIVE
Explanation:
THERE ARE TWO TYPES OF QUANTITATIVE VARIABLES:DISCRETE AND CONTINUOUS.WHAT DOES THE DATA REPRESENT?COUNTS OF INDIVIDUAL ITEMS OR VALUES.MEASUREMENTS OR CONTINUOUS OR NON-FINITE VALUES
if io is the intensity of the light incident on the first polarizer, what is the intensity of the light that passes through the second polarizer whose axis is oriented at an angle of 90 degrees with respect to the axis of the first polarizer?
Thus, light with an intensity of 2I will be incident on the second polarizer. The intensity will fall by a factor of cos2 across the second polarizer. As a result, the intensity is 2Icos2=2Icos2(450)=4I after going through the second polarizer.
How can you measure the brightness of light passing through a polarizer?I = Io cos2, where Io is the original intensity and is the angle formed by the polarization direction and the filter's axis, gives the intensity of polarized light after it has passed through a polarizing filter.
What is the right way to calculate intensity?I = P > A is the formula for intensity in physics. Power is measured in Watts while researching light waves, and since light is so large, area is typically measured in meters.
To know more about second polarizer visit:-
https://brainly.com/question/5017583
#SPJ4
the common 9 volt battery imparts how much energy to one coulomb of charge?
9 joules of energy in one coulomb of charge.
The energy of the battery means the amount of energy given by the battery.
The energy that a battery imparts to a charge can be calculated using the formula:
E = V * Q
where,
E is the energy in joules, '
V is the voltage in volts, and
Q is the charge in coulombs.
For a 9 volt battery, the energy imparted to one coulomb of charge can be calculated as:
E = 9 V * 1 C
E = 9 J/C
One joule per coulomb is equal to one volt.
Hence,
9 J/C = 9 V
9 volt battery, the energy imparted to one coulomb of charge is 9 V.
For similar questions on energy stored in the battery
https://brainly.com/question/14468791
#SPJ4
a person is dragging a packing crate of mass 100 kg across a rough horizontal floor where the coefficient of kinetic friction is 0.400. he exerts a force f sufficient to accelerate the crate forward. at what angle above horizontal should his pulling force be directed in order to achieve the maximum acceleration?
The pulling force should be directed at an angle of 45 degrees above horizontal to achieve the maximum acceleration.
To find the angle above horizontal at which the maximum acceleration can be achieved, we can use the following equation: \(F - f_k = ma\)
where F is the applied force,\(f_k\) is the force of kinetic friction, m is the mass of the crate, and a is the acceleration of the crate.
The force of kinetic friction is given by: \(f_k =\mu_k N\)
where μ_k is the coefficient of kinetic friction and N is the normal force.
The normal force is equal in magnitude to the weight of the crate, which is: N = mg
where g is the acceleration due to gravity.
Substituting the values given in the problem, we have:
\(f_k = 0.400 * 100 kg * 9.81 m/s^2 = 392.4 N\)
\(N = 100 kg * 9.81 m/s^2 = 981 N\)
\(f_k = \mu_k N = 0.400 * 981 N = 392.4 N\)
Now we can rewrite the first equation as:
F - 392.4 N = ma
Solving for F, we have:
F = ma + 392.4 N
To achieve the maximum acceleration, the force should be applied at an angle that maximizes the horizontal component of the force. This occurs when the force is applied parallel to the surface of the floor, so the angle above horizontal is 0 degrees. Therefore, the pulling force should be directed horizontally to achieve maximum acceleration.
To know more about maximum acceleration, refer here:
https://brainly.com/question/13674936#
#SPJ11
an object is experiencing a centripetal acceleration of 36m/s2 while traveling in a circle of radius 15m. what is it's velocity?
The velocity of the object is 23.24 m/s.
What is centripetal acceleration?An attribute of an object moving in a circular route is centripetal acceleration. Any object moving in a circle with an acceleration vector pointing in the direction of the circle's center is said to be experiencing centripetal acceleration.
Given that an object is experiencing a centripetal acceleration of 36m/s^2.
Radius of the circle: r = 15 m.
Then, the velocity of the object is = √(36×15) m/s = 23.24 m/s.
Learn centripetal acceleration here:
https://brainly.com/question/14465119
#SPJ1
A hydraulic jack is used to lift a car by applying a force of 120N at the pump piston,if the area of the ram and pump piston are 100cm squared and 1m squared respectively
Complete question:
A hydraulic jack is used to lift a car by applying a force of 120N at the pump piston, if the area of the ram and pump piston are 100cm squared and 1m squared respectively. What is the weight of the car?
Answer:
the weight of the car is 1.2 N
Explanation:
Given;
applied force, F₁ = 120 N
area of the effort (pump), A₁ = 1 m²
area of the load (ram), A₂ = 100 cm² = 1 x 10⁻² m²
let the weight of the car = F₂
The applied pressure is constant and the following equations can be used to calculate the weight of the car.
\(P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \\\\F_2 = \frac{F_1 \times A_2}{A_1} \\\\F_2 = \frac{120 \times (1\times 10^{-2})}{1} \\\\F_2 = 1.2 \ N\)
Therefore, the weight of the car is 1.2 N
Which of the following has the longest wave length and the lowest frequency
A.infrared waves
B.radio waves
C.x-ray waves
D.microwaves
Answer:
B. radio waves
Explanation:
Trust me It's correct
the name of the opening that lets light into any camera is called . a. the portal be. the aperture c. the lumen of. the iris e. the eye
The name of the opening that lets light into any camera is called the aperture.
The aperture is a circular opening within the camera lens that can be adjusted to control the amount of light that enters the camera. It is a crucial component in determining the exposure of a photograph.
The aperture is an adjustable opening in a camera's lens that controls the amount of light that enters the camera. It works similarly to the iris in the human eye. By adjusting the size of the aperture, you can control the exposure and depth of field in your photos.
The correct term for the opening that lets light into a camera is the aperture, which plays a crucial role in controlling exposure and depth of field. Therefore, the correct answer is b. the aperture.
To know more about aperture, visit;
https://brainly.com/question/13972212
#SPJ11
The fragments collided with Jupiter's atmosphere at a speed of about 60,000 m/s
(about 132,000 mph). The biggest fragment had a mass of 189,000,000,000 kg, or 1.39
x 10" kg. How much energy was released by the impact?
Answer: E = 5.004*10^(20) joules
Explanation:
We do not have a lot of information about the impact, so we can assume that the energy released on the impact was the kinetic energy of the large fragment.
Remember that the kinetic energy of an object of mass M that moves at a velocity V is:
K = (M/2)*V^2
in this case, we know that the speed (that is equivalent to the velocity) is:
V = 60,000 m/s
And the mass is:
M = 1.39*10^(11) kg
Then the kinetic energy of the large fragment was:
K = (1.39*10^(11) kg/2)*( 60,000 m/s)^2 = 5.004*10^(20) joules.
Then we could conclude that the energy released on the impact was:
E = 5.004*10^(20) joules
Pls help
The Q : Look at your recorded results and models for both the man and the boy. How close are the coefficients of friction for the sled on ice for two runs? How confident would you feel about specifying a coefficient of kinetic friction for this sled on this ice surface, based on these results? What other variables might impact this coefficient result?
Newton's second law, kinematics and graphic analysis we can find the results for the questions about the movement of the trine are:
The friction coefficients are man is0.8 and for the boy is0.98, the relationship between them is 0.82 The results are very accurate after the graphical analysis. The wind is a very important factor in the calculations that is not taken into account.Second law of Newton.
Newton's second law establishes a relationship between the net force, the mass and the acceleration of the body. In the attachment we can see a free body diagram which is a schematic of the forces without the details of the bodies.
N-W = 0
fr = ma
where N is the normal, W the weight of the body, fr the friction force, m the mass and a the acceleration
The friction force is a macroscopic representation of the interactions between the two surfaces, it is given by the expression
fr = μ N
where μ is the coefficient of friction between the two surfaces.
We substitute
μ mg = m a
a = μ g
Kinematics and graphic analysis.
Kinematics study the movement of bodies, looking for relationships between position, speed and acceleration.
v= v₀ – at t
In this case they give tables and graphs with the values of time and speed, where we can see that the relationship is a straight line that has as equation
y = ax +b
Where y is the dependent variable, x is the independent variable, a is the slope, and b is the cutoff point.
If we relate the two equations:
The independent variable x → time. The dependent variable y → speed. The cutoff point b → the initial velocity. The slope (a) is:a = mug
μ = \(\frac{a}{g}\)
Using linear regression the slope and cutoff point is:
The man.
The slope is a = -0.8 m/s² and the cut-off point b= 4.86 m/s.
Let's calculate the coefficient of friction.
μ = \(\frac{0.8}{9.8}\)
μ = 0.082
The child.
The slope is a = -0.98 m/s² and the cut-off point b= 4.72 m/s.
We calculate the coefficient of friction.
μ = \(\frac{0.98}{9.8}\)
μ = 0.1
The relationship between the two coefficients of friction is
\(\frac{\mu_{man} }{\mu_{boy}} = \frac{0.082}{0.1}\)
\(\frac{\mu_{man}}{\mu_{boy}} = 0.82\)
The results are very exact since there are values of several points in the route and the graphical analysis gives the best possible value for all the points.
There are some variables not taken into account, one of the most important is friction with the wind and wind speed.
In conclusion using Newton's second law, kinematics and graphic analysis we can find the results for the questions about the movement of the trine are:
The friction coefficients are man is0.8 and for the boy is0.98, the relationship between them is 0.82 The results are very accurate after the graphical analysis. The wind is a very important factor in the calculations that is not taken into account.
Learn more about kinematics and graphical analysis here: brainly.com/question/11579754