OBJECTIVE

For uniformly accelerated motion in both directions along a straight line,

Analyze position vs. time and velocity vs. time graphs.

Compare the accelerations determined theoretically and experimentally.

THEORY

For an object moving along an axis, the average acceleration aav, over a time interval Δt is defined as the ratio of change in the velocity of the object to the time interval ie.,

a_av=Δv/Δt ——————–(1)

If the velocity changes by a constant amount during equal time intervals, then the acceleration is said to be uniform. For uniformly accelerated motions, the basic kinematic relations are:

v= v_0+at

x- x_0= v_0 t+ 1/2 at^2

v^2= 〖v_0〗^2+ax

SIMULATION INTRODUCTION

Open the simulation from the link here : https://phet.colorado.edu/en/simulation/legacy/moving-man

Get familiarize with the simulation and its interface. Play with the different control buttons/tools of the simulation to discover what type of variables can be changed for creating different set of readings and graphs. Details of the tools/buttons are explained below.

```
There are two windows, Introduction and chart. Both works separately.
You can adjust the position, velocity and acceleration of the man either by entering a value in the boxes or by moving the slider.
Use the controls on the bottom to Pause, Step, or Record and Playback the motion.
You must select Record before you start an experiment if you want it saved.
On the Introduction Tab, the seek bar is grabbable in Playback mode to see the man’s motion at desired positions.
On the Chart tab, a vertical grey line ( Co-ordinate tool) appears in the Playback mode is grabbable to relate the Man's motion to the graphs. You can find the exact value of the position, velocity and acceleration at the time interval of 0.1 seconds by using the co-ordinate tool.
Barriers : You can restrict the motion by adding barriers. It is recommended to remove barriers while working on charts simulation to get good graphs.
```

PROCEDURE I – Investigating position, velocity and acceleration of a moving object.

```
Open Introduction window.
Choose the initial conditions for position, velocity and acceleration as shown in the table below. (Use the sliders or enter the values in the box).
```

Position (Blue slider)

Velocity (Red Slider)

Acceleration(Green Slider)

```
Choose small values for velocity and acceleration to avoid the motion of the man out of screen. Remove the barriers.
Check the velocity and acceleration vector.
Click record button and run the simulation for each condition.
Use playback button to playback the recorded motion at a desired pace to observe the motion and the behavior of velocity and acceleration vectors during motion.
Give your responses based on your observation of the motion in the following table for each moving man for each condition.
Reset all settings and repeat the above steps for the all the conditions mentioned in the table.
```

Initial Conditions Describe his motion? Comment on his velocity and acceleration vectors? Mention whether he speeds up or slows down or constant? Justify your answers. Draw a graph for his motion.

P = 0

V(-ve) = *_*

A = 0

Motion:

Velocity:

Acceleration:

P = 0

V(+ve) = *_*

A = 0

Motion:

Velocity:

Acceleration:

P = 8 m/s

V(-ve) = *_*

A(-ve) = *__*

Motion:

Velocity:

Acceleration:

P = -8 m/s

V(+ve) = *_*

A(+ve) = *__*

`Motion:`

Velocity:

Acceleration:

P = 0

V(+ve) = *_*

A (-ve) = *_*

`Motion:`

Velocity:

Acceleration:

P = 0

V(-ve) = *__*

A(+ve) = *__* Motion:

Velocity:

Acceleration:

PROCEDURE II– Plot and analyze graphs.

Part 1 : To plot and analyze velocity -. time graph.

```
Open “Introduction” window
Set an acceleration _____________. (Adjust the green slider or type value in the box)
Remove the walls by clicking on the red cross at top of the walls.
Select Record control and run the animation for 10 seconds so that the data are recorded by the software.
Now you are ready to record your data into an Excel spreadsheet to plot the graph.
Use playback option to view the animation as slowly as you want and use the grabbable seek bar to record the values of time, position and velocity.
Record the values of time, position and velocity every 1 second and note down in the table 1.
```

Table 1

Time (s) Position(m) Velocity (m/s)

1

2

3

4

5

6

7

8

9

10

```
Now use Excel to plot a Velocity vs. Time graph.
Choose Velocity on the vertical axis and time on the horizontal axis.
Use Excel to display a best fit straight line (trend line - linear fit)
Include the equation chart and the R-squared value on the graph:
Check the R- Squared value and determine whether the fit is good or bad?
What is the slope of the line?
Does the value of the slope agree with what you have expected for the acceleration?
Insert the velocity vs. time graphs from excel here.
```

Graph – Velocity vs. Time

Part 2: To plot and analyze the position – time graph.

```
Now use Excel to plot a Position-Time graph (Position Vs Time). Use data in the table 1.
Choose Position on the vertical axis and time on the horizontal axis.
Is it a straight line or a curve? Why?
With Excel try to add now a different kind of fit: click on trendline, more trendline options and select polynomial fit (order 2)
Polynomial fit of order 2 means that Excel will try to fit your data with a curve of equation like: y = A x2 + B x + C. Since, you have time on horizontal axis and position on vertical axis, here it look like x= A t2 + B t + C . Remembering your maths, which kind of curve is this?
Is it a good fit?
Use Excel to display the equation of the curve on the chart. Re-Write it here using the right symbols [remember excel calls x and y the horizontal and vertical axis, while for you they are called t and x] and get the value of acceleration from the equation.
Does this value of acceleration agree what you have expected for the acceleration?
Insert the position vs. time graph from excel here.
```

Graph – Position vs. Time

Part 3: Comparing the theoretical and experimental values.

Answer the following questions based on the scenario given below:

“A man started running along a straight line from a position marked 2 m with an initial velocity of 3 m/s at an acceleration of -2 m/s2.”

```
What will be his position after 8 seconds? Find out his exact position using kinematic relations.
Now open chart window of the simulation and run the simulation for the same scenario and find out the position of the moving man after 8 seconds?
To find out the value of the position at 8s, use the playback option and use the grabbable seek bar to find out the position at 8s. Note down the value:
Does the value of position match with what you have calculated using kinematics relations?
Take the screen shot of the simulation including the three graphs and paste it here.
```

Screenshot

Part 4: Creating scenarios and creating graphs.

```
Observe the screenshot of position vs. time graph given below and try to create a similar graph of your choice with the moving man. ( No need to meet the exact values as shown in the graph below. But, try to create a similar kind of graph).
You can choose your values for position, velocity, and acceleration, but should look similar.
Now test it!!
Are you getting a similar kind of graph now? ________if No, try again.
If yes, put the values you used to create the graph in the scenario below:
```

“A man started running along a straight line from a position marked at **with an initial velocity of** at an acceleration of **_**.”

`Take the screen shot of the simulation you created including the three graphs and paste it here.`

Screenshot

```
Now mark the following with the labels mentioned below on your graphs for the scenario.
Mark the point at which the man reverses its direction on position vs. time and velocity vs. time graph. ( Use Letter ‘T’ to label).
Mark the portion on the position vs. time graph where the velocity is negative with letter ‘N’. Label somewhere on that portion.
Mark the portion of the position vs. time graph where the velocity is positive with letter ‘P’. Label somewhere on that portion.
```

Sample Solution

Unique – This paper considers the utilization of facial acknowledgment advances to forestall wrongdoing. The most well-known advances that are being utilized for security and confirmation intentions are dissected. The Eigenface strategy is the most utilized facial acknowledgment innovation, it very well may be utilized for security and verification purposes. This strategy centers around the parts of the face improvements that are significant for ID, this is finished by disentangling face pictures into huge neighborhood and worldwide 'highlights'. There are numerous ways for law authorization to help them in diminishing the measure of wrongdoing. Four of these ways that utilization facial acknowledgment are: FaceIt, coordinating appearances from live security pictures, face acknowledgment in photos and face acknowledgment from draws. As these advancements are improving quickly, the perils and moral issues likewise must be considered before the innovations can really be utilized in our every day lives. From this paper can be reasoned that facial acknowledgment sets out a great deal of open doors to help forestall wrongdoing. Nonetheless, there are still a great deal of troubles that can cause issues when these methods are utilized in reality. 1. Presentation Consistently a great deal of violations occur. Guiltiness is a major issue everywhere on the world. It is a test to find crooks and Artificial Intelligence could assist with this. The advances that exist these days make it simpler to distinguish people. One of these innovations is facial acknowledgment. These advances can distinguish lawbreakers. Facial acknowledgment calculations can analyze two arrangements of information. At the point when a match has been discovered, an individual could be distinguished. This prompts the accompanying inquiry: "How might facial acknowledgment be utilized to forestall regular wrongdoing?" The examination question is restricted to ordinary wrongdoing, since facial acknowledgment is utilized in a great deal of fields. By regular wrongdoing is implied: burglary, savagery, drug deals, affronts, dangers, imitation, driving under impact, developing hemp, robbery, assault, (serious) misuse and murder. To address the fundamental exploration question a couple of subjects will be looked into. The facial acknowledgment advances which exists and how they work will be talked about. The consequences of what the innovations have brought so far will be assessed. Yet additionally the drawbacks, chances and moral issues of facial acknowledgment innovations will be considered in this paper. Besides the security law will be examined in this paper, with center around the European law. Contemplated every one of these things, there can be offered a response to our primary examination question. 2. Facial acknowledgment advancements I. Which facial acknowledgment innovations exist? A various of facial acknowledgment procedures and strategies are being utilized for security and validation purposes which remembers territories for analyst offices and military purposes[25]. Thusly, the facial acknowledgment procedures can assume a part in forestalling wrongdoing. There are different techniques thought about the two essential errands of facial acknowledgment, for example confirmation and recognizable proof. Check, likewise called confirmation, is introducing a face picture of an obscure individual alongside a case of personality, and afterward determining whether the individual is who he/she professes to be. Recognizable proof, likewise called acknowledgment, is introducing a picture of an obscure individual and verifying that individual's personality by contrasting that picture and an information base of pictures of known individuals[15]. There are even some facial acknowledgment methods that can see feelings. These strategies, just as check and recognizable proof are vital with regards to discovering hoodlums so wrongdoing can be forestalled. A couple of instances of the numerous techniques and calculation that can be utilized inside the field of facial acknowledgment are: Geometric Feature Based Methods, Template Based Methods, Correlation Based Methods, Matching, Pursuit Based Methods, Singular Value Decomposition Based Methods, The Dynamic Link, Matching Methods, Illumination Invariant Processing Methods, Support Vector Machine Approach, Karhunen-Loeve Expansion Based Methods, Feature Based Methods, Neural Network Based Algorithms and Model Based Methods [25]. Later on, perhaps the most realized techniques will be examined in a definite manner. The facial acknowledgment techniques that can be utilized, all have an alternate methodology. Some are more much of the time utilized for facial acknowledgment calculations than others. The utilization of a strategy additionally relies upon the required applications. For example, observation applications may best be served by catching face pictures by methods for a camcorder while picture information base examinations may require static power pictures taken by a standard camera. Some different applications, for example, admittance to top security spaces, may even require the renouncing of the nonintrusive nature of face acknowledgment by requiring the client to remain before a 3D scanner or an infrared sensor[15]. Subsequently, there can be presumed that there can be made a division of three gatherings of face acknowledgment strategies, contingent upon the needed kind of information results, for example techniques that analyze pictures, strategies that take a gander at information from camcorders and strategies that manage other tangible information, similar to 3D pictures or infrared symbolism. Every one of them can be utilized in an unexpected way, to keep wrongdoing from occurring or repeating. ii. How do these innovations work? As recorded above, there exists an extensive rundown of strategies and calculations that can be utilized for facial acknowledgment. Four of them are utilized often and are generally known in the writing, for example Eigenface Method, Correlation Method, Fisherface Method and the Linear Subspaces Method. In any case, how do these facial acknowledgment work? Due to word impediments, just one of those four facial acknowledgment procedures, i.e The Eigenface Method, will be examined. Ideally this will give an overall thought of how facial acknowledgment functions and can be utilized. One of the significant challenges of facial acknowledgment, is that you need to adapt to the way that an individual's appearance may change, with the end goal that the two pictures that are being looked at separate a lot from one another. Additionally natural changes in pictures, such as lightning, must be considered, to have fruitful facial acknowledgment. Consequently from an image of a face, just as from a live face, some yet more unique visual portrayal should be set up which can intervene acknowledgment regardless of the way that, all things considered, a similar face will barely ever shape an indistinguishable picture on progressive events. Our capacity to do this shows that we can infer primary codes for faces, which catch those parts of the construction of a face fundamental to recognize it from other faces[6]. One of the four most popular facial acknowledgment strategies is the Eigenface Method. This strategy centers around the parts of the face improvement that are significant for distinguishing proof. This is finished by translating face pictures into critical nearby and worldwide 'features'[24]. Such highlights could possibly be straightforwardly identified with our natural idea of face highlights, for example, the eyes, nose, lips and hair. Researchers Matthew Turk and Alex Pentland [24] built up a PC framework for the eigenface approach which functions as following: "In the language of data hypothesis, we need to extricate the important data in a face picture, encode it as productively as could really be expected, and contrast one face encoding and an information base of models encoded similarly."[24] This all occurs in the accompanying introduction activities: 1) Acquire an underlying arrangement of face pictures, additionally called the preparation set. Figure 1: Images of the preparation set [26] Figure 2: Eigenfaces of the preparation set [26] 2) Calculate the eigenfaces from the preparation set, keeping just the M pictures that relate to the most elevated eigenvalues. These M pictures characterize the face space. As new faces are capable, the eigenfaces can be refreshed or recalculated. 3) Calculate the relating dispersion in M-dimensional weight space for each known individual, by projecting their face pictures onto the 'face space'. After the introduction tasks, there are done more activities to perceive new face pictures. 4) Calculate a bunch of loads dependent on the information picture and the M eigenfaces by projecting the info picture onto every one of the eigenfaces. 5) Determine if the picture is a face at all by verifying whether the picture is adequately near 'face space'. 6) If it is a face, order the weight design as either a referred to individual or as obscure. 7) (Optional) Update the eigenfaces or potentially weight designs. 8) (Optional) If a similar obscure face is seen a few times, compute its trademark weight design and join into the known faces[24]. As referenced before, there is an extensive rundown of strategies that can be utilized for facial acknowledgment. Four of them, i.e Eigenface Method, Correlation Method, Fisherface Method and the Linear Subspaces Method, are the most top choice. Underneath here, you can discover the blunder paces of those four techniques, thought about pictures with close yield or the entire face. Figure 3: Graph and table of the consequence of an analysis with the four most utilized facial acknowledgment procedures [1] As should be obvious, the Eigenface Method has the most mistakes, and the Fisherface Method the least. You can likewise see that the mistake rate is higher with pictures of close yields faces, contrasted with a full face picture. This shows that it is more diligently for a facial acknowledgment calculation to remember somebody if their face isn't completely appeared in the image and the highlights are consequently not perceived. It likewise helps us to remember the way that facial acknowledgment strategies are not totally precise. Ideally they will turn out to be more exact later on, so e.g wrongdoing can be forestalled quicker and better. 3. Aftereffects of face acknowledgment advances in wrongdoing anticipation There are numerous ways for law authorization to assist them with diminishing>

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