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Experiment 3: Kinematics of Human Motion Laboratory Report Kamylle Consebido, Hazel Dacuycuy, Jose Gerardo Del Rosario, Ira Gabrielli Delos Reyes, Ancilla Diamante Department of Occupational Therapy College of Rehabilitation Sciences, University of Santo Tomas España, Manila Philippines Abstract Kinematics of the human motion such as displacement, velocity, and acceleration are discussed in the experiment. Displacement vs. time and velocity vs. time graphs were made as a method of graphical analysis in regards to human motion. All factors including time, speed, and distance could all affect the kinematics of human motion. The reaction time was also obtained which varies from person to person. 1. Introduction The concepts of kinematics have its relevance when it comes to transportation vehicles such as cars, buses and trucks. These vehicles have a built in speedometer that measures the instantaneous speed, which can be derived from distance and time. This experiment aims to inform students on how to draw displacements/velocity versus time graphs for uniform motion and uniformly accelerated motion. Students would also determine their normal reaction time and their reaction time while being distracted. 2. Theory Speed is a scalar quantity that refers to the distance covered by an object in a certain amount of time. Since it shows the distance/time ratio, it is also called the average speed.

Average speed =

distance time

Velocity is a vector quantity that refers to the rate at which an object changes its position. The change in the position from a starting point to an end point is called the displacement. Displacement : ∆ X= Xf −Xi Velocity=

∆ x Xf − Xi = ∆ t Tf −Ti

On the other hand, acceleration is a vector quantity that refers to the rate at which an object changes its velocity. Anytime an object’s velocity is changing, the object is said to be accelerating. This case is called the constant acceleration. The average acceleration of an object over a given interval of time can be found using this equation: Ave . Acceleration=

∆ velocity Vf −Vi = ∆ time Tf −Ti

3. Methodology This experiment needs a meter stick, timer and a Vernier Logger Pro. Through Logger Pro, a position vs. time graph, and a velocity vs. time graph entitled, “01b Graph Matching” was opened. A member of the group stood in front of the motion detector and moved to match the graph.

In order to have a graphical analysis of motion in our next activity, a group member was tasked to walk in a straight line for a total of ten (10) seconds, measured using a timer, starting from rest. The distance she travelled every second was measured with a meter stick. Her total displacement at each second was recorded, and divided by its corresponding time in order to determine the average velocity. The instantaneous velocity at the end of each time interval was calculated by multiplying the average velocity by 2.

In order to determine each of the group members’ reaction time, a group mate (Member B) held a meter stick vertically at the zero mark while the member being observed (Member A) positioned his/her thumb and index finger at the 50cm mark. The meter stick was dropped without Member A knowing beforehand and she/he caught it with his/her thumb and index finger. The mark where she/he caught it from the 50cm mark was recorded. The procedure was repeated but with Member A being distracted by another member.

4. Results and Discussion Table 1. Position vs. Time and Velocity vs. Time graph (moving away with constant velocity)

As it was shown, the person moving in a constant velocity have a linear graph. As time elapses, the distance between the starting point and the person increases which shows an upward slope, from the point of origin to the maximum distance traveled. Since the person moved in a constant velocity, the acceleration is also constant. Table 2. Position vs. Time and Velocity vs. Time graph (moving towards with constant velocity)

When a person approaches the point of origin at a constant velocity as time elapses, the effect is the same, as the graph is still linear and shows a slanted projection. But this time it starts from a distance to the point of origin, showing a downward slant as opposite to the previous graph. The graph

also has the same pattern as the one mentioned before since the person still moved in a constant velocity. Table 3. Position vs. Time and Velocity vs. Time graph (moving away with increasing velocity)

These tables show a person moving away from a starting point, thus showing a position vs. time graph with an upward slanting projection. However, the person moved with increasing speed which signifies an increasing acceleration. Thus, upward projections can be noted on the velocity vs. time graph. Table 4. Position vs. Time (graph matching)

In this velocity vs. time graph, our member is required to move in such a way that her acceleration should allow the red line to match the graph presented. As the line goes downward, the acceleration of the member should decrease and increase when the graph goes upward. When the graph forms a straight line, the acceleration must be constant. However, the red mark did not exactly match the graph since there might have been particles that may have interfered with the detection of the acceleration, instead of our member alone. The device might have sensed those random particles which caused the uneven results of the graph. Table 6. Total Displacement vs. Total Time

Position vs. Time 15

Throughout this activity, our member moved in such a way that her velocity remained constant. Matching of this position vs. time graph has been made possible because as the person moves away from the origin after a few seconds, the red line instantly makes an increasing slant. As the red line hits the straight mark, the person has stopped from a certain point, causing the red line to match the straight mark. Then a few seconds, the member walked back towards the origin, which formed a decreasing slant. Eventually, the red line hit the straight mark again, meaning our member stop from that point onwards. Table 5. Velocity vs. Time (graph matching)

10 5 0

0

1

2

3

4

5

6

7

8

9

Table 7. Instantaneous Velocity vs. Time

Instantaneous Velocity vs. Time 15 10 5 0

0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

Table 8. Total Displacement, Average Velocity and Instantaneous Velocity at each second. Time 1 2 3 4 5 6 7 8 9 10

Total Displacement (m) 0.72 1.45 2.28 2.93 3.66 4.35 5.22 6.13 6.99 7.82

Average Velocity (m/s) 0.72 0.73 0.76 0.73 0.73 0.73 0.75 0.77 0.78 0.78

Instantaneous Velocity (m/s) 1.44 1.45 1.52 1.47 1.46 1.45 1.49 1.53 1.55 1.56

Table 6 show the position in regards to time. The position moves away from the origin in respective to time. Tables 7and 8 are the results that show the values for average velocity of each total displacement are close to each other and they are expected since the average velocity is the total displacement during an extended period of time. Due to this, it is observed that when total displacement increases, the average velocity also increases. Through the use of the formula, VInstantaneous = 2(VAverage), the values for instantaneous velocity were attained. They, too, showed evidences of increase as the total displacement and average velocity increased. Table 9. Reaction times of each group member. Member Consebido Dacuycuy Delos Reyes Del Rosario Diamante

Reaction time (s) 0.21 0.21 0.08 0.17 0.21

Reaction time while distracted (s) 0.23 0.22 0.26 0.22 0.30

The results show that each member’s reaction times vary and that their reaction time while distracted are evidently higher than their normal reaction time. Reaction time was computed using the formula, , where d represents the distance

from the 50cm mark of the meter stick that was caught by the member and g represents acceleration of gravity (9.8 m/s2).

5. Conclusion According to the results gathered, the activities show that as the person moves in constant velocity, a linear graph is created in the position vs. time graph. As time elapses, the distance between the starting point and the location of the person increases thus it shows an upward slope. When the velocity is constant, the acceleration is also constant, thus a straight line is plotted in a graph to show constant acceleration. On the other hand, it has been also observed that when total displacement increases, the average velocity also increases. Lastly, reaction time varies from person to person and distraction can affect the reaction time of a person. 6. Applications 1. To determine the height of a building using a stopwatch is to drop a rock from the top and monitor the time taken to reach the ground. The physics formula of 1 H= a t 2 , where a is the constant 2 gravitational acceleration of 9.8 m/ s

2

,

and t is the duration of fall in seconds, thus the result of this equation H which is the distance travelled by the free-falling object, can be used to find the height of a building in meters. 2. To make a possible explanation based on physics principles, it is a must for a driver to be aware of the facts, like speed, position, possible acceleration etc. in order to have a stable maneuver for the vehicle. When cellphones are used while driving, the driver’s attention might be diverted from the road which might possibly to lead to sudden and unwanted accidents in the highway. A driver should be mindful of his position in the highway in order to set the right limit for his speed and acceleration in a certain lane. 3.

7. Reference Sternheim, M., & Kane, J. (1991). General physics. New Jersey: Wiley & Sons.

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Average speed =

distance time

Velocity is a vector quantity that refers to the rate at which an object changes its position. The change in the position from a starting point to an end point is called the displacement. Displacement : ∆ X= Xf −Xi Velocity=

∆ x Xf − Xi = ∆ t Tf −Ti

On the other hand, acceleration is a vector quantity that refers to the rate at which an object changes its velocity. Anytime an object’s velocity is changing, the object is said to be accelerating. This case is called the constant acceleration. The average acceleration of an object over a given interval of time can be found using this equation: Ave . Acceleration=

∆ velocity Vf −Vi = ∆ time Tf −Ti

3. Methodology This experiment needs a meter stick, timer and a Vernier Logger Pro. Through Logger Pro, a position vs. time graph, and a velocity vs. time graph entitled, “01b Graph Matching” was opened. A member of the group stood in front of the motion detector and moved to match the graph.

In order to have a graphical analysis of motion in our next activity, a group member was tasked to walk in a straight line for a total of ten (10) seconds, measured using a timer, starting from rest. The distance she travelled every second was measured with a meter stick. Her total displacement at each second was recorded, and divided by its corresponding time in order to determine the average velocity. The instantaneous velocity at the end of each time interval was calculated by multiplying the average velocity by 2.

In order to determine each of the group members’ reaction time, a group mate (Member B) held a meter stick vertically at the zero mark while the member being observed (Member A) positioned his/her thumb and index finger at the 50cm mark. The meter stick was dropped without Member A knowing beforehand and she/he caught it with his/her thumb and index finger. The mark where she/he caught it from the 50cm mark was recorded. The procedure was repeated but with Member A being distracted by another member.

4. Results and Discussion Table 1. Position vs. Time and Velocity vs. Time graph (moving away with constant velocity)

As it was shown, the person moving in a constant velocity have a linear graph. As time elapses, the distance between the starting point and the person increases which shows an upward slope, from the point of origin to the maximum distance traveled. Since the person moved in a constant velocity, the acceleration is also constant. Table 2. Position vs. Time and Velocity vs. Time graph (moving towards with constant velocity)

When a person approaches the point of origin at a constant velocity as time elapses, the effect is the same, as the graph is still linear and shows a slanted projection. But this time it starts from a distance to the point of origin, showing a downward slant as opposite to the previous graph. The graph

also has the same pattern as the one mentioned before since the person still moved in a constant velocity. Table 3. Position vs. Time and Velocity vs. Time graph (moving away with increasing velocity)

These tables show a person moving away from a starting point, thus showing a position vs. time graph with an upward slanting projection. However, the person moved with increasing speed which signifies an increasing acceleration. Thus, upward projections can be noted on the velocity vs. time graph. Table 4. Position vs. Time (graph matching)

In this velocity vs. time graph, our member is required to move in such a way that her acceleration should allow the red line to match the graph presented. As the line goes downward, the acceleration of the member should decrease and increase when the graph goes upward. When the graph forms a straight line, the acceleration must be constant. However, the red mark did not exactly match the graph since there might have been particles that may have interfered with the detection of the acceleration, instead of our member alone. The device might have sensed those random particles which caused the uneven results of the graph. Table 6. Total Displacement vs. Total Time

Position vs. Time 15

Throughout this activity, our member moved in such a way that her velocity remained constant. Matching of this position vs. time graph has been made possible because as the person moves away from the origin after a few seconds, the red line instantly makes an increasing slant. As the red line hits the straight mark, the person has stopped from a certain point, causing the red line to match the straight mark. Then a few seconds, the member walked back towards the origin, which formed a decreasing slant. Eventually, the red line hit the straight mark again, meaning our member stop from that point onwards. Table 5. Velocity vs. Time (graph matching)

10 5 0

0

1

2

3

4

5

6

7

8

9

Table 7. Instantaneous Velocity vs. Time

Instantaneous Velocity vs. Time 15 10 5 0

0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

Table 8. Total Displacement, Average Velocity and Instantaneous Velocity at each second. Time 1 2 3 4 5 6 7 8 9 10

Total Displacement (m) 0.72 1.45 2.28 2.93 3.66 4.35 5.22 6.13 6.99 7.82

Average Velocity (m/s) 0.72 0.73 0.76 0.73 0.73 0.73 0.75 0.77 0.78 0.78

Instantaneous Velocity (m/s) 1.44 1.45 1.52 1.47 1.46 1.45 1.49 1.53 1.55 1.56

Table 6 show the position in regards to time. The position moves away from the origin in respective to time. Tables 7and 8 are the results that show the values for average velocity of each total displacement are close to each other and they are expected since the average velocity is the total displacement during an extended period of time. Due to this, it is observed that when total displacement increases, the average velocity also increases. Through the use of the formula, VInstantaneous = 2(VAverage), the values for instantaneous velocity were attained. They, too, showed evidences of increase as the total displacement and average velocity increased. Table 9. Reaction times of each group member. Member Consebido Dacuycuy Delos Reyes Del Rosario Diamante

Reaction time (s) 0.21 0.21 0.08 0.17 0.21

Reaction time while distracted (s) 0.23 0.22 0.26 0.22 0.30

The results show that each member’s reaction times vary and that their reaction time while distracted are evidently higher than their normal reaction time. Reaction time was computed using the formula, , where d represents the distance

from the 50cm mark of the meter stick that was caught by the member and g represents acceleration of gravity (9.8 m/s2).

5. Conclusion According to the results gathered, the activities show that as the person moves in constant velocity, a linear graph is created in the position vs. time graph. As time elapses, the distance between the starting point and the location of the person increases thus it shows an upward slope. When the velocity is constant, the acceleration is also constant, thus a straight line is plotted in a graph to show constant acceleration. On the other hand, it has been also observed that when total displacement increases, the average velocity also increases. Lastly, reaction time varies from person to person and distraction can affect the reaction time of a person. 6. Applications 1. To determine the height of a building using a stopwatch is to drop a rock from the top and monitor the time taken to reach the ground. The physics formula of 1 H= a t 2 , where a is the constant 2 gravitational acceleration of 9.8 m/ s

2

,

and t is the duration of fall in seconds, thus the result of this equation H which is the distance travelled by the free-falling object, can be used to find the height of a building in meters. 2. To make a possible explanation based on physics principles, it is a must for a driver to be aware of the facts, like speed, position, possible acceleration etc. in order to have a stable maneuver for the vehicle. When cellphones are used while driving, the driver’s attention might be diverted from the road which might possibly to lead to sudden and unwanted accidents in the highway. A driver should be mindful of his position in the highway in order to set the right limit for his speed and acceleration in a certain lane. 3.

7. Reference Sternheim, M., & Kane, J. (1991). General physics. New Jersey: Wiley & Sons.

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