Jevais SterlingID: 1400420

Tiffany ArmstrongID: 1203540

September 19, 2014

Lab 2: Graph Matching

Topic: Graph Matching.

Aim: To analyze the motion of a student walking across the room as well as to predict, sketch and test graphs of Position vs. Time & Velocity vs. Time.

Materials and Apparatus: As described in lab manual.

Procedure: As described in lab manual.

Results:

i) Preliminary questions (please see sketches)

ii) Part I : Preliminary Experiments

Graph 1: Position vs. Time (at rest)

Graph 2: Position vs. Time (constant velocity)

Graph 3: Position vs. Time (constant speed negative direction)

Graph 4: Position vs. Time (accelerating in the positive direction starting from rest)

iii) Part II: Position vs. Time graph matching

Graph 5: Position vs. Time (b)

Graph 6: Position vs. Time (c)

Graph 7: Position vs. Time (f)

iv) Part III: Velocity vs. Time graph matching

Graph 8: Velocity vs. Time (g)

v) Analysis

Q1: To attain the motion desired by graph (b), the experimenter did the following actions:

Rest for one second at 1 m away from the wall. Walk from 1 m to 2.5 m away from the wall with a constant

velocity in two (2) seconds. Rest for three (3) seconds. Walk from 2.5 m to 1.7 m away from the wall with a constant

velocity in 1.5 seconds. Rest for 2.5 seconds.

To attain the motion desired by graph (c), the experimenter did the following actions:

Starting from 3 m away from the wall, walk 1.5 m toward the wall with a constant velocity in three (3) seconds.

Rest for one (1) second. Continue walking 1 m toward the wall with constant velocity in

one (1) second. Rest for two (2) seconds Walk in the opposite direction back to 3 m away from the wall

with constant velocity in three (3) seconds.

To attain the motion desired by graph (f), the experimenter did the following actions:

Starting from 0.9 m away from the wall, walk 1 meter away from the wall with constant velocity in 3.5 seconds.

Rest for three (3) seconds. Continue walking 1.4 m away from the wall with a constant

velocity in 3.5 seconds.

Q2: The slope of a Position vs. Time graph gives velocity. A positive slope shows that an object is moving away from its starting point. While a negative slope shows that it is returning to its starting point.

Q3: On a graph of Position vs. Time, a slope of zero signifies that an object is stationary.

Q4: A constant slope on a Position vs. Time graph, shows a motion with constant velocity.

Q5: As stated before, the slope of a Position vs. Time graph gives velocity. If the gradient is changing (a curve), the object must be accelerating or decelerating. It means that the velocity is changing.

Q6: (Return to procedure).

Q7: To attain the motion desired by graph (g), the experimenter did the following actions:

Walk away from the wall with a constant velocity of about 0.35 m/s for three (3) seconds.

Instantaneous acceleration (change in direction) in 0.5 seconds. Walk towards the wall with a constant velocity of about 0.35 m/s

for four (4) seconds. Instantaneous acceleration (deceleration) and stop in 0.5 seconds Rest for three (3) seconds.

Q8: This means the object is moving with constant velocity or no velocity.

Q9: This means the object is either accelerating or decelerating.

Discussion:

In the experiment we were given graphs of Position vs. Time (b, c, f) and of Velocity vs. Time. We were required to replicate these graphs as closely as possible. It can be said that this was accomplished to a fair extent. Meaning that the results were a satisfactory replication of the given graphs.

In graph (b), errors were evident. These were: error in initial distance and poor timing of motion. The experimenter was beyond the one (1) meter mark. The initial and final velocity times were not very accurate. These errors were shown on the graph by the observance of a positive slope below that which was depicted. Changes in motion (curved transitions), lagged behind those of the given graph.

Graph (c) was similar graph (b) in terms of the changes in motion. However, due to the greater number of these changes, errors were amplified. Edges (transitions) were consistently out of sync and values were either larger or smaller than expected. A notable error lies between the time interval 7-9 seconds. During this time, our graph depicted a downward curve. This indicates that there was an undesired acceleration followed by an undesired deceleration.

It is fair to say that graph (f) was the easiest graph to replicate. This was deduced by the fact that its replication showed the least number of errors. The experimenter was able to reproduce the required motion.

Graph (g) proved to be the most difficult to reproduce. This was due to moments of instantaneous acceleration. Which is defined as a change in velocity where t≈0.5 s. The graph required one to maintain a constant velocity, change directions and then come to a stop. These actions posed a challenge to the experimenter. They were not able to change direction as fluidly as the graph demanded. This resulted in irregularities.

To justify the many errors within the experiments sources of these errors must be identified. These are:

Slow reaction time of experimenter. Sudden or jittery movement of the target board which the experimenter held. Failure to stand at the proper distance from the motion detector.