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Motion

Introduction

The

objective of this lab report is to study the kinematics in two-dimensional

motion. This includes the relationship between different parameters like

distance, displacement, acceleration and velocity. We have also proved that

velocity is time integral of displacement and acceleration is time integral of

velocity. The better understanding of these quantities was demonstrated through

graphical analysis. Displacement is defined as an arbitrary parameter that is

measured when an object changes its distance over time. When this change in

displacement is divided by change in time, it gives velocity. This is vector

quantity and can be calculated by:

Equation

1

Theoretically, velocity is also arbitrary and

change its position. When this object’s velocity changes within the certain

time frame, this forms acceleration. This change in velocity is defined as is

given by:

Equation

2

The experiment was carried out by Data logger

by maintaining 2-3 m region to plot position. We have placed rangefinder at the

position of 0.5 m away, which sense the position of moving student. We measured

the distance of 2.5 m from the detector and marked a location on the floor

using marking tape. The sensor was subjected to the different speed of a

person, which generate different kinematic graphs on a separate word file.

Data

Following

graphical data was fetched during the experiment for different parameters with

arbitrary time.

Data

Analysis

Each

graph was critically analyzed that were generated through LoggerPro. Figure.1

shows the straight line graph between position and time for average velocity.

Since the person is moving in the direction towards the sensor, therefore the

directional axis is taken as positive. The slope of figure.1 was found to be 5

m/s. Figure 2. Shows the graph between distance and time for constant negative

velocity, so there is transition from 0.5m to 2.5m on marking tape. Average

velocity (V2) is -0.6 m/s which is negative. The slope of this trend

is also negative. Figure.3 shows that person is still in his position, since

there is no change in position with respect to time. There was no motion from 2.5m

to 0.5m as a person doesn’t change its position with respect to time. The slope

is 0 m/s. and (V3) is 0m/s. The trend in Figure.4 first shows no

change in position with respect to time, but increases after 2 seconds. This

trend was formed, when a person is delaying the time required to move towards

the sensor and a person operating the Loggerpro may have switched it pretty

earlier. Figure.5 trend possess curvilinear behavior, there are many

distortions in the velocity and increases after 3 seconds. This shows that a

person has changed different positions at different time intervals. Figure.6 shows a steady increase and decrease

in the position with respect to time. The smallest distance that was covered

during the interval was 0.6 m and largest distance was 2.6 m, marked as B and A

respectively on Figure.6. For point, A and B average velocity is given by:

= -0.6

m/s

Point C on Figure.3 shows the fastest instantaneous

velocity of a person moving towards the sensor position, as the trend obtained

shows decrease in positional gradient with a negative slope. Some errors that we have encountered throughout

the experiment were:

1.

The accuracy of the experiment was limited to

a certain position.

2.

The person was not still during the course of

motion and this results in distortion of the Graph. 2 and Graph. 3.

3.

The delayed time between graphing and sensing

of the position.

4.

Human and parallax errors

Conclusion

In

conclusion, this was an immense learning experience related to physical kinematics.

The fundamental principle was made clear through different graphs generated

through LoggerPro. Each graph has its own characteristic of the movement. The slope

of this line was calculated for each case. We have found that steeper the slope,

the greater the speed of person moving towards and away from the sensor. If the

slope was decreasing, then person moves away from the sensor. There was also a

case in which there is no movement through the interval of time, this happened the

case when the slope was almost equaled to zero. System, human and parallax errors

were the main causes of deviations between the actual and experimental values.

These can be sort through re-experimentation and take care of mistakes in the second

attempt.