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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.

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