mathematical research

THE RESEARCH OF MATHEMATIC
THE APPLICATION OF DIFFERENTIAL EQUATION IN POSITION, VELOCITY AND ACCELERATION




Arranged by:
Name : Anis Septiana Sari
NIM : 08305141039









YOGYAKARTA STATE UNIVERSITY
2009

PREFACE

In the name of Allah SWT, the Author want to say thanks to God, because only God help I can finished my mathematical research which have a title “The Application of Differential Equation in Position, Velocity and Acceleration” on time and without matter problem.
This mathematical research made for completed the final task in the English II in Yogyakarta State University..
This mathematical research explain about the function of possibly theorem in our life. It can help our to calculate the possible a happening.
Hopefully this mathematical research can be useful to whosever read this report, specially to the students. For sure the author need developed critics and suggestions for the author reports in the future can be better.
In this case the Author would say thanks to :
· Allah SWT
· My Parents and my sister, who support me until now
· Mr Marsigit as my lecture
· My friends
· And the last is for all who did help the author, and the author can’t put their name in this report because the spaces











BACKGROUND

We often go to somewhere by kind of transportation. We can use motorcycle, bicycle, car or another transportation. We can arrive at somewhere more quickly by motorcycle than by bicycle. It approve that each transportation has different velocity. Velocity influence arrival in somewhere. Courese, we will choose a transportation that have quicker velocity tha another transportatio.
In Physics, especially in Mathematical method in phisical science position, velocity and acceleration be studied. If we study it, we can know the relation of them. The relation of position, velocity and acceleration is very important to be studied because it’s all be needed in our life. Velocity can be gotten from position. Acceleration can be gotten from velocity. It’s all be gotten use differential equation.
From the reason above,I arrange the reasearch of mathematics with the tittle “The Application of Differential Equation in Position, Velocity and Acceleration”.















CONTENTS
A. Introduction
Mr. Marsigit’s opinion at Wednesday, December 16th 2009, The aim of reasearch of amthematics is to examine and develop mathematic. Mr. Marsigit also explain tah the nature of mathematics consist of three parts. They are formal mathematics/axioms mathematics/pure mathematiscs, applied mathematics and school mathematics/concret mathematics/real mathematics. Mathematics is a deductive system consist of definition, axioms, and theorem in which there is no contradiction inside. Formal mathematics consist of number theory, group theory, Ring Theory, Filed theory, Eudidion Geometry, Non Eudid Geometry, etc. applied mathematics can be found in our life. In this my mathematics research I take “The Application of Differential Equation in Position, Velocity and Acceleration”
B. The Definition of Position, Velocity and Acceleration
Position
Ÿ In physics science, position and removal are the different meaning. Removal is vector mulberry. Position is scalar mulberry. So, removal have direction and position haven’t direction. But, they have same large. In the physics science, two different points have position and removal.
Ÿ Velocity is defined by position of somethhing and interval of time which is needed to cover a distance.
Ÿ Acceleration is defined by change of velocity intime interval.
Ÿ The symbol of position is s, the symbol of velocity is v , the symbol of acceleration is a.
C. Establish The Velocity and The Acceleration from Position Function
Ø From definition of velocity, we can write
, for approach nol
To interval of time approach nol


So
Ø From definition of acceleration, we can write
, for approach nol
To interval of time approach nol



So or

D. Application of Position, Velocity and Acceleration in daily life
we can use the formula ofposition, velocity and acceleration to solve the daily problem. For example:
s=(3t2 + 9t + 6) m. determine the velocity and the acceleration from it!
Solution:
Given: s=(3t2 + 9t + 6) m
Ask: v=…?
a=…?
Solve:
m/s
So the velocity is 6t +9 m/s. The graph of velocity is
9
O
s
t






m/s2
So the velocity is 6 m/s2. The graph of velocity is
6
O
a
t




























BIBLIOGRAPHY

Boas, Mary. L. Mathematics Method in The Physical Methode. Canada, Depsul University : 1983.
Kamajaya. Fisika SMA. Bandung, Grafindo Media Utama: 2004.