FACULTY OF CIVIL AND ENVIRONMENTAL ENGINEERING BFC 14003 ENGINEERING MATHEMATICS II SECTION 1 TITLE: LINEAR MOTION LECTURER: DR MOHD HANIFI BIN OTHMAN
GROUP MEMBERS: NO
NAME
NO. MATRIC
1
MUHAMMAD AZRI BIN SAHARUM
DF160088
2
MUHAMMAD HANIF BIN KOSNAN
DF160063
3
MUHAMAD ZAHIN IMAN BIN ZABIDDI
DF160055
4
RAZIQ FAWWAZ BIN RAZAKI
DF160074
5
RD. KHIRILAKHBAR ARIF
DF160002
1
CONTENTS
TOPICS
PAGES
APPRECIATION
3
1.0 INTRODUCTION
4
2.0 PROBLEM STATEMENT
4
3.0 STUDY AREA
5
4.0 THEORIES
6
5.0 CALCULATION
7-9
6.0 DISCUSION & CONCLUSION
10
7.0 REFERENCE
11
8.0 APPENDIX
12
2
APPRECIATION
Assalamualaikum, f irstly we would like gratitude to God because giving us the
opportunity to complete this assignment within the time given by our lecturer. We also want to say thank you to our parent because they keep supporting us given words, money and facilities that we need to solve any work or assignments that have been received.
Not to forget our friends who had been very helpful, thanks you very much for your contribution of information as well as your cooperation in works and discussion till we can finish the assignment completely.
Last but not least, we would like to thank to our lecture Dr. Nor Amani Filzah Binti Mohd Kamil because she always helps and spends time although just for a while for us to complete this assignment. Once again, thank you to all of our teammate who had helped so much in completing this project.
3
1.0
INTRODUCTION
Calculus is a branch of mathematic involving or leading with calculation that dealing with continuously varying functions such as velocity and acceleration, rate of change and maximum and minimum value of curves. Calculus differentiation and integration was developed to improve this understanding. Differentiation and integration can help us solve many types of real-world problems. Calculus has widespread application in science and engineering and is used to solve complicated problem for which algebra alone is insufficient. By using differential equation, Mathematics is an aid to representing and attempting to resolve problem situations in all disciplines. We use the derivative to determine the maximum and minimum values of particular functions like cost, strength, amount of material used in a building, profit, loss, and etc. Derivatives are met in many engineering and science problems, especially when modelling the behavior of moving objects.
2.0
PROBLEM STATEMENT
As a student in UTHM, we always keep hearing bad news about buses that didn’t follow the university rule on speed in the university area. The speed that is allowed in university is 30 km/hr. Therefore, as an engineering student, we try investigate whether the bus driver didn’t follow the rule or it’s just some rumors from students. So we try to figure it using theory of physic and application of mathematic to define the speed of velocity of the buses and how long going it takes if the bus diver follows the rule of 30km/hr in campus area for safety of student.
4
3.0
STUDY AREA
Our study area is focused in area of University Tun Hussien Onn Malaysia (UTHM), that is, the area from the bus stop at Faculty Vocational Technology Education (FPTV) to the bus stop at the Faculty of Civil and Environmental Engineering (FKAAS). We select area in because, it is bus routes between the library to other faculties. Therefore, this area is a good spot among students waiting for the bus. So, this area is th e area most suitable to serve as our study area.
We have been carrying out activities to collect data using kinematic methods in which to find the displacement, velocity and acceleration. Bus stop at faculty vocational technology education (FPTV) as point A, while the bus stops at the faculty of civil and environmental engineering (FKAAS) as point B.
5
FILA TABLE :
4.0
THEORIES
Kinematics, is a description of motion where to find speed distance and direction. Kinematics deal with three quantities that is displacement, velocity and acceleration. An accelerating object will change its velocity by the same amount in each of second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity. If an object is changing its velocity (whether b y a constant amount or a varying amount) then it is an accelerating object. And an object with a constant velocity is not accelerating. The data tables below depict motions of objects with a constant acceleration and a changing acceleration. This is also similar to the mathematic topic that is “Rate Of Change” in differential equation application where the subject should be derived and differentiate to solve the problem occurred.
6
5.0
CALCULATION
To calculate the velocity of bus, we manage to record time and distance by the help of group members, we manage to record times that takes by the bus from point A to point B. Point A we set up at bus stop Falkuti Pendidikan Teknologi Vocational (FPTV) and point B we set up at bus stop Falkulti Kejuruteraan Awam dan Alam Sekitar (FKAAS) that is 500m distance between two point.
No try
Time taken from Point A - Point B
1
42 sec
2
44 sec
3
40 sec
Avg.
42 sec
Average time = 42+40+44 (sec) 3 = 42 sec
Distances from point A to B is 500m
km = 500 m 1000 m =0.5 km
When the time is 42sec what speed of velocity of the bus in km/hr
Convert sec to hour =
42
sec
(60x60) sec 7
=
42 sec 3600 sec
= 0.0117 hr
Velocity of the bus =
0.5 km 0.0117 hr
= 42.735 km/hr ~ 43 km/hr
Therefore, 43km/hr > 30 km/hr
1.
How to develop order Differential Equation ?
=
2.
How to determine the constant value ?
By using v (0) = 30
= 1 ∫ = ∫ ln V = kt + C V =
+ 8
V = A t = 0, v = 30 30 = A () A = 30
3.
How to determine rate (k)?
By using v (50) = 35 t = 50 s, v = 35 km/hr V = A 35 = 30 (5) k = 3.083× 10−3
4. How to determine time required for bus to stop? Find t if the velocity of bus is 43 km/hr. t = ?, v = 43 km/hr 43 = 30 3.83× ()
t = 116.77 s
9
6.0
DISCUSSION & CONCLUSION
After the investigation by using the simple physic rule and differential equation in mathematic engineering we can conclude that most bus driver didn’t follow the 30 km/hr speed limit rule in campus area. This is because most of them drive with the speed of velocity between 40-45 km/hr and this speed is totally out of the speed limit ranges that UTHM have provides to the all diver and can give harmful or bad scenario to student nor to the university like accident. When the speed of velocity is 43km/hr the time taken for the bus to stop at point B is 116.66 sec with distance of half kilometer from point A. In Conclusion, as a student or stuff when it’s come to rule we should follow all the rule and regulation that have been provided to us in term of safety. The speed limit that is allowed in campus areas is 30 km/hr and if any driver didn’t follow it will cause some dangerous to any other student. Therefore, the university should warn the bus driver or take an action to them so that they can follow the speed rule that is allowed in campus areas. And we also as engineering student should use what we have learn and applied it the knowledge that we have to solve all the problem because everything is related to application of mathematics and science in real life.
10
7.0
REFERENCE
1. Reference Book
Basic Engineering Mathematic, Fifth edition John Bird.
2.
Website: http://sdrc.uthm.edu.my/docs/SDRC-TR1.pdf
3.
Website: https://www.khanacademy.org/search?search_again=1&page_search_query=Ho
w+to+determine+first+order+equation+rate+%28k%29
11
8.0
APPENDIX
Sikun Jaya company, bus that being use by Uthm as a public transport in campus area.
UTHM Map
12
