KINEMATICS WITH VECTOR ANALYSIS
Suppose you are now a pilot. Your aircraft
has just leaved the airport. Your aircraft is
then accelerated to the sky and moving to
other airport. In your cabin, there are
instruments whose function is to inform the
position of the aircraft to controlling room
that is located in airport. How can these instruments inform the position, velocity and
acceleration of the air craft? You will learn it in this chapter. In order to understand that,
you must read the concepts listed below:
1. Derivation and integral of a mathematics function
2. Particle position on a plane
3. Particle velocity on a plane
4. Particle acceleration on a plane
In this section, I will give some exercises to check your understanding on first and second
concepts:
EXERCISES:
1. Determine first derivation (
dy
) of these functions :
dx
a. y = 2x
b. y = 2x – 5x2
c. y = 4
d. y = (x + 5)5
e. y =
x3  2x
x2
2. Determine the result of these integral:
a.
 (2t  6)dt
b.
 (3t
2
 6t )dt
2
c.
 (8t
3
 6t 2 ) dt
1
2
d.
 2 x( x
2
 4)dx
2
 4)dx
0
0
e.
 2 x( x
2
3. What is the difference between distance and displacement?
4. Position of a particle is given by : r = 4t2i – (6t2 + 2t)j where t is in second and r
is in meter. Determine the value and the direction of the displacement of the
particle from t = 1s to t = 2 s!
5. For a body that is moving to arbitrary directions, is it correct if we say that the
distance that is covered by the body is the same with the value of displacement
done by the body?
Hint:
To answer question number 1 and 2, ask your friend that is on XII grade or ask your
mathematic teacher. For question 3 and 4, read your text book