This document provides an introduction, definitions, and examples for analyzing rectilinear motion using vectors. It defines key terms like position vector, displacement, velocity, acceleration, and unit vectors. Examples are provided to demonstrate determining position from velocity functions and velocity from acceleration functions for rectilinear motion along the x, y, and z axes. One example problem calculates the displacement of a cat moving from position r1 = 5i + 6j to r2 = 5i + 2j, with the correct displacement being 4.

1. INSTRUCTIONAL MEDIA
THE MOVEMENT WITH
VEKTOR ANALYZE
LECTURER Drs.M.HIDAYAT,M.Pd.
COMPILED BY
TUTI RESRI
YANTI
RSA1C312017

2. INTRODUCTION
MATERIAL
EXAMPLE

3. INTRODUCTION
MATERIAL
POSITION
VECTOR
VELOCITY
ACCELERATIO
N
EXAMPLE

4. Introduction
THE MOVEMENT WITH VEKTOR
ANALYZE
Competition standart
. Analysist of natural indication and
regularity in scope mechanics point object.
BASIC COMPETENCE
1.1 Analyze straight motion, circular
motion and using the parabolic
motion vector.

5. RECTILINEAR MOTION ANALYSIS




DEFINITIONS
MEANING OF MOTION
An object is said to move when they change the
position of other objects that serve as a reference
point.
Body is said stationary (not moving)
position when the object was not changed to other
property used as a reference point.
MOTION STRAIGHT.
object-motion trajectory straight-called rectilinear
motion. -straight motion of an object in everyday life
generally irregular.

6. A. UNIT VECTOR
Unit vector is a vector whose
magnitude one, without force,
its direction along the
coordinate axes. For the
Cartesian coordinate system,
the unit vectors along the xaxis direction, y, and z.
The components of a vector to
the x and y axes, respectively
Ax = A cos α and Ay = A sin α.
Y
Ayj
α
x
Ax i

7. 1. position vector
The position of a car (A) of
the reference point (O) can
be expressed by a position
vector (position vector), ie
OA or r.
r = x i+y j -> twodimensional
Large (long) position vector
expressed
r = x i y j z k -> three
dimensional
A
yj
r=xi+yj
O
xi

8. Displacement experienced by
the point A in the time interval
t.
r = r2 – r1
r= xi+ yj
Large displacement can be
written
r
( x) 2 ( y ) 2
Direction of movement of point
A
y
tan
x
As a function of time, the
component vector
r(t ) x(t )i y(t ) j

9. 2. VELOCITY
Speed​​: displacement of the
object in a certain time
interval.Average speed:
position change interval
r
divided v
t
y
x
vx
vy
z
vz
t
t
t
The average speed
equation
v vx i v y j vz k
Large average speed
2
2
v
vx
vy
vz
Directions average
vy
speed tan
vx
2

10. INSTANTANEOUS VELOCITY : Velocity of object
r dr
any given moment
v lim
dx
dt
vx
t
dt
dy
dt
vy
The instantaneous velocity equation
dx
dy
dz
v
i
j
k
v vx i
dt
dt
dt
The instantaneous velocity
v
vx
2
vy
2
vz
2
Instantaneous velocity direction
tan
vy
vx
vz
dz
dt
v y j vz k

11. determine position of velocity function
dx
dt
vx
x
v x dt
y
t
dx
dx
t
vx dt
x0
0
dy
v y dt
y0
0
t
x x0
t
vx dt
y
y0
v y dt
0
t
x
0
t
x0
vx dt
0
y
y0
v y dt
0
On the z axis can be obtined in the same way

12. accaleration
Acceleration: change of
velocity per unit time
a. Average acceleration: a
change of pace once in a
while
a
ax
v
t
vy
vx
ay
t
t
az
vz
t
Average acceleration
aquation :
a
ax i a y j azk
The average acceleration :
2
2
a
ax
ay
az
Average acceleration
direction
tan
ay
ax
2

13. acceleration



b. instantaneous acceleration
Instantaneous acceleration (a) is defined as
the average acceleration for the time
interval approaches zero. Systematically,
instantaneous acceleration is formulated as
follows:
However, v = dr / dt to obtain

14. acceleration
c. Determine velocity from acceleration
function
dvx
ax
a x dt dvx
dt
v
v
t
dvx
v0
t
dv y
a x dt
v0
0
a y dt
0
t
t
vx v0 x
ax dt
vy
v0 y
a y dt
0
t
vx
0
t
v0 x
ax dt
0
vy
v0 y
a y dt
0
On the z axis can be obtined in the same way

15. example
1. Kedudukan awal seekor kucing terletak pada
r1 = 5i + 6j. Kemudian kucing bergerak sehingga
kedudukannya berpindah ke posisi r2 = 5i + 2j.
Perpindahan yang dialami kucing adalah....
A
4
B
5
C 7
D
9
E
25
Salah
Benar!