Kinematic With Vector Analysis

10 Feb 2012

my-son

If we observe a basket ball thrown into the basket, then the basket ball seems to move from one place to another. We can determine the position of the ball at any time by investigating the position of the ball as time function. The method of investigating and expressing object motion without reference to its cause, is the part of mechanics called kinematics.
We will learn the kinematics vectors of a plane which involves two-dimensional vector analysis where the position vector, displacement, velocity, and acceleration are expressed in unit vector (x axis) and unit vector (y axis).

A. Particle position on a plane
How do you express the particle position which is moving on a plane (two dimensional)? To express the position of a particle which moves on a plane, we can use the unit vector.
Those are which expresses the vector unit on x axis and which expresses the vector unit on y axis.
Observe, a particle is moving on plane, where as reference point. When t has coordinate , then the particle position on plane can be expressed by the following equation. persamaan-11

Where
=position vector on a plane
grafik1

The position vector can be described as in beside. If a particle moves forming a path on a plane during a certain time interval, at the time , the particle is at point where the position vector and at the time it is at point where the position vector (see Figure 1.4)

grafik2

The displacement of particles from point A1 to A2 can be represented as displacement vector of and it can be written as follows.
persamaan

In the relation to its components, the equation above can be written as follows.
persamaan1

B. Particle Velocity on a Plane
1. Average Velocity
Average velocity is displacement at each time interval. Determining the average velocity of a particle on a plane is the same as determining the average velocity of a particle on rectilinear path, but ?s is changed by vector position ? . Therefore, average velocity on a plane is mathematically can be determined as follows.

persamaan2

Where:

persamaan3

In this case, the average velocity

persamaan-12

is a vector quantity of which the direction is the same as

persamaan-13

The average velocity can be expressed in the form of vector components, by substituting

persamaan8

for the previous equation so we obtain the following relation.

persamaan7

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