Chapter 4
Motion in Two Dimension
4.0 The Displacement, Velocity, and Acceleration Vectors
Motion in Two Dimensions
The displacement, velocity and acceleration are all vectors involved in motion in two dimensions.
4.1 Application of Vectors to Equation of Motion
Knowing vectors, we can now apply them to position, velocity, and acceleration.
4.1.1 Position Vector
The position vector, also known as the radial vector, locates the position of a vector with unit vectors:
(position
vector) (4.1)
4.1.2 Displacement Vector
|
Fig. 4.1 Particle in motion.
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The displacement vector of a particle in motion can be defined as the change in position vector of the particle, see Fig 4.1:
Displacement 
(4.2)
This represents the displacement during the
interval 
.
In unit vector notation, we can write as per Eq. (4.1):
(position
vector) (4.3a)
where x1, y1, and z1 are the coordinates of point P1, (Fig. 4.1). Similarly for point P2, we have:
(4.3b)
Hence:
(displacement
vector) (4.4)
4.1.3 Average Velocity
The average velocity
is
the change in displacement vector, 
,
divided by the change in t (time),
Dt:
(average
velocity) (4.3)
4.1.4 Instantaneous velocity
The instantaneous velocity is the derivative
of the position vector, or the change in 
divided
by the change in t as the change in t approaches 0:
*
(4.4a)
Þ
(instantaneous
velocity) (4.4b)
where we have equated the like terms components, i.e.,
(4.5)
