Transcript position and displacement

Motion in Two and Three
Dimensions
4-2 Position and Displacement
The position vector is typically used to
indicate the location of a particle.
The position vector is a vector that extends
from a reference point (usually the origin)
to the particle.
The position vector
for a particle is the
vector sum of its
vector components.
In unit vector notation
can be written as:
The coefficients x, y, and z are the scalar
components.
The coefficients x, y, and z give the
particle’s location along the coordinate axes
and relative to the origin.
The figure shows a particle with position
vector:
As a particle moves, its position vector
changes in such a way that the position
vector always extends to the particle from
the reference point (origin).
If the position vector changes from
during a certain time interval, then the
particle’s displacement
during that
time interval is:
We can rewrite this displacement as:
Sample Problem 4-1
Sample Problem 4-1
In figure 4-2 the position vector for a
particle is initially
and then later it is
What is the particle’s displacement
from
?
Sample Problem 4-2
A rabbit runs across a parking lot on which
a set of coordinate axes has been drawn.
The coordinates of the rabbit’s position as
functions of time t are given by:
x = -0.3t2 + 7.2t + 28
y = 0.22t2 - 9.1t + 30
At t = 15 seconds, what is the rabbit’s
position vector in unit-vector notation
and as a magnitude and an angle?
Graph the rabbit’s path for t = 0 to t = 25 s.
Average Velocity and
Instantaneous Velocity
If a particle moves through a displacement
in time interval D t, then its average
velocity is:
Written as vector components:
The instantaneous velocity is the value that
approaches in the limit as Dt shrinks to
0.
The direction of the
instantaneous velocity
of a particle is always
tangent to the
particle’s path at the
particle’s position.
The velocity
of a
particle along with the
scalar components
of
Sample Problem 4-3
For the rabbit in sample problem 4-2, find
the velocity at time t = 15 s, in unit
vector notation and as a magnitude and an
angle.
Average
Acceleration and Instantaneous
Acceleration
When a particle’s velocity changes from
to
in a time interval Dt, its average
acceleration a avg during Dt is: