Motion is Relative
Everything moves
even though they
may appear to be
at rest
Frame of Reference
Allows you to
measure changes
in position.
A coordinate system for specifying the precise location of an object in space
Frame of Reference
This diagram shows a change in position along the x-axis.
What about the y-axis?
How do I know?
Frame of Reference
Positive and negative changes depend upon the frame of reference
Displacement
Δx = xf - xi
Change in position = final position – initial position
Displacement
Does not always equal distance traveled
Displacement
Displacement
A teacher walks 4 meters East, 2 meters South, 4 meters West, and
finally 2 meters North.
Even though the teacher has walked a total distance of 12 meters, her
displacement is 0 meters. During the course of her motion, she has
"covered 12 meters of ground" (distance = 12 m). Yet when she is
finished walking, she is not "out of place" - i.e., there is no displacement
for her motion (displacement = 0 m).
Displacement Example
The diagram below shows the position of a cross-country skier at various
times. At each of the indicated times, the skier turns around and reverses the
direction of travel. In other words, the skier moves from A to B to C to D.
Determine the resulting displacement and the distance traveled by the skier.
Displacement Example
Consider a football coach pacing back and forth along the sidelines. The diagram
below shows several of coach's positions at various times. At each marked
position, the coach makes a "U-turn" and moves in the opposite direction. In
other words, the coach moves from position A to B to C to D.
What is the coach's resulting displacement and distance of travel?
Scalar vs. Vector
Vectors
Can be
represented
graphically
Scalar vs. Vector Example
Determine whether the following are scalar or
vector quantities.
scalar
a. 5 m
b. 30 m/sec, East vector
vector
c. 5 mi., North
d. 20 degrees Celsius scalar
e. 256 bytes
scalar
f. 4000 Calories scalar
Velocity
Velocity is a vector
Velocity
Velocity Example
Heather and Matthew walk eastward with a
speed of 0.98 m/s. If it takes them 34 min to
walk to the store, how far have they walked?
Variables
Equation
v = 0.98 m/s
Δt = 34 min
Δd = ??
v = Δd
Δt
60 s
1 min
Δd =v Δt
Δd =(0.98 m/s)(2040 s)
Units don’t match!
34 min
Solve
= 2040 s
Δd = 1999.2 m = 2 km
Instantaneous Velocity
Velocity of an object at a specific point in its path
Acceleration
Change in velocity over time
constant positive acceleration
constant velocity
zero acceleration
constant negative acceleration
Acceleration
Acceleration
is a vector!
Kinematics
vf = vi + at
Δx = vit + ½
vf
2=
2
at
2
vi + 2aΔx
Uniform Straight Line Acceleration