Chapter 2
Motion in One Dimension
SECTION 1
DISPLACEMENT AND VELOCITY
Motion
 Motion happens all around us in different
directions and different speeds.
 One – dimensional motion is the simplest form of
motion.

Example : Commuter train can move only forward and
backward along the straight track.
Motion
 Motion takes place over time and depends on
frame of reference.
 Frame of Reference – what you use to measure
changes in position.
Frame of Reference
 Frame of reference is basically what you are using
to measure changes in position of an object.
 If an object is at rest (not moving), its position
does not change with respect to a frame of
reference.
 As any object moves from one position to another,
the length of the straight line drawn from its initial
position to the object’s final position is called the
displacement of the object.
Displacement
 Displacement is a change in
position.
 Displacement = final position –
initial position.
 Displacement is not always
equal to the distance traveled.
 Displacement can be positive or
negative!
 in your book (unless stated
otherwise) RIGHT & UP will
be considered positive and
LEFT & DOWN will be
considered negative.
Displacement
 Displacement is not always equal to the distance
traveled.
Displacement
 Displacement can be positive or negative.
 There are only two directions to move on X axis and
two to move on Y axis


Right : Positive Left : Negative
Up: Positive Down : Negative
Displacement
Velocity
 Average Velocity is displacement of an object (Δx)
divided by time interval (Δt).

Equation : vavg
= Δx = xf-xi
Δt tf-ti
 Average Velocity can be positive or negative
depending on the sign of the displacement.


If displacement is negative, avg. velocity is negative.
Time interval is always positive
Guided Practice
 Open Books to pg. 44
Velocity Vs. Speed
 Velocity is not the same
as speed.

Velocity describes motion
with direction and
magnitude (numerical
value); speed has no
direction, only magnitude.
Ex: 55 m/s and 55 m/s
North
Chapter 2
One Dimensional Motion
SECTION 2 ACCELERATION
Velocity can be interpreted graphically…
 The motion of an object moving with constant
velocity will provide a straight-line graph of
position versus time. The slope of this graph
indicates the average velocity.
2-2 Acceleration
 Acceleration measures the rate of change in
velocity (usually per second).
 Acceleration has dimensions of length divided
by time squared.
 The units of acceleration in SI are meters per
second per second.

m/s2
Acceleration
 Three ways to Accelerate:

Object speeding up

Object slowing down

Object changing direction
Formula for Average Acceleration
 Average Acceleration =
Change in velocity
time required for change
OR
a avg = vf – vi
tf - t i
Let’s Practice with Average Acceleration...
 Turn to page 49 in your books and we can work on
practice 2B.
Acceleration is Velocity/Time
 Acceleration has direction and magnitude.
 The slope and shape of a graph plotting velocity vs.
time describes the object’s motion.
 When velocity on graph is
increasing : acceleration is positive
decreasing : acceleration is negative
constant : there is no acceleration
Motion with constant acceleration.
Velocity Vs. Time Graphs
Review - Displacement with constant uniform
Acceleration
 Displacement depends on acceleration, initial
velocity, and time.
 Displacement with constant uniform acceleration
is equal to :
ΔX = ½ (initial velocity + final velocity)(time
interval)
Solving for Final Velocity (Vf)
 Final velocity depends on initial velocity,
acceleration, and time.
aavg = Δv = vf - vi
Δt
tf - ti
 Displacement of an object depends on initial velocity,
final velocity, and time.
Δx = ½ (vi + vf)
Δt
 How can we solve for displacement if we don’t have
final velocity?
Solving for Vf & Displacement
 By rearranging the equation for acceleration, we can
find a value for the final velocity.
vf = vi + aΔt
 To find displacement of an object moving with uniform
acceleration we substitute the above expression for vf
into our displacement formula.
Δx = vi Δt + ½ a(Δt)2
Guided Practice
 Sample Problem 2D on pg. 55
Final Velocity after Any Displacement
 We can also obtain an expression that relates
displacement, velocity, and acceleration
without using time interval.
vf2 = vi2 + 2aΔx
Guided Practice
 Sample Problem 2E pg. 57
Chapter 2
One Dimensional Motion
SECTION 3
FALLING OBJECTS
Free Fall
 Free fall is acceleration due to gravity.
 Free fall acceleration is constant.
 Magnitude of free fall is 9.81 m/s2
 Direction of free fall is directed downward.
 negative direction (-)
 Free fall is denoted with the symbol g. (Sometimes
may be ‘a’ for acceleration due to gravity)
Free Fall
 In a vacuum, in the absence of air resistance, all
objects fall at the same rate.
What goes up must come down.
 What causes an object
that has been thrown
up into the air to come
back down?
 Free-Fall Acceleration
due to gravity is
always directed
downward and pulling
an object towards
Earth’s surface.
Recall Information
 Remember we learned about a formula that can be
used to find final velocity at ANY displacement…
vf2 = vi2 + 2aΔx
 We use this same formula but we change x to y
vf2 = vi2 + 2aΔy
Guided Practice
 Open books to pg. 63 Sample Problem 2F