Motion
Unit 1: Motion
Chapter 2: Describing Motion
 2.1
Position, Velocity, and Acceleration
 2.2
Position vs. Time Graphs
 2.3
Velocity vs. Time Graphs
2.1 Investigation: Position, Speed, and
Velocity
Key Question:
How are position, speed, and
velocity related?
Objectives:

Measure positive and negative positions.

Measure positive and negative velocity.

Compare speed and velocity.
Position, Velocity, and Acceleration
 Position
is a variable.
 Position
and distance are similar but not the same.
Both use units of length.
 Position
is given relative to an origin.
If a car moves 20 cm, what is
it’s new position?
Position and displacement

A change in position is called displacement.

A displacement of –20 cm means the car leaves the 50-cm
mark and moves toward the origin.

A displacement of 20 cm means the car moves away from the
origin.
Velocity
 The
velocity of an object (v) tells
you both its speed and its
direction of motion.
 Velocity
can be positive or
negative, so it includes
information about the moving
object’s direction.
 Constant
velocity means that
both the speed and the direction
an object is traveling remains
constant.
Positive velocity
 The
sign for velocity is
based on the calculation of
a change in position.
 The
change in position is
the final position minus the
initial position.
Negative velocity

Negative velocity means
the position is decreasing
relative to the starting
point.
Velocity
Average and instantaneous velocity
 Average
velocity is the total displacement divided
by the total time taken.
 Instantaneous
velocity describes the velocity of an
object at one specific moment in time or at one
specific point in its path.
Relative velocity
 Relative
velocity
describes the velocity of
an object with respect to
a frame of reference.

If you are sitting in a
chair, you are not moving
relative to Earth, but you
are moving at about
67,000 mph relative to
the Sun.
Using relative velocity
1.
2.
3.
4.
A people mover has a velocity of 1 m/s and is 150 m long.
If a man walks 2 m/s relative to the people mover, how
long will it take him to reach the opposite end if he walks in
the direction that the people mover travels?
Looking for: …the time in seconds.
Given: … velocity of the people mover (1 m/s), the relative
velocity of the walker (2 m/s), and the displacement (150 m).
Relationship: Use this version of the velocity equation:
t = Δx ÷ v
Solution: t = 150 m ÷ (1 m/s + 2 m/s)
= 150 m ÷ 3 m/s = 50 s
Acceleration
 Acceleration
is the rate at which velocity changes.
Acceleration
 Acceleration
and velocity are completely different
ways to describe an object’s motion.
 An
object can be accelerating when its velocity is
zero.
 Like
velocity, acceleration can be positive or
negative.
 An
object will have a positive acceleration when it is
speeding up in the positive direction, and when it is
slowing down in a negative direction.
Calculating acceleration
Calculating acceleration
A sailboat moves at 1 m/s. Wind increases its velocity
to 4 m/s in 3 seconds. Calculate the acceleration.
Looking for: .. the acceleration in m/s/s.
2. Given: … the initial velocity (vi=1 m/s), final
velocity (vf=4 m/s), and time (t=3 s)
3. Relationship: Use: a = (vf – vi) ÷ t
1.
4.
Solution: a = 4 m/s – 1 m/s = 3 m/s = 1 m/s
3s
3s
Units of acceleration
 An
acceleration in “meters per second per second
(m/s/s) is often written m/s2 or meters per second
squared.
Unit 1: Motion
Chapter 2: Describing Motion
 2.1
Position, Velocity, and Acceleration
 2.2
Position vs. Time Graphs
 2.3
Velocity vs. Time Graphs
2.2 Investigation: Position, Velocity, and Time
Graphs
Key Question:
How are graphs used to
describe motion?
Objectives:

Create graphs of velocity versus position and time.

Create a predictive model for the velocity of car rolling
down a hill.
Position vs. Time Graphs

Motion graphs are an important
tool used to show the relationships
between position, velocity,
acceleration, and time.

Graphs help test drivers and
engineers see how much of the
straight track each car covered in
equal time intervals.

Drivers can make adjustments in
how they operate cars.
Slope
 The
slope of a line is the
ratio of the “rise,” or vertical
change, to the “run,” or
horizontal change.
 The
rise is equal to the
height of the triangle.
 The
run is equal to the
length along the base of the
triangle.
Position vs. Time Graphs
 A position
vs. time graph
can tell you whether an
object’s velocity is constant
or changing. (Both cars
have constant velocity, but
Car A is faster than Car B.)
 If
the velocity is constant,
the graph is a straight line
with a constant slope.
Position vs. time graphs of
accelerated motion
 If
the velocity is changing, the slope changes, so the
graph curves.
Position vs. time graphs of
accelerated motion
 The
graph of an
object slowing down
is also curved.
 An
example is a car
coming to a gradual
stop at a red light.
Unit 1: Motion
Chapter 2: Describing Motion
 2.1
Position, Velocity, and Acceleration
 2.2
Position vs. Time Graphs
 2.3
Velocity vs. Time Graphs
2.3 Investigation: Position, Velocity, and Time
Graphs
Key Question:
What happens to the velocity of
an object as it moves downhill?
Objectives:
Explain the motion of the Energy Car, in terms of velocity and
acceleration, as it moves along an inclined track.
 Infer the meaning of acceleration from a velocity versus time
graph.
 Apply the acceleration formula to solve problems.

Velocity vs. time graphs
 The
velocity vs. time graph
has velocity on the y-axis
and time on the x-axis.
 On
this graph, constant
velocity is shown with a
straight horizontal line.
Velocity vs. time graphs
 The
velocity vs. time graph is the best tool for
understanding acceleration.
 It
clearly shows how the velocity of an object
changes with time.
Constant acceleration
 The
velocity vs. time graph
shown is for a ball in free fall.
 Since
the ball is accelerated by
gravity, it’s velocity increases by
the same amount: 9.8 m/s2.
 What
is the velocity of the ball
after 4 seconds?
Ans: 29.4 + 9.8 = 39.2 m/s2 ,down
Constant acceleration
 Don’t
confuse constant velocity with constant
acceleration.
 Constant
velocity means an object’s position
changes by the same amount each second.
 Constant
acceleration means an object’s velocity
changes by the same amount each second.
Calculating acceleration
 The
slope of a velocity vs. time graph represents the
acceleration of the object.
Calculating acceleration
 The
slope of a graph is
equal to the ratio of rise
to run.
 The
rise is the amount
the velocity changes.
 The
run is the amount
the time changes.
Calculating acceleration from a graph
Calculate the acceleration shown on
the graph.
Looking for: … the acceleration in m/s/s.
2. Given: … a graph of velocity vs. time
3. Relationship: The acceleration is equal to the
slope of the line.
4. Solution: slope = rise = 40 m/s = 4 m/s2
run
10 s
1.
Displacement
 The
velocity vs. time graph gives us a way to
calculate the object’s displacement even when its
velocity is changing.
 The
displacement is equal to the area on the graph.
Direction
 To
show direction on a velocity vs. time graph, we
must include a portion of the graph that shows
negative velocities.
Motion Graph Summary
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