Introduction to Motion

Chapter 2 Lecture
Pearson Physics
© 2014 Pearson Education, Inc.
Introduction to
Motion
Prepared by
Chris Chiaverina

Chapter Contents
• Describing Motion
• Speed and Velocity
• Position-Time Graphs
• Equation of Motion

Describing Motion
• A frame of reference is referred to as a
coordinate system.
• A coordinate system in one dimension is
represented by an x axis with the origin located
at x = 0.
• Once an origin and a positive direction are
chosen, they must be used consistently.

Describing Motion
• The letter x is used to label position.
• An arrow drawn from the origin of a coordinate
system to an object is referred to as the object's
position vector.
• Whenever an object is in motion, its position is
changing.

Describing Motion
• Initial and final positions are indicated with xi
and xf, respectively.

Describing Motion
• Distance is the total length of the path taken on
a trip.
– No direction is associated with distance. It is a
scalar quantity.
– The SI unit of distance is the meter (m).
– When walking, distance is measured with a
pedometer.
– In a car, the distance is measured using an
odometer.

Describing Motion
• Displacement is defined as an object's change in
position.
– Displacement is a vector having both
magnitude and direction.
– The SI unit of displacement is the meter (m).
– The sign of the displacement vector indicates
the direction of motion. Motion in the positive
direction has a positive displacement. Motion
in the negative direction produces a negative
displacement.

Describing Motion
• Displacement is represented by the symbol Δx.
• Δx is shorthand for xf – xi. It does not mean Δ
times x.
• Δx is positive when the change in position is in
the positive direction and negative when the
change in position is in the negative direction.

Describing Motion
• Distance is the total length traveled;
displacement is the net change in position.
• An object's displacement is zero when it returns
to its starting point, even though it may have
traveled a considerable distance.

Describing Motion
• Example: The total length traveled in going from
the math classroom to the library and then to the
physics room is 13.0 m, whereas the
displacement is −3.0 m.

Speed and Velocity
• The rate of motion is referred to as speed.
• Speed describes how fast or slow something
moves.
• The average speed is defined as the distance
traveled divided by the elapsed time:
average speed = distance/elapsed time
• The SI units of average speed are meters per
second (m/s).
• Like distance, average speed is always positive.

Speed and Velocity
• An object's average velocity is defined as its
displacement per unit time:
average velocity = displacement/elapsed time
• The SI units of average velocity are meters per
second (m/s).
• The average velocity describes, on average,
how fast something is moving as well as the
average direction in which the object is moving.
• An object moving in the positive direction has a
positive average velocity. An object moving in
the negative direction has a negative average
velocity.

Position-Time Graphs
• A position-time graph is an alternative way of
representing data in a table.
• On a position-time graph, position data are
plotted on the y axis; time data are plotted on
the x axis.

• Example: Plotting the position and time
contained in a table results in a position-time
graph.

• A best-fit line drawn through data points can be
used to learn additional information about an
object's motion.

• To find position at a time not in original data,
– trace vertically from a given point on time axis
to the straight line, then
– trace sideways until you reach the position
axis.

• The slope of a straight line is equal to its rise
over its run.
• Any two points may be used to calculate the
slope of a straight line.
• On a position-time graph the rise corresponds to
the an object's position and the run to the
elapsed time.

• The slope of a position-time graph equals
average velocity.
• A straight line on a position-time graph
represents motion with constant velocity.

• A straight line on a
position-time graph
can have a positive,
negative, or zero
slope.
– A positive slope
means a positive
velocity.
– A negative slope
means a negative
velocity.
– Zero slope means
zero velocity.

• The greater the slope of a position-time graph,
the greater the velocity.
• The slope of a tangent line to a position-time
graph at a given instant equals the
instantaneous velocity.

Equation of Motion
• The position-time equation of motion gives an
object's position x at any time t if its initial
position and constant velocity are known.
• The position-time equation states that final
position = initial position + (velocity)(elapsed
time), or xf = xi + vt.

Equation of Motion
• The position-time equation of motion gives a
straight line for motion with constant velocity.
• The intercept of the straight line is the initial
position, and its slope is the velocity.

Equation of Motion
• Example: A skateboarder with an initial position of
1.5 m moves with a constant velocity of
3.0 m/s. What is the position of the
skateboarder?

Equation of Motion
• Solution: Substituting 1.5 m for the initial position
and 3.0 m/s for the constant velocity in the
equation of motion gives the following:
xf = 1.5 m + (3.0 m/s)(2.5 s) = 9.0 m

Equation of Motion
• The equation for a straight line is often written as
y = mx + b, where m is the slope and b is the y
intercept.
• This equation may be also written y = b + mx.

Equation of Motion
• Except for the labels, y = b + mx is the same
equation as the position-time equation of motion,
xf = xi + vt.

Equation of Motion
Position-time graphs intersect when objects have
the same location.

Introduction to Motion

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