Linear Motion
AP Physics B
2012-2013
Frame of Reference
 The frame of reference is dependent upon the
observer.
 It can change given the situation.
 Example: If a person is walking at 2 m/s towards the
back of a bus that is traveling forward at 17 m/s, how
fast is the person moving?
Coordinate System
 In order to solve any problems in physics, we need to set a
coordinate system.
 In general, up and to the right are positive while down and to
the left are negative.
 However, we can change these conventions depending on what
is most convenient for the problem that we are currently
solving.
 Just be consistent throughout the problem!
Distance vs. Displacement
 Distance is the total traveled.
 Displacement is the straight line “distance” between
a beginning and end point with a direction.
 Example: Find the total distance and displacement
traveled if Joe walks 4 m north, 2 m west, 6 m north,
then 7 m east.
Speed vs. Velocity
 Speed is a measure of how fast an object is traveling.
 Average speed = distance / time
 Velocity is a measure of how fast an object is traveling
in a direction.
 Average velocity = displacement / time
Instantaneous Velocity
 Instantaneous velocity is defined as the velocity that
an object has during an infinitesimally small time
interval.
Acceleration
 Acceleration is a change in velocity.
 An object may either be speeding up, slowing down,
or changing direction.
 Average acceleration is the average velocity divided
by the time taken to make this change.
Acceleration
 Negative acceleration doesn’t always mean that an
object is slowing down; only that it is accelerating in
the negative direction.
 Positive acceleration doesn’t always mean that an
object is speeding up; only that it is accelerating in the
positive direction.
Acceleration
 “Acceleration” occurs when the acceleration
experienced is in the same direction as the velocity.
 “Deceleration” occurs when the acceleration
experienced is in the opposite direction as the
velocity.
Motion at Constant Acceleration
 We have several equations that are useful in solving
problems where there is constant acceleration.
 These equations are derived from basic equations (we
can derive these if you want).
Motion at Constant Acceleration
Falling Objects
 All objects fall at the same rate when there is no air
resistance.
 Let’s consider the coordinate system for an object
that is simply falling.
 It is once again a one-dimensional problem, only now
occurring in the vertical plane.
Falling Objects
 This is an important piece of information, since this
means that we can use the exact same equations in
order to solve problems.
 The only difference is that now we have a value for
acceleration.
 The acceleration due to gravity is a constant – 9.80
m/s2.
Graphical Analysis
 Let’s now consider what happens when we want to
graph position vs. time.
 Which would we put on the x-axis? On the y-axis?
 x-axis – time
 y-axis – position
Graphical Analysis
 If we plot position vs. time, what possible information
will this provide?
 Let’s draw a sample graph and analyze it.
Position vs Time Graphs
 Particles moving with no acceleration
(constant velocity) have graphs of
position vs time with one slope. The
velocity is not changing since the
slope is constant.
 Position vs time graphs for particles
moving with constant acceleration
look parabolic. The instantaneous
slope is changing. In this graph it is
increasing, and the particle is speeding
up.
Graphical Analysis
 Let’s now consider what happens when we want to
graph velocity vs. time.
 Which would we put on the x-axis? On the y-axis?
 x-axis – time
 y-axis – velocity
Graphical Analysis
 If we plot velocity vs. time, what possible information
will this provide?
 Let’s draw a sample graph and analyze it.
Uniformly Accelerating Objects
 You see the car move
faster and faster. This is a
form of acceleration.
 The position vs time graph
for the accelerating car
reflects the bigger and
bigger Dx values.
 The velocity vs time graph
reflects the increasing
velocity.
Describe the motion
 This object is moving in the positive
direction and accelerating in the
positive direction (speeding up).
 This object is moving in the negative
direction and accelerating in the
negative direction (speeding up).
 This object is moving in the negative
direction and accelerating in the
positive direction (slowing down).
Pick the constant velocity
graph(s)…
x
v
A
x
C
t
v
B
t
D
t
t
Draw Graphs for
Stationary Particles
x
v
a
t
Position
vs
time
t
Velocity
vs
time
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Acceleration
vs
time
Draw Graphs for
Constant Non-zero Velocity
x
v
a
t
Position
vs
time
t
Velocity
vs
time
t
Acceleration
vs
time
Draw Graphs for Constant
Non-zero Acceleration
x
v
a
t
Position
vs
time
t
Velocity
vs
time
t
Acceleration
vs
time