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Chapter 11
Motion
Measuring Motion
• Motion: an object’s change in position to a reference point
– Frame of reference: a system for specifying the precise location of
objects in space and time
• When an object changes position with respect to a
frame of reference, the object is in motion
– You can describe the direction of an object’s motion with a
reference direction, such as north, south, east, west, up, or down
– Displacement is the change of an object’s position
• Measures how far it is between the starting and ending point
• Must always indicate direction
– Distance measures how far an object moves along a path
Measuring Motion
• Speed:
– Describes how fast an
object moves
– The distance traveled
divided by the time
interval during which
the motion occurred
• meters/second
(m/s), miles/hour
(miles/hr)
Measuring Motion
Measuring Motion
Measuring Motion
• Velocity is described relative to a reference
point
• Velocity: the speed of an object in a
particular direction
– Speed and direction of motion
• m/s North, miles/hr South
Measuring Motion
• Combined velocities determine the
resultant velocity
Measuring Motion
Measuring Motion
Measuring Motion
• Instantaneous speed:
speed measured in an
infinitely small time
interval
– Car’s speedometer
Measuring Motion
• The slope of a distance
vs. time graph equals
speed
Acceleration
• Acceleration: the rate
at which velocity
changes over time
– An object accelerates if
its speed, direction, or
both change
Acceleration
Linear Acceleration
Acceleration
• Acceleration can also
be a change in
direction
Centripetal Acceleration
• Constant speed in a
circle
– Speed same but
direction always
changing
Calculating Acceleration
Calculating Acceleration
Calculating Acceleration
Acceleration
• Acceleration is negative when slowing
down
Velocity-Time Graphs
•
•
Given below is a strobe picture of a ball rolling across a table. Strobe pictures
reveal the position of the object at regular intervals of time, in this case, once
each 0.1 seconds.
Notice that the ball covers an equal distance between flashes. Let's assume this
distance equals 20 cm and display the ball's behavior on a graph plotting its xposition versus time.
Velocity-Time Graphs
• The slope of the
position versus time
graph shown above
would equal 20 cm
divided by 0.1 sec or
200 cm/sec.
Velocity-Time Graphs
• The following graph
displays this exact
same information in a
new format, a velocity
versus time graph.
Velocity-Time Graphs
• This graph very clearly
communicates that the ball's
velocity never changes since the
slope of the line equals zero.
Note that during the interval of
time being graphed, the ball
maintained a constant velocity
of 200 cm/sec. We can also
infer that it is moving in a
positive direction since the
graph is in quadrant I where
velocities are positive.
•
Velocity-Time Graphs
• To determine how far
the ball travels on this
type of graph we must
calculate the area
bounded by the
"curve" and the x- or
time axis.
Velocity-Time Graphs
• As you can see, the
area between 0.1 and
0.3 seconds confirms
that the ball
experienced a
displacement of 40 cm
while moving in a
positive direction.
•
Velocity-Time Graphs
• Velocity is determined by the height of the graph (the yaxis coordinate
• Acceleration is determined by the slope of the graph
• Displacement is found by calculating the area bounded by
the velocity-graph and the x-axis
• Distance traveled would be the absolute value of each
sectional area since it is a scalar quantity that does not
depend on the direction of travel
• Average speed during a time interval is defined as the total
distance it traveled by the total time taken
• Average velocity during a time interval is defined as the
net displacement divided by the total time taken
Graphing Accelerated Motion
• Moving in a negative direction
and losing speed: no match
• Moving in a positive direction
and gaining speed at a slow
rate: D
• Traveling at a steady rate in a
positive direction: C
• At rest for an extended time: no
match
• Moving in a positive direction
but losing speed: A
• Moving in a positive direction
and gaining speed at a rapid
rate: B
Graphing Accelerated Motion
• During which time
interval(s) did it travel in a
positive direction?
• 0-10 min / 10-15 min / 1530 min
• During which time
interval(s) did it travel in a
negative direction?
• 30-40 min / 40-55 min
Graphing Accelerated Motion
• How far did the cart travel in
the first 10 minutes?
– Area of triangle a = ½ (b x
h)
– ½ (d=s x t)
– ½ (60m/ min x 10min) =
300m
• What was its average
acceleration?
• a = V2 – V1 / t2 – t1 =
• a = 60m/min – 0m/min/10min0min = 6m/min2
Graphing Accelerated Motion
• What was its average
acceleration between
10 and 15 minutes?
• a = V2 – V1 / t2 – t1 =
• 60m/min60m/min/15min10min=
• 0m/min/5min =
• 0m/min2
Graphing Accelerated Motion
•
•
•
•
•
•
•
•
How far did it travel between 15
and 30 minutes?
Area of triangle
A=1/2 (b x h)
½ x (15 min x 60 m/min) = 450m
What was its average acceleration
during this time interval?
a = V2 – V1 / t2 – t1 =
a = 0m/min - - 60 m/min/ 30min15min =
-4 m/min2
Graphing Accelerated Motion
• How far did it travel
between 30 and 40
minutes?
• A = ½ (b x h) +
• ½ (10 min x -40 m/ min) =
• ½ (-400) = -200m (200m)
• What was its average
acceleration during this
time interval?
•
•
•
a = V2 – V1 / t2 – t1 =
a = -40m/min – 0m/min/40min30min =
a= -40n/min / 10min = -4m/min2
Graphing Accelerated Motion
•
•
•
•
•
•
•
•
•
•
How far did it travel between 40
and 55 minutes?
A = ½ (b x h)
½ (15min x -40m/min) =
½(-600m)=
-300m (300m)
What was its average acceleration
during this time interval?
a = V2 – V1 / t2 – t1 =
a= 0m/min - -40m/min / 55min40min =
-40m/min / 15min =
2.66 m/min2 = 2.7m/min2
Graphing Accelerated Motion
• What was the total
distance it traveled?
• 0-10 (300m)
• 10-15 (300m) (lxh)
• 15-30 (450m)
• 30-40 (200m)
• 40-55 (300m)
–
•
1550m
What was its final
displacement?
• 550m
Graphing Accelerated Motion
• What was the cart’s
average speed for the
entire 55 minutes?
• s = d/t
• s = 1550m / 55min
• s = 28.18m/mim =
28.2m/min
• Its average velocity?
• Net displacement / total
time =
• 1050m – 500m / 55min =
• 550m/55min = 10m/min
Motion and Force
• Fundamental Forces:
– Are the forces of gravity, the electromagnetic force, the
strong nuclear force, and the weak nuclear force
• Vary in strength
• Can act through a contact
– Pushes and pulls of contact forces
• Balanced and Unbalanced Forces
– Whenever there is a net force acting, the object
accelerates in the direction of the net force
• Balance forces do not change motion
• Unbalanced forces do not cancel completely
Motion and Force
• The force of friction always opposes the motion:
friction is a force that opposes motion between
two surfaces that are in contact
– Static: friction between surfaces that are stationary
• Force that resists the initiation of sliding motion between two
surfaces that are in contact and at rest
– Kinetic: friction between moving surfaces
• Friction that opposes the movement of two surfaces that are in
contact and are moving over each other
– Sliding
– Rolling