Chapter 3: Describing Motion
Chapter 3: Describing Motion
$5 word of the day…
• Kinematics:
– Branch of mechanics that studies the MOTION of a
body or a system of bodies without consideration
to its mass or forces acting on it
Section 3.1: Picturing Motion
• Motion:
– change in position (any which way)
• Motion Diagrams:
– series of images of a moving object that records
its position after equal time intervals
– At rest
– Speeding up
– Slowing down
– Constant speed
Motion Diagrams
• Sketch 3-5 consecutive “frames” of the position
of the object
1. Start by drawing object in initial positions
2. Draw a second “frame” with object in its next
position
– If object is moving to right, how far it is placed to
right depends on how fast it is moving (greater
separation of 2 objects = faster movement, less
separation of objects = slower movement…)
3. Same approach should be followed for the other
frames.
Position vs. time Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10m
Position vs. time Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10m
Position vs. time Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10m
Using The Particle Model
• Warning: size of object must be LESS than the
distance it moves & you must ignore internal
movements (ex. runner’s waving)
• Replace object with a single point,
concentrate on a center point of the body
• SIMPLY a simplified version of motion
diagrams
Rolling Ball Activity
• Motion diagram Sharades…
Section 3.2: Where & When?
Coordinate Systems
• One of the MOST important concepts in
Physics!!! ALWAYS define YOUR coordinate
system
– Decide where to put the measuring tape, when to
start/stop timing, which direction is +/– Origin = point at which the variables = 0
Scalars & Vectors
• Scalar quantity: tells ONLY magnitude (42 g,
50 s, 37 °C)
– Represented by: m (mass), t (time) & T (temp.)
• Vector quantity: tells magnitude AND
direction
– Represented by letter with arrow above (ex. v for
velocity, a for acceleration)
– In your text vectors = boldface letters (v, a)
• Length is proportional to magnitude
Position Vectors
• Draw through origin to center of mass of
object (or center of particle)
Vector & Scalar Practice
Time Intervals and Displacements
• Time interval: the difference between to (starting
time) and t1 (final time).
– Δ (Greek letter delta) = a change in a quantity
– Time interval mathematically is:
• Δt = tf – t0
• Displacement: defines distance and direction
between two positions I
I
0m
– Can be represented by x (text uses d)
– Δx = xf – x0
10m
Displacement Examples
0 1
5
2
4
3
3
4
2
5 (distance in meters)
1
0
Section 3.3 Velocity and Acceleration
Velocity
• Average Velocity, v = change in displacement over
time
– Mathematically: v = Δx = xf – x0 = m/s
Δt
tf – t0
• Average Speed = ratio of total distance traveled to
the time interval
– It is a scalar quantity (ex. mph or km/h)
• Instantaneous Velocity = the speed and direction
of an object at a particular instant in time
• Velocity can change when magnitude OR
direction changes
Velocity (continued)
• Review: v = Δx =
Δt
xf – x0
tf – t0
• Solve for displacement:
 Δx = vΔt
 xf – x0= vΔt
 xf = x0 + vΔt
Acceleration
• Average Acceleration
– Relates the change in velocity to the time interval
– a = Δv = v1 – v0
Δt = t1 – t0
– Velocity = m/s ÷ time = s
– acceleration = m × 1 = m/s2
s s
Using Motion Diagrams with Velocity
and Acceleration
• Point: To reduce confusion and enhance
understanding of terms such as position,
velocity and acceleration
• Review:
– Position = location of object
– Avg. Velocity = change in position ÷ by change in
time (a.k.a. rate of change of position of object)
– Avg. Acceleration = change in velocity ÷ change in
time (a.k.a. rate of change of velocity of object)
Drawing Velocity Vectors (arrows)
• Look at the separation between 2 consecutive
objects (rate of change of position) and draw the
length of the velocity arrow (the magnitude)
based on the position of separation
– Longer arrow = greater velocity,
– shorter arrow = shorter velocity
• Direction of velocity vector is in the direction of
motion
• Draw vector either directly below object or at
center of object mass (using particle model)
Velocity Motion Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10
m
Velocity Motion Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10
m
Velocity Motion Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10
m
Drawing Acceleration Vectors
• To draw the acceleration “arrow” (only one arrow
for constant acceleration motion diagrams) look
at the separtion between the velocity arrows
(rate of change of velocity).
– If velocity arrows are not changing in length AND/OR
direction, then the acceleration is ZERO
– If the velocity arrows are getting longer then the
acceleration is some constant in the same direction as
the velocity arrows.
– If the velocity arrows are getting shorter, then the
acceleration is some constant in the opposite
direction to the velocity arrows
Acceleration Motion Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10
m
Acceleration Motion Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10
m
Acceleration Motion Diagram
0 s------1 s-------------2 s-------------3 s--------------4 s
0 m---------------------------------------------------------10
m
Your Turn
• Get in groups of 3-4 and complete the motion
diagrams worksheet together
Relating Velocity, Acceleration, Time,
and Distance
• Kinematic Equations for Linear Motion and
constant acceleration only!