Kinematics

1
Kinematics

• AP Physics

2
Motion Position

• An objects position at any moment is relative to
  some arbitrary, stationary reference point
• Ex the person sitting next to you
• Motion is a change in position
• You do not need to witness movement for motion to
  take place

3
Restrictions

• The moving object is considered to move like a
  particle (no rolling).
• We dont care WHY an object moves. In kinematics,
  we will only examine HOW it moves.

4
Distance vs. Displacement

• Distance is a scalar quantity (it has magnitude
  only).
• Displacement is a vector quantity and is always
  relative to the origin.

5
Distance vs. Displacement

• Stand in one of tiles on the floor (leave a good
  amount of room between you and your neighbor.)
• This is your origin. Determine /- directions.
• Move 3 tiles to the right.
• Move 2 tiles forward.
• Move 5 tiles to the left.
• Move 2 tiles backward.

6
Distance vs. Displacement

• What is your displacement?
• What is the total distance you traveled?
• Displacement is noted ?x.
• ?x x x0

7
Position vs. time graphs

• Consider a car moving with a constant velocity,
  as shown below

8
Position vs. time graphs (cont.)

• Create a data table for time and position (dont
  forget your units!)

9
Position vs. time graphs (cont.)

• Now graph the cars position versus time.
• Put time on the horizontal axis (x-axis)
• Place position on the vertical axis (y-axis)
• Use appropriate divisions for time and position
• Dont forget to label each axis with its name and
  units (also label the table as a position vs.
  time table)

10
Position vs. time graphs

• Your graph should look something like this
  (without the dotted lines)

11
Slope of x(t)

• What are the units associated with the slope of a
  position vs. time graph?
• m/s
• Through that incredibly useful tool Dimensional
  Analysis you can conclude the slope of an x(t)
  graph is velocity.

12
Position vs. time graphs

• On a distance-time graph, the slope of the line
  is velocity
• A straight line represents constant velocity
• What is the velocity of the car in the previous
  example?

13
Position vs. time graphs

• How are the velocities different in the following
  graphs?

14
Position vs. time graphs

• How about these two graphs, how are the
  velocities different?

15
Position vs. time graphs

• A negative slope on a position vs. time graph
  indicates a negative velocity

16
Position vs. time graphs

• What do you think is happening in this graph?

17
Position vs. time graphs

• The graph indicates an increasing velocity . . .
  this time there is acceleration.

18
Sketching v(t)

• Sketch a graph of velocity vs. time given the
  following graph

19
Velocity vs. time

• Your graph should look like this

10
Velocity (m/s)
8
6
4
2
1 2 3 4
5
time (s)
20
Velocity

• Velocity is the rate of change in position (a
  measure of how fast something is moving)
• Units distance/time (mph m/h)
• SI m/s
• Velocity is a vector quantity.
• Speed is the scalar quantity associated with
  velocity.

21
Velocity vs. time

• According to dimensional analysis, what are the
  units associated with the slope of a v(t) graph?

10
Velocity (m/s)
8
6
4
2
1 2 3 4
5
time (s)
22
Velocity vs. time

• Sketch the graph of acceleration vs. time.

10
Velocity (m/s)
8
6
4
2
1 2 3 4
5
time (s)
23
Velocity vs. time

• Your graph should look like this

5
Acceleration (m/s2)
4
3
2
1
1 2 3 4
5
time (s)
24
Acceleration

• Acceleration is the rate of change in velocity (a
  measure of how fast velocity is changing)
• Units velocity / time
• SI m/s2
• Acceleration is a vector quantity.

25
Fun with Graphs
x (m)
1.2
1.0
0.8
0.6
0.4
0.2
5
10
15
-0.2
t (s)
-0.4
Sketch the velocity vs. time graph associated
with the above motion. Include velocity values
and units!