1. GRAPHICAL ANALYSIS OF MOTION
Chapter 2.3
GRAPHICAL ANALYSIS OF MOTION 1

2. Describe the following motion

3. from the graph to an actual motion and
In Kinematic, when you work on a graph analysis problem you must translate:
from the graph to an actual motion and
from an actual motion to its representation on a graph. 3

4. Objective Solve “slope of a curve” with unit a graph.
Identify direction of motion from a graph
Transfer a position vs. time graph to velocity vs. time graph.
Solve “area under a curve” with right unit
Solve displacement and distance from speed vs. time graph. 4

5. Example: a line drawn at 45° always has a slope of 1 (no units),
 “slope of a curve”
Students don’t recognize that a slope has units or how to determine those units.
Example: a line drawn at 45° always has a slope of 1 (no units),
Position vs. time graph, slope is a velocity and unit is [m/s] 5

6. When the velocity is constant, the average velocity is equal to the instantaneous velocity at any time. 6

7. a. x
Object starts at the origin and moves in the positive direction with constant velocity. t
Object starts to the right of the origin and moves in the negative direction with constant velocity ending at the origin. x b. t 7

8. Object moving to the right at a fast constant speed.
A qualitative description of the motion depicted in the following v-versus-t graphs: a. v
Object moving to the right at a fast constant speed. t b. v
Object moving to the left at a slow constant speed. t

9. Object starts to the right of x
Object starts to the right of
the origin and moves in the positive direction with
constant velocity. t x d.
Object starts to the left of the origin and moves in the positive direction with constant velocity ending at the origin. t 9

10. Object starts to the left of the origin and moves in x
Object starts to the left of the origin and moves in
the negative direction with constant velocity. t x f.
Object starts to the right of the origin and moves in the negative direction with constant velocity. t 10

11. v t
Object starts at R of origin.
Moves R at constant v, stands still
then moves L at faster constant v.

12. Object moves L at constant v, then x t
Object moves L at constant v, then
moves R at constant v but slower, then stands still. 12

13. • Students don’t recognize that an “area under the curve”
Area under a curve
• Students don’t recognize that an “area under the curve”
has units or how the units of an “area” can be something other than area units.
The area under the v-versus-t curve is displacement.
But distance is a length?
How can a length equal an area? 13

14. The students should be able to calculate the area under the v-t curve and understand that the value obtained is the displacement 14

15. Object starts at R of origin. Moves L at constant v, stands still then
moves L again at constant v but faster. 15

16. then moves L at constant v but slower.x v t
Object is at rest.
Moves R at constant v,
then moves L at constant v but slower. 16

17. Practice: find displacement

18. Practice: find displacement

19. INTERPRETING GRAPHS
Give a qualitative description of the motion at the different time intervals. v
(m/s) t
(s)

20. INTERPRETING GRAPHS
Give a qualitative description of the motion at the different time intervals.
Stops, Resting,
speeding up + direction
Slowing down + direction,
speeding up - direction,
Slowing down - direction,
Constant speed + direction,
constant speed - direction v
(m/s) t
(s)

21. Motion diagram and Position vs, Time graph
Look at the following motion diagram
Transfer this motion into position vs. time graph.
What is mathematical equation of this graph?