1. Position vs. Time (PT) graphs Velocity vs. Time (VT) graphs
Motion Graphs 1 - Slope
Position vs. Time (PT) graphs
Velocity vs. Time (VT) graphs

2. Motion Graphs
Pictorial representations of data (or predictions/calculations)
There are two motion graphs that are
normally analyzed
Position vs. Time (PT) graphs
d = Vit +(1/2)at2 (accelerated motion)
d = Vt (constant motion, a = 0 so V = Vi = Vf)
Velocity vs. Time (VT) graphs
Vf = Vi + at (accelerated motion)
Vf = Vi (constant motion, a = 0 trivial case)

3. Role of Slope A slope shows ratio of a change (m =DY/DX)
A slope represents the rate that the Y changes with respect to how the X changes.
For many motion graphs the X axis represents time
Position vs. Time graph (in PT slope = velocity)
Velocity vs. Time graph (in VT slope = acceleration)
There are often 4 cases that have to be recognized
Increasing slope
Decreasing slope
Constant slope
No slope or slope is zero

4. Recognizing increasing slopes
(Curving-up parabola)
(Curving-down parabola)
Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

5. Recognizing decreasing slopes
(Curving-down parabola)
(curving-up parabola)
Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

6. Recognizing constant slopes
Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

7. Recognizing No Slope (slope=0)
Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

8. Slopes in PT and VT graphs
Velocity is the slope of a Position vs. Time graph
Acceleration is the slope of a Velocity vs. Time graph

9. Curving up or down (in PT graphs)
Curving up or down describes the way the graph curves;
in other words, how the slope is changing
For a Position vs. Time graph the curving up or down represents the acceleration

10. Curving up or down (in PT graphs)
Curving up parabola
The object’s acceleration is +
Curving down parabola
The object’s acceleration is -
No Curving
The object’s acceleration is 0

11. Graphs of increasing velocity
Position
Acceleration
+ parabola
- parabola
Velocity
+ slope
- slope
Position

12. Graphs of decreasing velocity
Position
Acceleration
- parabola
+ parabola
Velocity
+ slope
- slope
Position

13. Sample Problem 1 From the Position versus Time graph shown, graph the
velocity versus time graph.
d (m)
t (s)
V(m/s)
t (s)

14. Sample Problem 2 From the Position vs. Time graph shown, graph the
Velocity vs. Time graph.
For one moment here the slope is 0.
d (m)
t (s)
V(m/s)
t (s)