1. ERRATIC MOTION Objectives:
Determine position, velocity, and acceleration using graphs.

2. APPLICATION
Having a v-s graph, can we determine a at s = 300m?
How?

3. GRAPHING
-Better to handle complex motions difficult to describe with formulas.
-Graphs provide a visual description of motion.
-Graphs are true meaning of dynamics

4. S-T GRAPH
V-t: Find slope of s-t (v = ds/dt) at various points.

5. V-T GRAPH
a-t: Find slope of v-t (a = dv/dt) at various points.

6. A-T GRAPH v-t is the area under the a-t curve.
We need initial velocity of the particle.

7. A-S GRAPH
Area under a-s curve= change in velocity (recall ∫a ds = ∫ v dv ).
½ (v1² – vo²) = ò s2 s1
a ds
We need initial velocity

8. V-S GRAPH
Knowing velocity v and the slope (dv/ds) at a point, acceleration is.
a = v (dv/ds)

9. EXAMPLE Given: v-t graph for a train moving between two stations
Find: a-t graph and s-t graph

10. EXAMPLE (Solution:) a0-30 = dv/dt = 40/30 = 4/3 m/s2 a30-90 = 0
a = -4/3 m/s2 4 -4 3
a(m/s2)
t(s)

11. EXAMPLE (continued)

12. GROUP PROBLEM SOLVING Given: The v-t graph shown
Find: The a-t graph, average speed,
and distance traveled for the 30 s interval

13. GROUP PROBLEM SOLVING
a(m/s²)
t(s)

14. GROUP PROBLEM SOLVING (continued)
Ds0-10 = ò v dt = = 400/3 m
Ds10-30 = ò v dt = =
s0-30 = = m
vavg(0-30) = total distance / time

15. End of 12.3
Let Learning Continue