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

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

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

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

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

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

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

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

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

EXAMPLE (Solution:) a0-30 = dv/dt = 40/30 = 4/3 m/s2 a30-90 = 0 a90-120 = -4/3 m/s2 4 -4 3 a(m/s2) t(s)

EXAMPLE (continued)

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

GROUP PROBLEM SOLVING a(m/s²) t(s)

GROUP PROBLEM SOLVING (continued) Ds0-10 = ò v dt = = 400/3 m Ds10-30 = ò v dt = = s0-30 = = 1133.3 m vavg(0-30) = total distance / time

End of 12.3 Let Learning Continue