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

We need initial velocity

Area under a-s curve= change in velocity (recall ∫a ds = ∫ v dv ).

½ (v1² – vo²) = s2

s1

a ds

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:)

4

-43

3

a(m/s2)

t(s)

a0-30 = dv/dt = 40/30 = 4/3 m/s2 a30-90 = 0 a90-120 = -4/3 m/s2

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)

s0-10 = v dt = = 400/3 m

s10-30 = v dt =

=

s0-30 = = 1133.3 m

vavg(0-30) = total distance / time

=