1. Example
Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t3-21t2+60t+3 Analyze the motion of the particle for t>0
position
velocity
Acceleration

2. Example Graphically Algebraically Meaning 
Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t3-21t2+60t+3
Analyze the motion of the particle for t>0
Example
Graphically
Algebraically
Meaning 
Always on postive side of number line
Position
Never 0 (t>0), always postive
0<t<2 going pos direction
t=2 turning
2<t<5 going neg. direction + - +
Velocity
t=5 turning 2 5
t>5 going pos. direction
t=5
t=2
t=0
0<t<2 slowing down
2<t<3.5 speeding up 2 5
3.5 v a - - + +
3.5<t<5 slowing down
Acceleration + - - +
5<t speeding up

3. Position Direction of motion t --- v(t) positive direction negative
+++
+++ 2 5
+++
---
+++
a(t)
++++++ 2 5
7/2
slowing
down
speeding up
slowing
down
speeding up
stop
stop
position
velocity
Acceleration