1. 3.7 Rates of Change In the Natural and Social Sciences
Position, Velocity, and Acceleration with rates of change,

2. A particle moves according to the law of motion 𝑠=𝑓 𝑡 , 𝑡≥0
A particle moves according to the law of motion 𝑠=𝑓 𝑡 , 𝑡≥0. t is measured in seconds and s in feet.
𝑓 𝑡 = 𝑡 3 −6 𝑡 2 +9𝑡
Find the velocity at time t.
What is the velocity after 1 second?
When is the particle at rest?
When is the particle moving in the positive direction?

3. Find the total distance traveled during the first 6 seconds.
Draw a diagram like Figure 2 (p225) to illustrate the motion of the particle.
Find the accelerations at time t and after 1 second.
Graph the position , velocity, and acceleration functions for 0≤𝑡≤6

4. When is the particle speeding up? When is it slowing down?
Speeding up when velocity and acceleration are either both positive (v>0 and a>0) or both negative (v<0 and a<0). When they have the same sign. (The particle is pushed in the direction it is going.)
Slowing down when velocity and acceleration have opposite signs.