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

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?

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

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.