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

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

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