Motion Along the x-axis

𝑥′ 𝑡 = 𝑣 𝑡 = 𝑡2 − 2𝑡 − 3 = 0(t – 3)(t +1)=0

t = 3, -1

On the interval (0,2)

𝑥′ 𝑡 = 𝑣 𝑡 = 3𝑡2 − 12𝑡 + 9

𝑥′′ 𝑡 = 𝑣′ 𝑡 = 𝑎 𝑡 = 6𝑡 − 12

3𝑡2 − 12𝑡 + 9 = 0𝑡2 − 4𝑡 + 3 = 0

(t-1)(t-3)=0t=1,3

+ 1 - 3 +