Find the velocity v(t) and speed ∥v(t)∥ of a particle whose motion is described by x=9, y=2t²−20t, z=6t³−45t².
a) v(t) = ⟨18t - 20, 4t - 20, 18t² - 90t⟩; ∥v(t)∥ = √(324t⁴ - 3240t³ + 8100t²)
b) v(t) = ⟨18t - 20, 4t - 20, 18t² - 90t⟩; ∥v(t)∥ = 18t² - 90t
c) v(t) = ⟨9, 4, 18t²⟩; ∥v(t)∥ = 18t² - 90t
d) v(t) = ⟨9, 4, 18t²⟩; ∥v(t)∥ = √(324t⁴ - 3240t³ + 8100t²)