Question

A particle moves along a line according to the law s(t) = 2t³ – 9t² + 12t – 4, where t ≥ 0. At what times the particle changes direction?

Answer 1

s = f(t) = 2t³ – 9t² + 12t – 4

V = f'(t) = 6t² – 18t + 12

V = 0 ⇒ 6(t² – 3t – 2) = 0

(t – 1)(t – 2) = 0

t = 1, 2

When t < 1, (say t = 0.5)

V = 6(0.25 – 1.5 + 2) = +ve

When 1 < t < 2, (say t = 1.5)

V = 6(2.25 – 4.5 + 2) = – ve

When t > 2, (say t = 3)

V = 6(9 – 6 + 2) = +ve

So the particle changes its direction when t lies between 1 and 2 secs.