3.107: Cubic displacement; direction change and distance

0606/21/O/N/24 — Question 8 · 10 marks

(a)
A particle has displacement x=t3−8t2+12tx=t^{3}-8t^{2}+12t for t⩾0t\geqslant 0. Find the time when the particle changes direction.
[3]
(b)
Show that the particle is moving towards OO when t=0t=0.
[3]
(c)
Find the total distance travelled during the first 22 seconds.
[4]