A car moves so that its position $s(t) = 3t^3 - 12t^2 + 5$ (m, t in s)…

Question

A car moves so that its position $s(t) = 3t^3 - 12t^2 + 5$ (m, t in s). The time at which the car comes to **momentary rest** (and reverses direction) and the position at that time are:

Accepted Answer

D. Two points exist; $t = 0$ and $t = 8/3$

$v(t) = ds/dt = 9t^2 - 24t = 3t(3t - 8) = 0$ ⇒ $t = 0$ or $t = 8/3$ s. At $t = 0$: $s = 5$. At $t = 8/3$: $s = 3(512/27) - 12(64/9) + 5 = 512/9 - 768/9 + 45/9 = -211/9$.

Answer

$t = 8/3$ s, $s = 5 - 256/9$

Answer

$t = 0$ s, $s = 5$

Answer

$t = 4$ s, $s = ...$ (one critical point of v, not when v = 0)