Answer
$( 2, 4)\ sec$ or from 2 to 4 sec.
Work Step by Step
Step 1. Given $v=3t^2-18t+24$, let $v\lt0$, we have $3t^2-18t+24\lt0$
Step 2. Factor the inequality as $(3t-6)(t-4)\lt0$
Step 3. Identify the boundary points as $t=2, 4$
Step 4. Use test points at $t=1, 3, 5$ for the signs of the left side expression and get $+, -, +$ for the three regions.
Step 5. The solution requires negative (middle region), thus the time interval is $( 2, 4)\ sec$ that is from 2 to 4 sec.
