Answer
$( -\frac{3}{2}, 4)\ sec$ or from -1.5 to 4 sec.
Work Step by Step
Step 1. Given $v=2t^2-5t-12$, let $v\lt0$, we have $2t^2-5t-12\lt0$
Step 2. Factor the inequality as $(2t+3)(t-4)\lt0$
Step 3. Identify the boundary points as $t= -\frac{3}{2}, 4$
Step 4. Use test points at $t=-2, 0, 5$ 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 $( -\frac{3}{2}, 4)\ sec$ that is from -1.5 to 4 sec.
