Answer
$[1, \frac{7}{4}]\ sec$ or from (and inclusive) 1 to 1.75 sec.
Work Step by Step
Step 1. Given $s=-16t^2+44t+4$, let $s\ge32$, we have $-16t^2+44t+4\ge32$
Step 2. Rewrite the inequality as $16t^2-44t+28\le0$ or $(4t-4)(4t-7)\le0$
Step 3. Identify the boundary points as $t=1, \frac{7}{4}$
Step 4. Use test points at $t=0, \frac{3}{2}, 2$ 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 $[1, \frac{7}{4}]\ sec$ that is from (and inclusive) 1 to 1.75 sec.
