Answer
$t=\sqrt {12}s\approx3.46s$
Work Step by Step
Determine the times when the particle reaches the edge of the screen:
First set the position function to $x=0$:
$0=9.00t-0.750t^{3}$
$9.00t=0.750t^{3}$ We can ignore when $t=0$ because that is the starting point. We divide both sides of the equation by .75 to obtain:
$9.00=0.750t^{2}$
$t^{2}=\frac{9.00}{0.750}$
$t=\sqrt {12}s$
$t\approx3.46s$
Then set the position function to $x=15$
$15=9.00t-0.750t^{3}$
The particle never reaches $x=15cm$ after $t=0$.
The first time that the particle reaches the edge of the screen is at $t\approx3.46s$
