Answer
$t=-0.82$ s
Work Step by Step
To find t when $x(t)=0,$
we solve the $x(t)$ function and substitute $x(t)=0$ in the equation;
$4.0-6.0t^{2}=0$
$4.0=6.0t^{2}$
$\displaystyle \frac{4.0}{6.0}=t^{2}$
$t=\sqrt{\frac{4.0}{6.0}}\approx\pm 0.82$ s
So, the negative time at which x passes through the origin is $-0.82$ s.
