Question A particle moves along the $x$-axis so that at time $t \geq 0$ its velocity is given by $v(t)=6 t^{2}-48 t-54$. Determine all intervals when the acceleration of the particle is positive.

Step 1 ：Given a particle moving along the x-axis with its velocity function as \(v(t)=6 t^{2}-48 t-54\) for \(t \geq 0\).

Step 2 ：We need to find the intervals when the acceleration of the particle is positive. The acceleration is the derivative of the velocity function.

Step 3 ：Taking the derivative of the velocity function, we get the acceleration function as \(a(t) = 12t - 48\).

Step 4 ：We need to find when this acceleration function is positive, i.e., \(a(t) > 0\).

Step 5 ：Solving the inequality \(12t - 48 > 0\), we get \(t > 4\).

Step 6 ：Thus, the acceleration of the particle is positive for \(t > 4\).

Step 7 ：Final Answer: The interval when the acceleration is positive is \(\boxed{(4, \infty)}\).