Question: A particle moves along the \(x\) -axis so that its acceleration at any time \(t \geq 0\) is given by \(a(t)=4 t-20\). At time \(t=0\) the velocity of the particle is \(v(0)=18\), and at time \(t=3\) the position of the particle is \(x(3)=2\)

1. Write an expression for the velocity \(v(t)\) of the particle at any time \(t \geq 0\).
2. For what values of \(t\) is the particle at rest?
3. Write an expression for the position \(x(t)\) of the particle at any time \(t \geq 0\).
4. Find the total distance traveled by the particle from \(t=0\) to \(t=3\).
5. Complete the following table for the particle:

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