A particle moves along the \(x\)-axis with an initial velocity \(v_{x}=50 \mathrm{ft} / \mathrm{sec}\) at the origin when \(t=0\). For the first 4 seconds it has no acceleration, and thereafter it is acted on by a retarding force which gives it a constant acceleration \(a_{x}=-10 \mathrm{ft} / \mathrm{sec}^{2}\). Calculate the velocity and the \(x\)-coordinate of the particle for the conditions of \(t=8 \mathrm{sec}\) and \(t=12 \mathrm{sec}\) and find the maximum positive \(x\)-coordinate reached by the particle.

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