Serway & Jewett — Motion in Two Dimensions: Problem 36

A particle starts from the origin with velocity \(5\hat{i} \text{ m/s}\) at \(t = 0\) and moves in the \(xy\) plane with a varying acceleration given by \(\vec{a} = (6\sqrt{t}\hat{j})\), where \(\vec{a}\) is in meters per second squared and \(t\) is in seconds. (a) Determine the velocity of the particle as a function of time. (b) Determine the position of the particle as a function of time.