Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 19

19 The acceleration of a particle moving only on a horizontal xy plane is given by \(\vec{a} = 3t\hat{i} + 4t\hat{j}\), where \(\vec{a}\) is in meters per second squared and \(t\) is in seconds. At \(t = 0\), the position vector \(\vec{r} = (20.0 \text{ m})\hat{i} + (40.0 \text{ m})\hat{j}\) locates the particle, which then has the velocity vector \(\vec{v} = (5.00 \text{ m/s})\hat{i} + (2.00 \text{ m/s})\hat{j}\). At \(t = 4.00 \text{ s}\), what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis?