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