Motion in two dimensions

The idea

In two dimensions, position, velocity and acceleration are vectors. With constant velocity, $\mathbf{r} = \mathbf{r}_0 + \mathbf{v}t$. With variable motion, differentiate $\mathbf{r}$ component by component to get $\mathbf{v}$, and again for $\mathbf{a}$.

1. Write the position as $\mathbf{r} = x\mathbf{i} + y\mathbf{j}$.
2. Differentiate or integrate each component separately.
3. Speed is the magnitude of velocity: $\sqrt{v_x^2 + v_y^2}$.

Watch out Include the starting position: $\mathbf{r} = \mathbf{r}_0 + \mathbf{v}t$.