Similar to the previous section, 1D kinematics, this section quantifies the movement of objects. This time it will take into account movement in more than one dimension, for example a car driving in a parking lot or an astronaut in outer space.
Take a look at this introduction to 2D kinematics
Vectors and 2D Motion: Crash Course Physics #4
Read the BoxSand Introduction and watch the pre-lecture videos before doing the pre-lecture homework or attending class. If you have time, or would like more preparation, please read the OpenStax textbook and/or try the fundamental examples provided below.
Motion obviously is not always along a straight line and two or three dimensional analysis is required. Here we will focus on two dimensions since including the third dimension add difficulties that are not necessary to illuminate the essence of the concept. The position of an object can be defined by it's position vector,
$\overrightarrow{r}=\langle x, y \rangle$
where x and y are the coordinates of the object relative to the origin. Similarly you can define the velocity and acceleration as vectors.
$\overrightarrow{v}=\langle v_x, v_y \rangle$
$\overrightarrow{a}=\langle a_x, a_y \rangle$
The vector nature of position, velocity and acceleration, allows us to break problem down to each separate component. This means you can have a set of constant acceleration kinematic equations for just the x-component,
$x_f = x_i+v_{i_x} \Delta t + \frac{1}{2} a_x \Delta t ^2$
$v_{f_x} = v_{i_x} + a_x \Delta t$
$v_{f_x}^2 =v_{i_x}^2+2a_x \Delta x$
and also a set for the y-component.
$y_f = y_i+v_{i_y} \Delta t + \frac{1}{2} a_y \Delta t ^2$
$v_{f_y} = v_{i_y} + a_y \Delta t$
$v_{f_y}^2 =v_{i_y}^2+2a_y \Delta y$
This ability to decouple the motion along one direction from another direction, perpendicular to the first, helps a great deal in analyzing motion. The feature that it brings along though, is that now you have doubled the number of kinematic variables and possible equations. Organization is key and setting up a table of known and unknown variables, for the x and y directions separately, will help with all this information.
Note that the kinematic equations can also be written in vector notation, for example,
$\overrightarrow{r}_f = \overrightarrow{r}_i+\overrightarrow{v}_i \Delta t + \frac{1}{2} \overrightarrow{a} \Delta t ^2$
which implies more than one equation, one for each component, x, y, and z. When ever you see a vector symbol on anything, think of that thing being more than one thing.
The Excel File below can be used to study motion in 2 dimensions.
Kinematic equation for final position
Kinematic equation for final velocity as a function of velocity, acceleration, and change in position
Kinematic equation for final velocity as a function of velocity, acceleration, and time
