# Regents Physics - Kinematic Equations

## Developing the Toolset

Motion graphs such as the d-t, v-t, and a-t graphs are terrific tools for understanding motion.  However, there are times when graphing motion may not be the most efficient or effective way of understanding the motion of an object.  To assist in these situations, we need to develop a few more problem solving tools, known as the kinematic equations.

Thankfully, you don’t have to memorize these equations, you can find them on the back page of the reference table.  The variables in these equations describe the motion of the object under study for the given time window. For one-dimensional motion, it's typically useful to set up your equations and variables with the understanding that the object's initial direction of motion will be your positive axis.

## Problem Solving Strategy

Key Kinematics Variables
Variable Meaning
vi Initial velocity
vf Final velocity
d Displacement
a Acceleration
t Time elapsed

In using these to solve motion problems, it’s important to take care in setting up your analysis before diving in to a solution.  Key steps to solving kinematics problems include:

1. Labeling your analysis for horizontal (x-axis) or vertical (y-axis) motion.
2. Choosing and indicating a positive direction (typically the direction of initial motion).
3. Creating a motion analysis table (vi, vf, d, a, t).
4. Using what you know about the problem to fill in your “givens” in the table.
5. Once you know three items in the table, use kinematic equations to solve for any unknowns.
6. Verify that your solution makes sense.

## Sample Problems

These equations and problem solving steps are applicable to both horizontal and vertical motion problems. Let’s try them out:

This problem solving strategy and the kinematic equations work for vertical motion problems as well:

In some cases, you may not be able to solve directly for the "find" quantity. In these cases, you can solve for the other unknown variable first, then choose an equation to give you your final answer: