HELP: Original Lessons on Motion: Kinematic Equations

Kinematic Equations

Kinematics comes from the Greek word for "motion", which means that kinematic equations are the "equations of motion". These equations use the following symbols:

$\bar{v}$ stands for "average velocity", and is measured in m/s
v_i or stands for "initial velocity", and is measured in m/s. Sometimes they also use the symbol v₀, which means "velocity at time zero". They're actually the same thing.
v_f stands for "final velocity", and is measured in m/s
d stands for "distance", and is measured in meters
t stands for "time", and is measured in seconds
a stands for "acceleration", and is measured in m/s^2

The following kinematic equations use these symbols to describe motion:

$d=\frac{1}{2}(v_i+v_f)t$

$v_f=v_i+at$

$d=v_it+\frac{1}{2}at^2$

$d=v_ft-\frac{1}{2}at^2$

$v_f^2=v_i^2+2ad$

$\bar{v}=\frac{v_i+v_f}{2}$

These equations apply to situations with uniform acceleration, which means that your acceleration does not change. Watch the following videos for a few examples of how to use these equations.

Tips and Tricks:

When deciding what equation to use, make a list of the variables given to you in the problem, and the variable you want to find out. Then use the equation that includes all of those symbols.
Check to make sure all of your units match up. All distance units should match and all time units should match.
Follow order of operations carefully as you work with these equations.