Reasoning Strategy for Applying the Equations of Kinematics
The one-dimensional kinematics equations for constant acceleration are
v  v 0  at
x  v 0 t  21 at 2
v 2  v 02  2ax
x  21 vt  21 (v  v 0 )t
1. Each of the kinematics equations contains four variables. The goal of these equations is if
three are known, then the fourth variable can be solved for.
2. One way to organize this information is to create “data tables” that look like
∆x
a
Data
v
vo
t
The idea is to insert the know quantities into this data table and insert a question mark “?”
for the unknown variable.
∆x
a
v
vo
t
―
X
X
X
X
v  v  2ax
X
X
X
X
―
x  v 0 t  at
X
X
―
X
X
X
―
X
X
X
Kinematics
v  v 0  at
2
2
0
1
2
2
x  (v  v 0 )t
1
2
3. From the data table information, one needs to identify which equation to use in order to
solve for the need physical variable. Let’s summarize the information in a kinematics table.
Starting with the first equation v = v0 + at, we note that this equation contains four variables:
v, v0, a, and t. The variable that is missing is the displacement x. If in a particular problem
the displacement is not given, one can use this equation to solve for one of an unknown
variable in terms of three known's. The table indicates this by using X to indicate that the
variable is present and a dash to indicate that it is not present in the equation.
4. Reasoning Strategy for Applying the Equations of Kinematics
Step 1. Make a drawing of the situation and interpret the question.
Step 2. Define the direction of motion (velocity) to be always positive!
Step 3. Create a Data Table with all units converted into the mks-system.
Step 4. Use the kinematics table to organize you thinking into selecting the correct equation
to use.
Step 5. Solve for the correct variable and interpret your result.