Kinematic equations in one dimension

In this lesson, we will learn:

• The four kinematic equations
• How to choose which kinematic equation to use
• Problem solving with the kinematic equations

The four kinematic equations describe the relationship of the initial velocity ($v_{i}$), final velocity ($v_{f}$), acceleration ($a$), displacement ($d$), and time ($t$) for an object moving in one dimension. Each of the equations is made up of four of the five of these variables. If we know three of these variables, we can use the kinematic equations to solve for the two remaining unknown variables.

1. $v_{f}=v_{i}+at$(No $d$)
2. $v_{f}^{2}=v_{i}^{2}+2ad$(No $t$)
3. $d=v_{i}t+\frac{1}{2}at^{2}$(No $v_{f}$)
4. $d=(\frac{v_{i}+v_{f}}{2})t$(No $a$)

$v_{i}$: initial velocity, in meters per second (m/s)

$v_{f}$: final velocity, in meters per second (m/s)

$a$: acceleration, in meters per second squared $(m/s^{2})$

$t:$ time, in seconds (s)

$d:$ displacement, in meters (m)