Equations of 1-D Kinematics

Equations of 1-D Kinematics

Describing motion in one dimension is very easy if a body has constant velocity.
```
             (x - xo)   =   v * (t - to)
```

It's still not too bad if a body has constant acceleration. One can derive a set of four equations which connect time and the body's position, velocity, and acceleration.

             (v - vo)   =   a * (t - to)

             (x - xo)   =   (avg v) * (t - to)

                                               1                2
             (x - xo)   =   vo * (t - to)  +  --- * a * (t - to)
                                               2

                             2        2
     2 * a * (x - xo)   =   v   -   vo

The key to solving problems in kinematics is to understand what's going on. Only if you comprehend the situation will you be able to pick the equation(s) which take the information given and yield the desired result.

Sometimes, the four kinematic equations for constant acceleration are written under the assumption that to = 0 and xo = 0; they then take the form

                   v    =   a * t
    
                   x    =   (avg v) * t

                                         1         2
                   x    =   vo * t   +  --- * a * t
                                         2

                             2        2
           2 * a * x    =   v   -   vo

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