### Constant acceleration equations

These equations relate displacement, velocity, acceleration, and time, and apply for constant acceleration in the +x direction starting at t=0.

v = vo + at       (1)

x = xo + vo t + ½ a t2       (2)

Using Eq. (1),  at = v - vo,   in Eq. (2), we get:

x = xo + vo t + ½ (v - vo) t

=xo + ½ (v + vo) t       (3)

= xo + vav t

Rearranging (1), t = (v- vo)/a, and substituting for t in (3) gives:

x = xo +½(v + vo) (v- vo)/a
or
2 a (x - xo)= v2 - vo2       (4)

Eqs. (1) - (4) are the basic equations of kinematics that relate acceleration, velocity, and displacement.
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