The SUVAT equations describe motion in a given direction when ACCELERATION IS CONSTANT. The full set of equations that you should commit to memory are given by:

  1. \hspace{10pt}V=U+AT
  2. \hspace{10pt}S=\left(\frac{U+V}{2}\right)T
  3. \hspace{10pt}V^2=U^2+2AS
  4. \hspace{10pt}S=UT+\frac{1}{2}AT^2
  5. \hspace{10pt}S=VT-\frac{1}{2}AT^2


Variable/Constant Description SI unit
S displacement m (metres)
U initial velocity m/s (metres per second)
V final velocity m/s (metres per second)
A acceleration m/s/s (metres per second per second)
T total time s (seconds)

SUVAT equations 1. and 2. have already been seen here: motion in a straight line. The remaining SUVAT equations can be derived using these two equations.

Equation 3 – equation 1. can be rearranged to make T the subject so that T=\frac{V-U}{A} which can be substituted into equation 2:
S=\left(\frac{U+V}{2}\right)\left(\frac{V-U}{A}\right) and rearranged gives

Equation 4 – the expression for V in equation 1. can be substituted directly into equation 2:

Equation 5 – equation 1. can be rearranged to make U the subject so that U=V-AT. This can be substituted into equation 4 to give