SUVAT Functions : Quick Reference

SUVAT Functions : Quick reference

Base Equations
v = u + a*t
v^2 = u^2 + 2*a*s
2s = (u + v)*t
s = u*t + a*t*t/2
s = v*t - a*t*t/2

None of these functions involve dividing by a variable, so they can always be computed no matter what values we input.
We can rearrange these five equations to create an expanded set of 20 functions. Then given any three variables, we can (usually) compute the remaining two.

"Usually", because some of these functions will involve dividing by a variable or computing a square-root. These may not be computationally possible with some input values, as they may involve dividing by zero, or square-rooting a negative. In these cases, the given set of input values may not be physically possible.

eg, if speed changes (u!=v), yet acceleration (a) is specified as zero. This is not physically possible.

In some cases, however, a function that cannot be computed may mean that the variable can take any value. These cases need special handling.

eg, consider computing t = (v-u)/a, where speed is specified as unchanging (u=v) and acceleration (a) is zero. See then see that time (t) can take any value. Time plays no role in an unchanging system.


Want to compute s:
Given u,a,t then s=(u+a*t/2)*t
Given v,a,t then s=(v-a*t/2)*t
Given u,v,t then s=(u+v)*t/2
Given u,v,a then s=(v+u)*(v-u)/(2*a)

Want to compute a:
Given u,s,t then a=2*(s-ut)/(t*t)
Given v,s,t then a=2*(s-v*t)/(t*t)
Given u,v,t then a=(v-u)/t
Given u,v,s then a=(v+u)*(v-u)/(2*s)

Want to compute t:
Given u,a,s then ???
Given v,a,s then ???
Given u,v,a then t=(v-u)/a
Given u,v,s then t=2*s/(u+v)

Want to compute u:
Given v,a,t then u=v-a*t
Given v,s,t then u=2*s/t-v
Given v,a,s then ???
Given t,a,s then ???

Want to compute v:
Given u,a,t then v=u+a*t
Given u,s,t then v=2*s/t-u
Given u,a,s then ???
Given t,a,s then ???

The ??? are left as an exercise for the reader :D