If x(t) is measured in meters (m) and t is measured in seconds (s), then we must have [tex]a,b,c[/tex] such that the units remain consistent:
[tex]x\,\rm m=a(t\,\rm s)+b(t\,\rm s)^2+c(t\,\rm s)^3[/tex]
For this to happen, we need s to cancel in the first term and produce a length in m; for this, we would get a in m/s.
In the second term, s^2 needs to be canceled, so b has unit m/s^2.
In the third term, s^3, so c has unit m/s^3.
