If v(t) is speed measured in meters per second (m/s), and t is time measured in seconds (s), then the constants A and B in
v(t) = At ³ - Bt
must have units of m/s⁴ and m/s², respectively; otherwise, the equation is dimensionally inconsistent.
[m/s] = A [s]³ - B [s]
[m/s] = [m/s⁴] [s]³ - [m/s²] [s]
[m/s] = [m/s] - [m/s]
[m/s] = [m/s]