Question

if v = At^3 - Bt^4 what are the dimensions of A? what are the dimensions of B?

Answer 1

dimention for v must be length/time if it is velocity or speed
so \[v = t ^{3} (A - Bt)\]
so dimentions for (A - Bt) must be length/time^3
and thus A has dimentions length/time^3
and B length/time^4

Answer 2

As there are two unknowns in one equation, A and B have to be expressed with respect to each other.
v = d/t Therefore the equation can be written as
d/t = t^3(A-Bt)
d/t^4 = A-Bt
So A = d/t^4 + Bt and B = t^-1(A-dt^-4)