"If distance(x) is in m, time (t) in s, and acceleration (a) in m/s^2 is the following equation dimensionally correct?

Question

^{x = 1/2 at}3

Answer 1

Do you mean x=½at³? If so, then the equation is not dimensionally correct since:

[LT^-2]T³=[LT]≠[L] where L is length measure and T is time measure.

x=½at² has the correct dimensions: [L]=[LT^-2]T².