Question

Show that 1/2 gt² has the same dimensions of distance

Answer 1

As distance has dimensions, [L]

If we look at 1/2 gt square
Here g is acceleration due to the gravity
T is time

As a has dimensions [LT-2]
And time has dimensions [T-2]

Using above we get that
[L] = [LT-2] /[T-2] which is equal to L.

Hope you get your answer.