Question

The position x of a particle at time t is given by x=v0a(1−e−at) where v0 is constant and a>0 find the dimensions of v0 and a

Answer 1

x = v0 ( 1-e^-at)
So,
Since any number that is raised to any other real number, then it'll be dimension less.

So,
at will be dimension less
So, Dimension of A = [ T^-1]

And Dimension of v0 = [ Length ] So as to make the dimensions on both sides of equation same.