the position X of a particle at time T is given by :?

Question

X = V/a ( 1- e^-at )
V is a constant
a is + ve (a>0)
find the dimensions of V and a

Answer 1

a is in 1/seconds or 1/time, V is in meters/second or length/time. Reason is that the argument of the exponential has to be dimensionless so if t is time, a has to have dimensions of inverse time. If x is position which has dimensions of length, and a is inverse time, then V has to have dimensions of length/time.