Write the dimension of a / b in the x = at + bt2. Where x is the distance and t is the time?​

The dimension of a/b where x is the distance and t is the time is T

Given the expression

x = at + bt²

where

x is the distance

t is the time

Based on the homogeneity principle, the expression on the left-hand side must be equal to that on the right. Hence;

x = at

Since x is the distance and distance is measured in metres, the dimension equivalent will be the length 'L'

Since t is the time and time is measured in seconds, the dimension equivalent will be the seconds 'T'

Similarly;

x  = bt²

Next is to get a/b;

Hence the dimension of a/b is T