Question

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

Answer 1

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

$a = \frac{x}{t}$

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'

$a=\frac{L}{T}$

Similarly;

x  = bt²

$b=\frac{x}{t^2}\\b=\frac{L}{T^2}$

Next is to get a/b;

$\frac{a}{b} = \frac{L}{T} \div \frac{L}{T^2}\\\frac{a}{b} = \frac{L}{T}*\frac{T^2}{L} \\\frac{a}{b} =\frac{T^2}{T}\\\frac{a}{b} =T$

Hence the dimension of a/b is T