If force (F), acceleration (A), Time (T) are used as fundamental units, the dimensional formula for length will be-

CONCEPT:

• Dimensional Formula: The dimensions of a physical quantity represents its nature. 
• ​Dimensional Formula can help us in finding the relationship between different physical quantities.
  • For example, Dimensional Formula for work done and Kinetic Energy is the same. So, we can say they are related.
• For dimensionless quantities, dimensional analysis can't be possible.
  • For example, Relative density is a dimensionless quantity which is the ratio of two densities. we cannot find the dimension of relative density
• The dimension of fundamental quantities are known and dimensional formulas for other quantities are derived from fundamental units.
• Example:
  • Finding Dimension of Density:
  1. The expression for density is Mass / Volume
  2. Mass is a fundamental unit with dimension M.
  3. Volume is a cube of length. So, Dimensional Formula for Length L3
  4. Dimensional Formula for density M / L3 = ML -3

EXPLANATION:

From the definition of acceleration,

\(A = \frac{{dv}}{{dt}} = \frac{{{d^2}x}}{{d{t^2}}}\)

\(\smallint dv = \smallint A\;dt\)

V = A × T

\(\frac{x}{T} = A\;T\)

⇒ x = A T²

To write in the form of Dimensions

⇒ x = [F⁰AT²]