Question

An equation of motion is given by s=ut + (1/2)gt^2. Determine the dimension of (1/2)gt^2​

Answer 1

The Dimensions of $\frac{1}{2}$ gt²   =  [M⁰LT⁰]

Explanation:

The dimensions of a physical quantity are the powers to which the fundamental quantities must be raised to represent that quantity completely.

S = ut +$\frac{1}{2}$ gt²

where   s= displacement covered (m)

             u = Initial velocity (ms⁻¹)

              g = Acceleration due to gravity (ms⁻²)

              t = time (sec)

      Dimensions of $\frac{1}{2}$ gt² ;

g =  [M⁰LT⁻²]           ;         t² = [M⁰L⁰T⁻²]²

gt²   =     [M⁰LT⁰]