By the method of dimensional analysis,derive the relation:
Dimensional Consistency of an equation of motion :
s(displacement) = u(initial velocity) X t(time) + 1/2 X a(acceleration)X t2(time)
Or, s = u.t + 1/2 a.t2
Step 1: Identify the terms in the equation and identify which symbol stands for which physical quantity.
The terms here are : s, u.t, a.t2
Step 2: Write down the dimensional formula of each symbol used in the equation. If you are unclear how to do it, go to the first article in this series.
[s] = [L]
[u] = [LT-1]
[t] = [T]
[a] = [LT-2]
Step 3: Calculate the dimension of each term in the equation.
Term 1: [s] = [L]
Term 2: [u.t] = [LT -1.T] = [L]
Term 3: [a.t2] = [LT -2.T2] = [L]
Note that, as stated above, we have canceled dimensions from numerator and denominator like [T -2.T2] .
Conclusion: The equation is dimensionally consistent since all the terms have the same dimensions.