Question
Fri April 27, 2012 By: Hemchand

By the method of dimensional analysis,derive the relation:

Expert Reply
Mon April 30, 2012

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.

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