Question

Is this relation dimensionally correct-x=x0+vt+1/2at^2

Answer 1

Hi,

Here is your answer

Given:

x=x₀+vt+1/2 at²

To find:

Whether the equation is dimensionally correct or not

Solution:

By using dimensional analysis,

The first term=x=[L]

Second term=x₀=[l]

Third term=vt=[LT][T⁻¹]=[L]

Fourth term=1/2at²=[LT⁻²][T²]=[L]-ignoring constant 1/2

Since all the terms have same dimensional formula[L], The equation is dimensionally correct.

Notes:

Every dimensionally correct equation may not be correct,but

Every correct equation is dimensionally correct.

Hope this helps you.