Homogeneous equations
Physical Quantities & Units - OCR A-Level Physics
Worked Example [3 marks]
Show that the equation \(v^{2}\) = \(u^{2}\) + 2as is homogeneous.
Show Solution
1
LHS
\(v^{2}\) has units ($m s^{-1}$)^2 = \(m^{2}\) $s^{-2}$
[1]2
RHS first term
\(u^{2}\) has units ($m s^{-1}$)^2 = \(m^{2}\) $s^{-2}$
[1]3
RHS second term
2as has units ($m s^{-2}$)(m) = \(m^{2}\) $s^{-2}$. The 2 is dimensionless.
[1]Answer
All three terms have units \(m^{2}\) $s^{-2}$, so the equation is homogeneous.