dimensional analysis

Question

Velocity v = A t + B t^2. Dimensions of B are:

RankGuru · Accepted Answer

According to the **Principle of Homogeneity**, the dimensions of each term in a physical equation must be the same.
- $[v] = [L T^{-1}]$
- The term $[B t^2]$ must have the same dimensions as velocity:
$[B] \cdot [T^2] = [L T^{-1}]$
$[B] = \frac{[L T^{-1}]}{[T^2]} = [L T^{-3}]$.

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