dimensional analysis (checking formula)

Question

For a formula for speed v = A t + B/t, dimensions of A and B must be respectively?

RankGuru · Accepted Answer

1. **Homogeneity**: The dimensions of $v$ must match the dimensions of each term on the right ($At$ and $B/t$).
2. **Speed dimension**: $[v] = [LT^{-1}]$.
3. **Solve for A**:
   - $[At] = [LT^{-1}]$
   - $[A] [T] = [LT^{-1}] \implies [A] = [LT^{-2}]$ (Acceleration dimensions).
4. **Solve for B**:
   - $[B/t] = [LT^{-1}]$
   - $[B] [T^{-1}] = [LT^{-1}] \implies [B] = [L]$ (Length dimensions).
5. **Conclusion**: A has dimensions of **$LT^{-2}$** and B has dimensions of **$L$**.

Rank Guru

dimensional analysis (checking formula)

Select the correct option: