Dimensions of Constants in Kinematic Equation – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Dimensions of Constants in Kinematic Equation

The velocity (v) of a particle at time (t) is given by \[v = at + \frac{b}{t+c}\] where (a), (b) and (c) are constants. The dimensions of (a), (b) and (c) are respectively:

[2006]

\((LT^{-2}), (L) and (T)\)
\((L), (T) and (LT^2)\)
\((L^2T^{-2}), (LT) and (L)\)
\((L), (LT) and (T^2)\)

Solution:

From dimensional homogeneity: ([c] = [t] = [T]). ([at] = [v]) so ([a] = [v]/[t] = [LT^{-1}]/[T] = [LT^{-2}]). ([b/(t+c)] = [v]) so ([b] = [v][t] = [LT^{-1}][T] = [L]).

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