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Physics · UNITS AND MEASUREMENT
हिन्दीThe position \( x \) of a particle at time \( t \) is given by \( x = \frac{v_0}{A}(1 - e^{-A t}) \), where \( v_0 \) is constant and \( A > 0 \). The dimensions of \( v_0 \) and \( A \) respectively are:
Correct answer · Option 1
\( [\text{M}^0 \text{L T}^{-1}] \) and \( [\text{M}^0 \text{L}^0 \text{T}^{-1}] \)
Explanation
The exponent \( A t \) must be dimensionless, so \( [A] = [\text{T}^{-1}] \). Then \( [x] = \frac{[v_0]}{[A]} \implies [v_0] = [x][A] = [\text{L}][\text{T}^{-1}] = [\text{L T}^{-1}] \).
