Correct Answer: Option A

Explanation

To find the minimum time \( t \) it takes for a vehicle of mass \( m \) to acquire a speed \( v \) when driven by an engine of power \( P \), we use the work-energy principle. 

The relationship is given by:
\(t = \frac{m v^2}{2P}\)

Thus, the minimum time \( t \) to acquire speed \( v \) is:
\(t = \frac{m v^2}{2P}\).

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