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: \(t = \frac{m v^2}{2P}\).