A body of mass \( 2 \, \text{kg} \) is initially at rest. It starts moving unidirectionally under the influence of a source of constant power \( P \). Its displacement in \( 4 \, \text{s} \) is \( \dfrac{1}{3} \alpha^{2} \sqrt{P} \, \text{m} \). The value of \( \alpha \) will be _____.
