A point moves in a straight line under the retardation a $v^{2}$, where ' $a$ ' is a positive constant and $v$ is speed. If the initial speed is $u$, the distance covered in ' $t$ ' seconds is:

(A) a ut

(B) $\frac{1}{a} \log (a u t)$

(C) $\frac{1}{a} \log (1+a u t)$

(D) $a \log (a u t)$