A point mass $$m$$ moves in a straight line under a retardation $$kv^2$$ where $$k$$ is a positive constant and $$v$$ is the instantaneous velocity. The initial velocity of the point mass is $$u$$. The displacement of the point mass at time $$t$$ is

A

$$\frac{1}{k}\ln\left(1 + kut\right)$$

B

$$\frac{1}{k}\ln\left(kut\right)$$

C

$$k\ln\left(kut\right)$$

D

$$\frac{1}{k}\ln\left(1 - kut\right)$$