Direction: A particle initially (i.e., at time \[t=0\]) moving with a velocity u subjected to a retarding force, as a result of which it decelerates at a rate \[a=-k\,\sqrt{v}\] where v is the instantaneous velocity and k is a positive constant.The distance covered by the particle before coming to rest is

• A. \[\frac{{{u}^{3/2}}}{k}\]
• B. \[\frac{2{{u}^{3/2}}}{k}\]
• C. \[\frac{3{{u}^{3/2}}}{2k}\]
• D. \[\frac{2{{u}^{3/2}}}{3k}\]