1. The problem statement, all variables and given/known data A rock with mass m slides with initial velocity v0 on a horizontal surface. A retarding force F that the surface exerts on the rock is proportional to the square root of the instantaneous velocity of the rock (F = -kv1/2) . a) Find expression for the velocity of the rock as a function of time. b) Find expression for the position of the rock as a function of time. c) In terms of m,k, and V0 , at what time will the rock come to rest? d) In terms of m ,k and V0, what is the distance of the rock from its starting point when it comes to rest? 2. Relevant equation f=ma A= dv/dt 3. The attempt at a solution I solved parts a and b and I'm fairly certain my answers are correct. F=−kv^(1/2) a=dv/dt= (-kv^(1/2))/m dv/(v^1/2)=(-kdt)/(m) Integrate both sides and solve for the constant C V= (k2 t2 )/ (4m2 ) - (ktv01/2)/m + v0 Then I integrated again to find position as a function of time. The only way I can think to solve parts c and d is to solve V(t)=0 but this would require the quadratic equation and be very messy. Then, to solve part d, I would have to plug in answer to c into x(t) which is even messier. Is there another way? Am I missing something? Any help would be great. Thank you.