Yeah, the u_c is included. So you could make those half-open intervals. Which post in particular did you have in mind for me to review?
Quoting post # 11:
Right. The particle will not escape the potential well.b) if u<0 we need E>=0 and if u=0 then E=-1/20 and our condition is not satisfied.
I buy that.a) 0<=0.5*v^2-1/20<1/16 leads to the solution sqrt(10)/10 <= v < 3* sqrt(10)/20, since v is speed and is always positive! But since we need positive velocity for this case then sqrt(10)/10 <= u (velocity) < 3* sqrt(10)/20
Yep. Looks good to me.b) 0.5*v^2-1/20>=0 leads to the solution v>= sqrt(10) / 10 but we need negative velocity so u<= -sqrt(10)/10
Our final solution is u exists in [sqrt(10)/10, 3*sqrt(10)/20) or u<= -sqrt(10)/10