Please read Open letter to students with homework problems. — Stephen Leppik 47 secs ago

I'm voting to close this question as off-topic because it is about Mathematics instead of programming or software development. — Pang 47 secs ago

Your question is not so much on how to use software but on the effects of software on your solution. This is slightly off-topic here, you might have better success at scicomp.stackexchange.com. -- To be better understood, you should say that xs(t) is piecewise constant with the value xs(t)=x(te) taken at the apex points dotx(te)=0. -- It would be helpful to have access to the graphs mentioned in the questions. (And yes, a jump in the second derivative gives a kink in the first derivative.) — LutzL 32 secs ago

Perhaps you should ask that question here and you will get more replies. — CodingYoshi 49 secs ago