Now, that's a complicated script, showing the might of "Mathematica".

Green text is your homework problems.
Blue indicates "Can be changed by user" -  r[t], Range [a,b] and reference point, Tref. 
Assumptions are used to help "Mathematica" simplify the result of integration.
Red is for the output and also see this L[[1]] in red? It's the choice of solutions for  t in terms of s. 
Run the first cell twice (needed for longer scripts to compile). This problem is so simple that, 
actually, there is no choice - second red line just has one function { s/Root[2] }. 
Chose any point you want in the range for NewPoint, second cell compares the t ans s positions. 
Third cell is animation.

Now take on #24, t in terms of s can be solved in 4 different ways - "Mathematica" offers you 4 choices. 
Let's say, you keep [[1]] choice, the graphs in second cell do not match! If you can not judge algebraically, 
what choice is right (one and only one), test them all till you get matching blue and red graphs. 
In this case, only choice 4 - ArcCos[ Root[ 1- 2/3 s] ] produces matching graphs (Why?). Thus, to 
get meaningful formulas you need to have   K = r[ L[[4]]].
Make sure, you change the Tref, it can only be between 0 and Pi/2 for this problem.