Hi David,
If s(t) is the distance function then v(t) = s'(t) is the velocity function and a(t) = v'(t) is the acceleration function. Thus you need to antidifferentiate twice to get from a(t) to s(t). As you know, the process of differentiation destroys constants (the derivative of a constant is zero) and hence antidifferentiation can't recover this constant uniquely. Thus each antidifferentiation is going to produce an undetermined constant and your function s(t) will have two undetermined constants.
The first step is to antidifferentiate a(t) to produce v(t). Can you antidifferentiate
a(t)= sin(0.1t)/ cos^{3}(0.1t)
Let us know if this is still a problem.
Penny
