To convert acceleration defined as a function of position, a(x), into a function of time, a(t), one can use the relationship between velocity and position. Starting with a(x) = x/s², the general solution for position is x = c*e^(sqrt(m)*t/s) + d*e^(-sqrt(m)*t/s). By differentiating this solution twice, one can derive a(t) as a function of time. An alternative method involves using the work-energy theorem, where a(x) = v*dv/dx, to find velocity as a function of position, then integrating to express time as a function of position, t(x), which can be inverted to find x(t). This approach allows for the substitution back into a(x(t)) to obtain the desired acceleration function in terms of time.
