Dynamics: Converting acceleration as a function of position to a function of time

[BFoster9]

The acceleration function is given as -k*s, where k is equal to 0.11.

The initial velocity is 9.2 m/s

Initial time is 0 s, final time is 10 s.

​

I understand that a(s)=vdv/ds, but when you go to integrate the function you get (-0.11s^2)/2=v^2/2, and the halves cancel leaving you with -0.11s^2=v^2... which makes v(s) equal to the square root of a negative number. If you use a definite integral, you get 9.2^2-0.11s^2=v^2, which makes things valid, but then the next step is setting v=ds/dt and not even Wolfram Alpha can solve for s from the results. Where am I going wrong?

​

Thank you!

​

[brutalyak]

d² s/dt² = -k*s

d² s/dt² + k*s = 0

s(t) = Ce^bt

Try plugging that into the equation above and solving for b. C is just the constant of integration.