When acceleration depends on the distance

[svkptr]

Homework Statement

i am trying to find out velocity at a point of time and distance covered by a particle whose acceleration (a) depends on distance (s). to start with let a = k*s+c were k and c are contants.

Homework Equations

a= k*s+c
we know a=ds/st

The Attempt at a Solution

a=k*s+c
∴
(dv/dt)=k*s+c
or
v=k*s*t+s*t

but i know (s) is not to be treated as conatant... then what to do here?? please help
i cannot frame the differential equation

 

[voko]

a = dv/dt = dv/ds ds/dt = dv/ds v

 

[Dick]

a(t)=v'(t)=s''(t). So s''(t)=k*s(t)+c. It's a second order ode. Like a harmonic oscillator.