Distance covered under variable acceleration

1. Sep 13, 2011

lsmiley

Is it possible to find the distance covered in a certain time when acceleration depends on velocity, such as an electric-powered vehicle might do??
Acceleration := K*velocity + Const

2. Sep 13, 2011

rock.freak667

a=Kv+C

a=mv(dv/dx)

mv(dv/dx)=Kv+C

you would need to solve that equation, m,K and C are constants most likely by separation of variables.

3. Sep 13, 2011

Khashishi

Assuming K and C are constants, you can integrate to find v, then integrate to find x.
In this case, assuming starting from stand still, v=C/K*(exp(K*t)-1)
x = C/K*(exp(K*t)/K-t)