physics
posted by karan on .
A particle moves according to the eqn a=kv where a is acceleration and v is the velocity and k is a constant. If initial speed is V0 find the speed at any instant

dv/dt = kv
dv/v =  k dt
ln v =  k t + c
e^ln v = v = e^(kt +c) = e^c e^(kt)
when t = 0, v = Vo
Vo = e^c e^0 = e^c
so
v = Vo e^kt