Separate dv/dt=kv variables and integrate them:

dv/dt = kv-& gt； ∫dv/v=∫kdt, integral limit (v0-> v), (0->; t)

ln(v/v 0)= kt-& gt； v=v0.e^(kt)

②v=v0.e^kt->； That is dx/dt = v0.e (kt). Separate variables from the formula and integrate them:

∫ dx = ∫ dx = ∫dx=∫v0.e^ktdt, integral limit (0-> x), (0-> t)

x=( 1/k)v0.e^(kt)

* The answers (1) and (2) in the original question are problematic.