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

Answer 1

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