1. ## particle moving

a particle starts from rest and moves in a horizontal line with speed v given by dv/dt = 80-v
(i)find the time taken for the particle to increase its speed from 20 m/s to 40 m/s
(ii)using the fact that the integral of (v/80-v) dv = 80-v-80ln(80-v)+c find how far the particle travels in going from rest to a speed 60 m/s
(iii) determine the limiting speed of the particle i.e v->v1 as t-> infinity

I was able to do part i using definite integrals and the answer I got was .405

I am stuck on (ii) and (iii)

2. ## Re: particle moving

ii) $\dfrac{ds}{dv} = \dfrac{\dfrac{ds}{dt}}{\dfrac{dv}{dt}}=\dfrac{v}{ \dfrac{dv}{dt}}=\dfrac{v}{80-v}$

3. ## Re: particle moving

thanks I will try it again now