# Thread: Forming a DE from F=ma

1. ## Forming a DE from F=ma

A particle of mass $m$ is projected with speed $u$ along a straight horizontal track. The first section of the track has length $d$. On this section of the track the motion is resisted by a
constant force of magnitude $mk$, where $k$ is a positive constant. The particle does not come to rest on this first section of the track.

Show that the speed $V$ of the particle at the end of the first section of the track is given by:

$V = \sqrt{u^2 - 2kd}$

Using the equation $ma = F$, I got the following equation.

If we let the speed of the particle = $v$

$m\frac{dv}{dt} = v-mk$, however in the solutions they just have $m\frac{dv}{dt} = -mk$, what's happened to the $v$, I would have thought that the forces acting on the paticle would be $v$ and $-mk$?

Thanks for the help

2. If you think about your units for a second, $v$ cannot possibly be a force.

3. Ohh yeh, actually that's rather obvious isn't it :S Think I must be used to dealing with a constant force produced by the engine.

Thanks for spotting that obvious mistake!