How Does a Magnet's Position Change Over Time When Falling Near an Iron Wall?

[Peter Persoff]

I posted this in general math, but then I saw that calculus and analysis was a more appropriate place for it. I am looking for a solution to this problem:

When a magnet is dropped from rest near an iron wall, it accelerates downward due to gravity at constant acceleration. It also accelerates toward the wall, and the closer it gets to the wall, the greater the acceleration. Can anyone refer me to a solution that would give the position of the magnet as a function of time?

 

[BobbyBear]

It would just be a uniformly accelerated motion in each of the directions, no? One direction would be the vertical one due to gravity, the other would be normal to the wall (horizontal if the wall is vertical).

 

[bowma166]

Looks to me like the vertical position would have a uniform negative second derivative, and the horizontal position would have a uniform positive third derivative, perhaps?

i.e.

x=\frac{1}{6}kt^{3}+\frac{1}{2}a_{0}t^{2}+v_{0}t+x_{0}

where k is the constant third derivative

 

[BobbyBear]

Oops, my bad, bowma is right, the horizontal position would have a uniform third derivate, not uniform second derivate:P