This looks OK (accept the acceleration is in the opposite direction to the

velocity and in the direction of decreasing x so we ned a - sign here), but

given what the next part of this question is I would arrange it differently,

like:

a = -(v^2 + 10000)/800.

As I had above:b) By choosing an appropriate derivative form for acceleration, show that the differential equation relating v to x is:

dv/dx = -(10^4 + v^2)/(800v)

Now, im thinking that there is a form for acceleration which goes:

d((1/2)v^2)/dx = a

which looks awfully similar to my (1/2v^2)

but im not too sure where to take it to show that equation.

Any help?

a = -(v^2 + 10000)/800,

or:

dv/dt = -(v^2 + 10000)/800

but dv/dt = dv/dx dx/dt = v dv/dx, so

v dv/dx = -(v^2 + 10000)/800,

rearranging:

dv/dx = -(v^2 + 10000)/(800v)

RonL