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,
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.
a = -(v^2 + 10000)/800,
dv/dt = -(v^2 + 10000)/800
but dv/dt = dv/dx dx/dt = v dv/dx, so
v dv/dx = -(v^2 + 10000)/800,
dv/dx = -(v^2 + 10000)/(800v)