Suppose that a neutron with with mass M and initial speed v0 is traveling through a material, such as graphite. As the neutron moves, it makes collisions with atoms in the material, so teh faster it is moving, the more collisions it makes per unit time. Another model of teh net effect of this is that the neutron experiences a resistive force proportional to the square of its speed, e.g., the force exerted by the material on teh neutron goes like F=-bv^2. Determine the velocity and position of the neutron as a function of time??
The Attempt at a Solution
I calculated the velocity and got v(t)= m/[bt+(m/v0)] and this makes sense dimensionally at t=0 v=v0 but when i calculated the position I got x(t)= m/b [ln(bt+(m/v0))]+C .. The problem is this does not make sense dimensionally and conceptually.