I need a differential equation, for determining an accelerated person K' (9.8 m/s^2) moving in the +Z axis, K' starts at the origin Z=0. While a point particle, is a distance of 2*(3*10^8)^2 meters from the Origin (Z=0) This point particle we will say, will start in -Z axis and will call it K. K than moves at constant velocity of (3*10^8) meters/second, Toward K' . Can someone describe this to be a function of time until K meets with K' ???

Question

I need a differential equation, for determining an accelerated person K' (9.8 m/s^2) moving in the +Z axis, K' starts at the origin Z=0. While a point particle, is a distance of 2*(3*10^8)^2 meters from the Origin (Z=0) This point particle we will say, will start in -Z axis and will call it K.  K than moves at constant velocity of (3*10^8) meters/second, Toward K' . Can someone describe this to be a function of time until K meets with K'  ???