M1 mechanics problem

[TheFly]

I am struggling with this

A stone of mass m is released from rest on the surface of a tank of water of depth d. During the motion the water exerts a constant resistive force of magnitude R. The stone takes t seconds to reach the bottom of the tank. Show that R=m(g-(2d)/t^2)

[MathsMan]

Simply resolve downwards to get the acceleration a, then use a 'suvat' equation, rearranging to get R

Resolve downwards

mg-R = ma
so a= (mg-R)/m

use s=ut+at^2/2 with u=0

so s= at^2/2

then d=(mg-R)t^2/(2m)

then 2md = mgt^2 -Rt^2

then Rt^2 = mgt^2 - 2md
so
R=m(g-(2d)/t^2)