a depth of mass 100 kg is released from a warship into the sea and allowed to sink. While gravity is pulling it down, a buoyancy force of 1/40 times its weight (=mg) is pulling it up. therefore, water resistance also exerts a force on the weapon that is proportional to its velocity, with a constant of proportionality of 10 kg/s. How long will it take for the weight to reach the velocity of 70 m/s?

i've tried and my de equation is :

f = ma

mg-1/40(mg)-10v = m(dv/dt)

dv/dt = g - (1/40)g - (10/m) v

dv/dt = (39/40)g - (10/m) v

v(t) = (39/40)gt - 5(10/m) vt + c

applying the initial condition (x=0, t=o, v=0) => c=0

thus v(t) = (39/40)gt - 5(10/m) vt

is my de is right??? how i get t expression from this equation???

pls help me....