a car travelling in a straight line experiences a retardation which is proportional to its speed cubed. the speed of the car reduces from 20 to 10 m/s^-1 in a time of t seconds

show that the distance travelled in this time is 40t/3 m

so what I tried to do was let dv/dt =-kv^3 I put in the limits and I got k=1/40t

I then let vdv/ds =-kv^3 and I put in the limits and I got 1/20 =ks and I subbed in k and i got the wrong answer.