Math Help - boat speed equation

1. boat speed equation

" if a boat is moving straight in a line, with speed = v, through water with a resistance which is proportional to v^2; with initial speed v_o and position x_o, find v(t) and x(t)"

2. Re: boat speed equation

Originally Posted by learning
" if a boat is moving straight in a line, with speed = v, through water with a resistance which is proportional to v^2; with initial speed v_o and position x_o, find v(t) and x(t)"
Hi learning!

If there are no other external forces, the boat is slowed down with an acceleration of $a = - c v^2$.
We can write this as $\frac {dv} {dt} = -c v^2$.
Can you solve that and find v(t)?