Drag forces on someone diving into a pool

[Serik]

Homework Statement

You dive straight down into a pool of water. You hit the water with a speed of 7.0 m/s, and your mass is 75 kg.

Assuming a drag force of the form F_D= (−1.00×10⁴ kg/s)v, how long does it take you to reach 2% of your original speed? (Ignore any effects of buoyancy.)

Homework Equations

$$\Sigma$$F=ma
V=V_o+at (?)

The Attempt at a Solution

I summed the forces in the y-direction (down is positive):
$$\Sigma$$F=mg-F_D=ma_y

2% of 7 m/s = 0.14 m/s

But I don't know what to do from here. How do I solve for a_y when the drag force varies with velocity? If a_y varies, then how can I use the kinematic equations for constant a?

I figured this out the hard way after plugging in 7.0 m/s for v and solving for a, which is an absurdly large number. (-923 m/s²)

 

[Lazyshot]

Are you sure that F_D=(-1.00x10⁴)v?
This coefficient seems kind of large to be for drag, recheck the numbers.

 

[Serik]

Lazyshot,

I should've placed the negative sign outside the parenthesis, but yes, according to my book and MasteringPhysics, that is the coefficient.

FD=-(1.00x10⁴)v