Solve Diving Drag Homework: Time to Reach 2% Speed

[Torrencio]

Homework Statement

You dive straight down into a pool of water. You hit the water with a speed of 7.0m/s, and your mass is 65kg.
Assuming a drag force of the form Fd=(-1.40x10^4)v, how long does it take you to reach 2% of your original speed? (Ignore any effects of buoyancy.)

Homework Equations

Fd=(-1.40x10^4)v
Fg=mg
Fnet=ma
a=(vf-vi)/t

The Attempt at a Solution

Fnet=mg-(-1.40x10^4)v
a =(mg-(-1.40x10^4)v)/m
a = -1500= vf-vi/t=0.14-7/t
t= -6.86/-1500
t= o.oo46s

When I enter this number or 4.6x10^-3, says it is wrong?? could someone help me, thisi s really frustrating me. The physics all seems to make sense to me.

 

[Doc Al]

The Attempt at a Solution

Fnet=mg-(-1.40x10^4)v

Careful with signs. The drag force acts up; gravity acts down.

Since the force varies with speed, the acceleration is not constant. You have to set up and solve a differential equation to get the time. Hint: a = dv/dt.