How Long to Reach Half Terminal Speed with Air Resistance?

[heartyface]

Homework Statement

An object of mass m falls from rest subject to air resistance force directly proportional to the object's speed, F=-bv, where b is the proportionality constant in N/(m/s) and the negative sign indicates the direction of the force opposite to the direction of the velocity. How long does it take this object to reach half of its terminal speed?

Homework Equations

a=g-bv/m, a=dv/dt, etc...

The Attempt at a Solution

tried, all failed.

 

[haruspex]

Using the two equations you posted, and eliminating a between them, should give you a differential equation involving v and t. What is it? Can you solve it?