Originally Posted by **alanjkim** Here's the problem:
Suppose an object with mass m is projected with initial velocity v 0 along the horizontal direction. Assume quadratic air resistance of the form F drag = αv^2 , where F drag is the magnitude of the drag force. Find an expression for the
velocity v as a function of time.
Here's what I have so far:
ma = αv^2
m(dv/dt) = αv^2
(dv/dt) =( αv^2/m)
v(t) = integral of (( αv^2/m))
Am I on the right track here? Can someone help me finish this problem. |

You are fine until the last line! You can write dv= (av^2/m)dt but v is an

**unknown** function of t. You cannot integrate av^2/m with respect to t.

Instead write dv/v^2= a/m dt and integrate both sides, the left side with respect to v and the right side with respect to t.