Physics Help Forum Finding an expression for the velcoity v as a function of time.

 General Physics General Physics Help Forum

 Oct 8th 2017, 05:20 PM #1 Junior Member   Join Date: Oct 2017 Posts: 2 Finding an expression for the velcoity v as a function of time. 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.
Oct 8th 2017, 05:30 PM   #2

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,167
 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)
You are good up to here. This is the Bernoulli differential equation. See here. (Set p(x) = 0.)

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

Oct 8th 2017, 05:54 PM   #3
Junior Member

Join Date: Oct 2017
Posts: 2
 Originally Posted by topsquark You are good up to here. This is the Bernoulli differential equation. See here. (Set p(x) = 0.) -Dan
So then getting the integral of (dv/dt) gets v(t) which is the left side of the equation. Any help on the right side? I'm very confused as to how to get the integral of the algebraic equation with multiple variables, if that is even how to go about the problem.

Oct 10th 2017, 12:42 PM   #4
Senior Member

Join Date: Aug 2010
Posts: 281
 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.

Oct 10th 2017, 02:26 PM   #5

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,167
 Originally Posted by HallsofIvy 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.
@alanjkim: Yes, do it this way. The equation is separable. I always do things the hard way!

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Tags expression, finding, function, time, velcoity

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post ling233 Kinematics and Dynamics 5 Dec 3rd 2015 11:10 AM lilshaunh Kinematics and Dynamics 1 Jan 4th 2011 05:44 PM freud Kinematics and Dynamics 1 Oct 18th 2010 01:01 PM juggalomike Kinematics and Dynamics 4 Jan 28th 2010 03:58 PM juggalomike Advanced Mechanics 2 Jan 15th 2010 05:34 AM