Differential Equation Word Problem

[maherelharake]

An object having mass 70kg falls from rest under the influence of gravity. The terminal velocity of the object is -20 m/s. Assume that air resistance is proportional to velocity.
Q) Find the velocity and distance traveled at the end of 2 seconds.

I got an answer for the velocity, but I am having trouble with the part about distance travelled. I know I just integrate the equation I had for velocity, but I do not know how to solve for the constant that appears after integrating. Thanks!

 

[Mark44]

Show us what you have and we'll help you out.

 

[maherelharake]

Sorry this is my first time using the forum. The furthest I got was this equation for the distance...


x(t)= -40.82e^(-.49t)-20t+A


I need help solving for A, so I can solve for the distance after 2 seconds.

 

[Mark44]

If the object is at x = 0 at t = 0, then x(0) = 0. Use that to solve for A. Also, since it is falling from rest, you know that v(0) = 0 as well.

 

[maherelharake]

So since it is falling from rest, you take the initial position to be 0? That makes sense since it is just used as a reference point, right?

 

[Mark44]

Or wherever. I didn't see any information in the problem you posted that said it fell from a particular height.

 

[maherelharake]

Exactly. That is why I think it makes sense to take the initial position as 0 since nothing else was given. I will give this a shot. Thanks a lot for your time.