Who can differentiate this one?

1. Nov 25, 2009

Fiasal teslla

For a falling object, who can find the time in terms of the velocity for this journey( before reaching terminal velocity) with considering the resistive force?

2. Nov 25, 2009

g_edgar

Force equals mass times acceleration
Choose what resistive force to use, inverse velocity or inverse square velocity
Write down the differential equation
Solve it

3. Nov 26, 2009

HallsofIvy

Staff Emeritus
I can"! But are you clear on the terminology? Your title asked "how can differentiate this one" implying you have a function to differentiate but that doesn't appear to be the case. You are just asking about setting up the dynamic equation.

As g edgar says, "Force equals mass times acceleration" so ma= m dv/dt= -g- f(v) where "f(v)" is the resistive force. That can be a very complicated function of the velocity depending on the situation. I do not agree with g edgar's "inverse" formulas. Typically, the faster something is going, the greater the drag, not the other way around. Normally, the drag is simplified to either -kv or -kv2 where k is the constant of proportionallity and v is the speed.

4. Nov 26, 2009

Fiasal teslla

When I tried to solve it, I started with this equation
F-R=ma, where F= mg, snd R is the risitive force which equals bv (b is a constant)
So, mg-bv=ma
mg-bv=m dv/dt then we seperate the variables to get the time in terms of the velocity

Am I correct with that?

5. Nov 26, 2009

HallsofIvy

Staff Emeritus
Yes, in that case, with resistive force proportional to v, you get a fairly simple equation:m dv/dt= mg- bv, a separable equation. But be careful about signs. If you are taking "upward" to be positive, then it is m dv/dt= -mg- bv. Since drag always acts opposite to velocity, the coefficient of v is always negative.