# Terminal Velocity formula

1. Jan 18, 2010

We have the following formula for the velocity of an object moving in a fluid.
v = vt -vte-kt/m.
This formula shows that an object can never achieve terminal velocity but in the derivation of this formula given in "Fundamental of Physics" by H D Young and Freedman 10 edition we use the formula mg=kvt which shows that object achieves terminal velocity?

2. Jan 18, 2010

### Staff: Mentor

What do you mean by "never"? In an exponential equation like that, you only have to go out a few time constants to get arbitrarily close to the final value...

3. Jan 18, 2010

But sir vt=v only when time t = infinity.
and hence v can never equal to vt.
But while deriving it we have supposed that we have achieved vt.

4. Jan 18, 2010

### Stonebridge

There are a number of laws in physics that have an exponential like this one. Radioactive decay is one. Another is the rate of loss of heat from a hot body. In both of these cases, the maths says that the value never reaches zero because t would need to be infinity. In that you are perfectly correct.
However, this is the maths. In the real world, we find that we don't need to wait until infinity before the value falls to such a low level that it is so near to zero that the difference cannot be measured, or the difference is of no significance.

5. Jan 18, 2010

### dacruick

Yes and just to add an example to what stronebridge is saying. Newton's law of heating and cooling which you may be familiar with or population modelling. These both have similar concepts behind them. If you put a steel ball in a 30F room. and The steel ball is at 0F, they will never become the same temperature except at infinity. This is because there is a point where the steel ball is 29.999999999999999999999999999999999999999999999999999999 F, and since the law of heating and cooling depends on difference in temperature, it will take forever for them to be equal.

6. Jan 18, 2010