# Need HELP! equation of motion with variable acceleration

1. Homework Statement
A particle is dropped from rest, at the surface, into a tank containing oil
The acceleration of the particle in the oil is a = g – kv
where g is the gravitational acceleration and –kv being denoted by
the resistance put on the particle by the oil.
Solve for x as a function of time!

3. The Attempt at a Solution
I'm attaching an image file containing my calculations.
As can be seen I get a differential equation of the second order
but as I proceed to solve this equation and try to determine the
constants the whole thing turns into ZERO?!!?! What am I doing wrong??

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## Answers and Replies

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You don't need to consider this as a 2. order diff. equation. You can view the equation as

$$\ddot{x} = g - k\dot{x}$$
or
$$\dot{v} = g - kv$$

The second equation is just a 1. order diff. equation with respect to the velocity v.

You don't need to consider this as a 2. order diff. equation. You can view the equation as

$$\ddot{x} = g - k\dot{x}$$
or
$$\dot{v} = g - kv$$

The second equation is just a 1. order diff. equation with respect to the velocity v.
Yeah, you're right.. but one SHOULD be able solve it by puting it up as a second order right? I just wanna know what I'm doing wrong, it really bugs me.

what have you got? Kind of hard to know whats wrong when we just have a generic list of eqns....
John S