# Changing force on a moving object

1. Nov 20, 2008

### trilex987

Hi there

If an object is affected by space-dependent force (for example wind , or electric field, or whatever), one can calculate its speed at any point in space by integrating the acceleration along its path, but what about if the force was time dependent , like for example an AC electric field, so you need to consider time also.
So how does one go about calculating the objects position and speed at any point in time?
Let's simplify it to just one dimension, for example

thanks

2. Nov 21, 2008

### sr_philosophy

Let us take a simple example. There is a body of mass 'm' Kg which experiences a force that is a linear function of time, F=kt acting in the direction of motion. Let us try to calculate the Work done by the force in a time 'T'. Final Velocity 'v'= integral {(from 0 to T) of [F/m dt]}. Hence work done = change in kinetic energy = 1/2*m*v*v.

3. Nov 21, 2008

### ZapperZ

Staff Emeritus
I'm not exactly sure if I read this problem correct, because it looks rather..... er ... obvious.

If you have F(t), then one can write F(t) = ma, or a = F(t)/m.

Doing the integration with respect to t will give you the velocity, and a subsequent integration will give you the position, i.e.

$$a = \frac{dv}{dt} = \frac{F(t)}{m}$$

This means that

$$v = \int{\frac{F(t)}{m}dt}$$

Similarly with position x, since v = dx/dt.

Zz.

4. Nov 21, 2008

### sr_philosophy

Sir. That's exactly what i have done above except that i have not used the symbols that you have.

5. Nov 21, 2008

### ZapperZ

Staff Emeritus
Except that I dealt with the more general situation, and I didn't try to confuse the OP by including "work done" and "kinetic energy", which isn't part of the question.

Zz.

6. Nov 21, 2008

### trilex987

Thank you both, but you are talking about force as a function of time only.

What I'm talking is a force as a function of both space and time.

For example. an electrode with a time changing electric field, and force upon a free charge.
As the charge moves away from its initial position, it experiences a change in force both as a function of time and position.
That way you can't integrate over time without knowing exactly where is the object positioned in space in each dt moment, and vice versa
you can't integrate over space because you need to know when exactly is the object located at a dx location