Light Intensity rate

• Jan 7th 2006, 12:03 PM
mathletes
Math Questttttttt
An object is moving away from the light source at a rate of 4 units/s. Find the rate of change of the intensity of illumination when it is 2 units from the light source.

rate of change = k(1/unit²xsecond)
:confused:
• Jan 7th 2006, 01:01 PM
CaptainBlack
Quote:

Originally Posted by mathletes
An object is moving away from the light source at a rate of 4 units/s. Find the rate of change of the intensity of illumination when it is 2 units from the light source.

rate of change = k(1/unit²xsecond)
:confused:

The intesity of illumination as a function of distance $r$ from a point source is:

$I(r)=I(1)/r^2$,

where $I(1)$ is the intensity of illumination at a distance of $1$ unit from the source.

Now:

$\frac{d}{dt} I(r)=I(1)\frac{-2}{r^3}\ \frac{dr}{dt}$.

So now you only need to plug in $r=2$ and $\frac{dr}{dt}=4$ to get the answer, in units of
(whatever you are using as units of intensity)/s.

RonL
• Jan 7th 2006, 01:12 PM
mathletes
thank you, i obviously didn't know what i was doing.