If your own software includes software covered by the GPLv2 (for example by copying source code, or by linking dynamically) then your own software is also covered by the GPLv2, and you will have to provide the source code. This is called a "work based on the Program" on the GPLv2.
In this case, however, it seems that your own software does not include software covered by the GPLv2, but you want to put it onto an SD card together with software covered by the GPLv2. That would most likely fall under "mere aggregation of another work", as long as your software and the other software do not interact very closely (such as dynamic linking).
To quote the GPLv2:
In addition, mere aggregation of another work not based on the Program
with the Program (or with a work based on the Program) on a volume of
a storage or distribution medium does not bring the other work under
the scope of this License.
So in that case the GPLv2 does not cover your program. You will still have to supply the source code for the GPLv2 software on the SD card. This is covered by section 3 of the GPLv2. Basically, you have two options:
- send along the complete source code for all the software (would be quite bothersome for a complete distro)
- or provide a written offer to provide the source code on demand to anyone who asks (you may charge for this, but only to cover your cost)
GPLv2 contains a third option, but that only applies to non-commercial distribution.
Practically speaking, it should be enough to include a README.txt or similar explaining that the SD card contains software covered by GPLv2, and that you will provide the source code on demand for a certain, reasonable fee (say $5 or $10 per CD).
In practice, it is unlikely that anyone would ask for this, as the source code can usually be downloaded for free elsewhere, but if someone does ask, you just charge them $5 and send a CD.
Of course, to reduce legal risks it may be prudent to contact a lawyer for your jurisdiction, as this is only general advice.