Welcome to Reaper!
If your project is all audio, you can automate the playrate slider:
1. Hit CTRL+ALT+M to show the master track
2. Click the env button on the master track
3. Arm the play rate envelope
4. Create some envelope points at the right place and adjust them to stop the tape.
This works best when the project has only audio tracks since MIDI tracks and their VSTi audio output are not pitched down, only the speed change matches.
You can also try this free tapestop plugin:
http://hem.bredband.net/tbtaudio/arc...vstplugins.htm (never tried it, YMMV)