Let my friend check my locations while I am taking a stranger's car?
As there's no on-board feature covering your needs, I'd recommend taking a look at Glympse. With this app you can decide when to start or stop sharing your location, you could even set a timeout. Only you would need to have the app installed, and those you've shared your location to can watch it on any web-enabled device:

Glympse is a fast, free, and simple way to share your location safely using GPS tracking in real time with friends and family!
No sign up required! Only those you share with can view your Glympse from any web-enabled device.

For alternatives, please take a look at my Location Sharing list.
Any solution will depend on your phone having internet access: it can't work with GPS alone. GPS is only a way for your phone to find out where it is: it doesn't itself allow anyone else to know your location. If you go outside of data coverage, your location will stop updating.