We are often used to seeing vehicle engines (motors) by simply opening the hood and taking a peek. Well for Tesla, BMW i3 and few others, that is not an easy endeavor. Tesla keeps their motor(s) on the axle and the only real way to see one is to go to a Tesla showroom and see the chassis display. BMW i8 for example requires two people to open the hood.
The BMW i3's motor and if equipped with a range extender motor (REx) can be accessed through the trunk by removing a few hex screws. What we find inside is single assembly of the motor and the axle, effectively making the motor (and REx engine) move along with axle in both acceleration and deceleration.
There have been plenty motor footage with the cover removed, but none this extreme. The video (below) you see was shot during a BMW CCA Peachtree Chapter Autocross and shows both front and back movement, as well as, to my surprise lateral movements of the motor.
At 1:07 mark you can clearly see the great stresses the motor experiences and it is no wonder BMW issued a bolt replacement for the i3 motor for early models as the engine would simply detach from the frame after passing over a bump or a bridge joint. Don't be alarmed about your i3, you were probably contacted by your local BMW store to perform the work if it was required.
The video clearly illustrates the technical challenges BMW team had to overcome in order to fit such a compact motor in a very small space. Enjoy!