Check out the case emf = B dA/dt, where the circuit moves and the area changes. This is an example of a magnetic brake, where the loop will start to slow down due to the weird induction phenomena.
Then, a special example of this type of induction, where the circuit falls through a magnetic field (in other words, when there is a constant force trying to accelerate the circuit/loop. This is going to end up looking a lot like air friction on a skydiver, with a terminal velocity!
By the way, check this one out if you want to see a strange case of finding the magnetic flux through a circuit due to the magnetism from a long, straight wire next to the circuit.
On Wednesday, which you have off, check out a preview of the other case, where emf = A dB/dt. This is going to involve a circulating electric field! Weird, but welcome to the world of electromagnetism. Here is a video specifically on the circulating E-field that is created when there is dB/dt. :-)