How do they do that effect where the action speeds up and slows down in the same take?
Internet Filmmakers' FAQ
This technique is called "ramping". It involves increasing or decreasing the frame-rate, with accompanying adjustment of the shutter angle to compensate for F-stop adjustment during the ramp.
There are also accessories, such as the Arri RCU, which can be fitted to a camera not designed to ramp that will accomplish the same thing by adjusting the iris ring on the lens during a ramp. The reason the shutter angle and/or stop is adjusted during a ramp is that the differing frame rates require different levels of light to be made available to the film... example: if your stop is 5.6 @ 24 fps, and the end of your ramp is 48 fps, you'll need to open a full stop, as the film is running faster through the gate, requiring more light to expose properly. The stop @48 fps would be 4. You set all this in the Arri RCU. During the ramp, the camera will slowly adjust the shutter to the exact rate as the camera ramps up and down; it doesn't happen all at once, so timed adjustment is critical to make the shot look right.
For those with persistent budget constraints just simply shooting at higher than normal speeds and controlling the "ramp" via a non linear editing or compositing program like the Avid Media Composer or Adobe After Effects; even Adobe Premiere can often yield better results with much greater control over exact times of the speed change. The results can be fine tuned even further by having the ability to control the ramp speeds to whatever you desire from x (whatever the duration you desire) to zero ramp. The reason for the higher shooting speeds is to eliminate motion stutter or strobing when attempting to slow down shots in post-production (mainly because the frames aren't there and interpolation can only go so far). However, if you shot at higher filming rates (50fps to 100fps), speeding the shutter looks like 25fps and results in no strobe like effects and the only perceptible change is the lack in motion blur.