The effect looks like a simple speed warp. What editing suite are you using? We use Adobe CC here, and to do that effect I’d zoom into the video track on the timeline in Premiere, right click the keyframe line that you’d normally use for opacity and select Show Clip Keyframes > Time Remapping > Speed and then add in a start and end frame for the section you’d like to speed up. Then just drag the line in between the keyframes up to increase the speed of that clip. That’s all that’s done here.
The smooth slow motion looks like it’s coming from the camera- i.e. the camera was set to a high frame-rate (only about 60fps by the looks of things). If you have footage shot at a higher frame-rate than your timeline in Premiere, you’ll need to go to the interpret window (right click the clip in the project panel) and set the correct frame-rate there.
Hope this helps!
Head of Post Production