Why do scientists need to measure extremely small intervals of time? Why do scientists need to measure extremely small intervals of time? Why is it necessary?
 A: It all depends on the phenomena one is studying. If you need to make an analysis about the general pick up of a car engine, i.e. how much time it take to go from 0 to 100 Km/h, one does not need to bother about femto-seconds rather seconds will suffice. However, for the time scales involved in atomic transitions or sub-atomic interactions have very short time scales. Hence, there one needs to have faster measuring device to have relevant data set to that phenomena. 
One can think of it like Shutter speed of the camera. If you want to capture a moving object then you need a fast shutter speed. The faster the object is, the commensurate shutter speed needed to capture the object in motion. Otherwise, with slow shutter speed and faster body all you get is a hazy picture. This is the closest analogy i could think of.
A: Our world can be modeled with three spatial dimensions and on time dimension. So, to describe an event correctly in that model, the accurate measurement of time interval is essential. Although, this is easier said than done. Uncertainty relations prohibit exact measurement of time interval.
