Speed calculations are important. Automatic systems gather distance and time data to calculate speed - as in speed enforcement devices such as Gatso cameras, radar guns etc.
Manual calculations are just as important and extremely wide ranging.
Police accident investigators will gather evidence - particularly after a serious or fatal accident to try to work out the speeds and movement of vehicles before the accident. Skid marks, surface of the road, conditions of the cars etc. All commercial air traffic movements are meticulously planned in advance - and the intended flight path passed on to all en route controllers. The flight crew and controllers will constantly monitor the aircraft position - performing many rapid speed, distance and time calculations to ensure a safe and trouble free flight. On board computers can help in ocean passages, but it still remains for navigators to make rapid decisions close to markers - and based on split second mental calculations of distance to run, speed etc.