Drag races are completed in less than a third of a minute, with some runs finishing in under five seconds!  Solvers are invited to take notice of the exclamation point at the end of the previous sentence and the next one.  To complete the course in under five seconds at constant speed, a vehicle would need to cruise at 180 mph!

The photograph below depicts a typical heat featuring Top Fuel Dragsters part-way along the race-course.

The car in the right lane appears to be leading and, if able to maintain that lead all the way to the finish line, will win the heat.  Nevertheless, it is possible that the car in the left lane is actually traveling faster and will post a higher speed than the winner upon reaching the end of quarter-mile run. The World's Fastest Dragster puzzle will explore this speed / time anomaly.

Finishing speeds range all the way up to over 300 mph.  Faster vehicles must deploy parachute(s) to slow down immediately after completing each run.  Then, too, aerodynamic forces play an important role in drag racing, as witness the inverted wings both front and rear that apply thousands of pounds of "down-force" for improved traction at high speed, much like spoilers on an airliner rolling out on the runway. 

On September 14, 2008 in Concord, North Carolina, Tony Schumacher, who has been sponsored for several years by the U.S. Army, became the winningest Top Fuel driver in the history of National Hot Rod Association, breaking and setting records.  He was the first driver to exceed 330 mph in competition and has actually reached 337.58 mph.

One prominent reference reports that the World's Fastest Dragster covered the quarter-mile in 4.45 seconds and attained a terminal speed of 329 miles per hour.  In reality, drag racing is about acceleration.  Accordingly, we can let t = time for the quarter-mile, v = terminal velocity, and a = peak acceleration, then ...