A car accelerates from rest to a final constant velocity \(V_{f}\) and a police officer records the following velocities at various locations \(x\) along the highway:

Find a mathematical Eulerian expression for the velocity \(V\) traveled by the car as a function of the final velocity \(V_{f}\) of the car and \(x\) if \(t=0\) at \(V=0\). Try an exponential fit to the data.

x = 0 x = 100 ft V = 0 mph V = 34.8 mph x = 200 ft V = 47.6 mph x = 300 ft V = 52.3 mph x = 400 ft V = 54.0 mph x = 1000 ft V 55.0 mph - V. =