If the fastest roller coaster reaches its top speed of 128 mph in five seconds and total ride lasts for fifty how far has traveled ten seconds?

* Initial velocity (u) = 0 mph (since it starts from rest)

* Final velocity (v) = 128 mph = 128 * 5280/3600 = 186.67 ft/s

* Acceleration (a) = (v - u) / t = (186.67 - 0) / 5 = 37.33 ft/s²

Now, let's calculate the distance traveled in ten seconds (t = 10 s), including the initial five seconds:

* Distance (s) = ut + 0.5 * a * t²

* s = (0 ft/s) * 10 s + 0.5 * 37.33 ft/s² * (10 s)²

* s = 1866.5 ft

Therefore, the roller coaster has traveled approximately 1867 feet in ten seconds, including the time taken to reach its top speed.