A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s^2. Its maximum cruising speed is 120mi/h.
What is the maximum distance (in miles) the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?
The train can accelerate at a rate of 10 ft/s^2. It starts from rest and accelerates to its maximum cruising speed of 120 mi/h. 120 mi/hr = 176 ft/sec.
The distance traveled by the train while it accelerates is s = 176^2/(2*10) = 1548.8 ft. This in terms of miles is 0.293. The train then travels at 120 mi/h for 15 minutes. The distance traveled is equal to 120/4 = 30 mi.
The total distance traveled by the train is 30.293 miles.