Question

A high-speed ""bullet"" train accelerates and decelerates at the rate 4 ft/s 2 . Its maximum cruising speed is 90 mi/hr. (a) 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? Maximum distance = miles

Answer 1

23 mi

Step-by-step explanation:

Let us first record all the values we have

acceleration = 4 ft/s

max speed = 90 mi/hr * 1 hr/3600s * 5280 ft/1 mi = 132 ft/s

We can use the equation of linear motion since acceleration is constant

distance covered = distance during acceleration + distance during costant

velocity

`s = (v_(f) ^(2) - v_(i) ^(2)  )/(2a)  + v_(i)t\\\\s = (132 ^(2) - 0^(2)  )/(2*4)  + 132*900\\s = 120 978ft`

distance in miles = 120 978 ft * 1 mi/5280 ft = 22.9125 mi ≈ 23 mi