# A high-speed bullet train accelerates at the rate of 4 ft/s2. Its maximum cruising speed is 120mi/h. What is the maximum distance travelled in miles if the train constantly accelerates from rest...

A high-speed bullet train accelerates at the rate of 4 ft/s2. Its maximum cruising speed is 120mi/h. What is the maximum distance travelled in miles if the train constantly accelerates from rest then cruises for 15 minutes?

mathsworkmusic | (Level 2) Educator

Posted on

The cruising speed is 120mi/h

There are 5280 ft in a mile and 3600 seconds in an hour so this is

120*5280/3600 = 176 ft/s

In the acceleration phase, the distance in ft after t seconds is given by

`d = 4/2t^2 = 2t^2`

And the velocity in ft/s is given by

`v = 4t`

To reach cruising speed the train must travel for 176/4 = 44s

Therefore it travels 2(44)^2 = 3872 ft

In the cruising phase, the distance in ft after t seconds is given by

`d = 176t`

So after 15 minutes = 15(60) = 900s, the distance travelled is 176(900)

= 158400 ft

The maximum distance travelled is then 3872+158400 ft = 162272 ft

There are 5280 feet in a mile.

Therefore the maximum distance travelled is 30.72 miles