A high-speed "bullet" train accelerates and decelerates at the rate 4ft/s2. Its maximum cruising speed is 90 mi/hr.

Question

(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?

(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance (in miles) it can travel under these conditions?

(c) Find the minimum time (in minutes) that the train takes to travel between two consecutive stations that are 45 miles apart.

(d) The trip from one station to the next takes 37.5 minutes. How far apart (in miles) are the stations?

Answer 1

I will help you with Part a and hopefully you will be able to use that information to solve the rest.

First of all you need to use consistent units.

Convert 4 ft/sec² to miles/hr². It is a messy conversion--call it a

Then since the acceleration is constant (which you got by the conversion), velocity v(t)=v(0)+at

s(t)=s(0)+∫v(t) where the limits of integration are 0 and t.

You should be able to work out the details of the rest for yourself.