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Question

A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s210 ft/s2. Its maximum cruising speed is 90 mi/h90 mi/h. (Round your answers to three decimal places.)

(a) What is the maximum distance 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 it can travel under these conditions?

(c) Find the minimum time 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 at minimum 37.5 minutes. How far apart are the stations?

Answer 1

For motion with cancer acceleration one of the relationships is between the starting velocity V_i , final velocity V_f , acceleration a and the displacement Δx:

V_f²-V_i²=2aΔx

If the train accelerates and decelerates with the same SIZE of acceleration |a| then the displacement when it would ACcelerate from V_i to V_f and the displacement it would DEcelerate from V_f to V_i would be the SAME.

Also, the average velocity of a body accelerating from V_i to V_f would be equal to its average velocity of decelerating from V_f to V_i. V_av=(V_i+ V_f)/2

Therefore, the times of accelerating. from V_i to V_f (and decelerating from V_f to Vi on the same |Δx| must be the same

Use what is stated above, in (b) we see that the train would make a round trip having spent 7.5min=450 sec on each part.

In part (3) we'd use that the average speeds on both parts of the travel is the same and equal to 90/2=45mi/hr so the time needed to go starting (from the rest) at one station and stopping at the next station 45mi apart would be 1hr b/c the average velocity would be 45mi/V_av=1hr

As for part (d) the result should be the product of average speed V_av and the time (37.5/60)hrs

Finally, in part (a) we need to add I) a distance to be traveled till reaching the max speed 2) a distance traveled at the top speed in 15min

The rest is carefully substituting the numbers. One needs to be careful to make sure that the units would be used consistently and correctly

Best,

Dr.Ariel B.