An AMTRAK train starts from Atlanta and heads non-stop to Greensboro (distance:

Question

An AMTRAK train starts from Atlanta and heads non-stop to Greensboro

(distance:

350 miles). The train starts from rest and accelerates uniformly (at 0.35g) to reach its top

(i.e. max) speed of 150 mph. On its way (i.e. somewhere before reaching Greensboro),

the train decelerates (at -0.5g) so that it comes to a halt at the Greensboro station.

Determine the time t for the train to make the 350-mile trip. [Assume there are no delays,

obstructions, etc. on the way --- hardly the reality if you have ever traveled with

AMTRAK]. [g = 10 ms-2]

Draw the v-t, s-t, a-t graphs.

An AMTRAK train starts from Atlanta and heads non-stop to Greensboro (distance: 350 miles). The train starts from rest and accelerates uniformly (at 0.35g) to reach its top (i.e. max) speed of 150 mph. On its way (i.e. somewhere before reaching Greensboro), the train decelerates (at -0.5g) so that it comes to a halt at the Greensboro station. Determine the time t for the train to make the 350-mile trip. [Assume there are no delays, obstructions, etc. on the way --- hardly the reality if you have ever traveled with AMTRAK].[ g=10ms-2] Draw the v-t, s-t, a-t graphs.

Explanation / Answer

solution )

Train starts from rest, u0 = 0 m/s, a = 0.35g

V = u0 + at

150 mph = 0 + (0.35g)*t_a

But g = 10m/s^2, converting 150mph into m/s, as 1mph = 0.447 m/s

Therefore, 150mph = 150*0.447 m/s = 67.05 m/s

I;e 67.05 m/s = 0 + (0.35*10 m/s^2) *t_a

67.05 m/s = 3.5 m/s^2 *t_a

Hence t_a = (67.05 m/s) / (3.5 m/s^2) = 19.157 s

So time taken by train to reach the max speed of 150 mph is 19.157s

As 1 mile = 1609.34 m, so 350 mile = 350 * 1609.34 m = 563269 m

As train retards at -0.5g, therefore

Vf = V + at_d

So t_d = (Vf

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