Answer to Question #96776 in Mechanics | Relativity for John

Question

A train travels between station 1 and 2, the engineer of the train is instructed to start from rest at station 1 and accelerate uniformly between points A and B, then coast with a uniform velocity between points B and C, and finally accelerate uniformly between points C and D until the train stops at station 2. The distances AB, BC, and CD are all equal, and it takes 5 minutes to travel between the two stations. Assume that the uniform accelerations have the same magnitude, even when they are in opposite directions.
a.) How much of this 5 minute period does the train spend traveling between points A and B?
b.)How much of this 5 minute period does the train spend traveling between points B and C?
c.) How much of this 5 minute period does the train spend traveling between points C and D?

Answer 1

$AB=BC=CD=d$

AB:

$d=0.5at_1^2\to t_1=\sqrt{\frac{2d}{a}}$

$v=at_1=\sqrt{2ad}$

BC:

$t_2=\frac{d}{v}=\frac{d}{\sqrt{2ad}}=\sqrt{\frac{d}{2a}}$

CD:

$t_3=\sqrt{\frac{2d}{a}}$

Thus,

$T=2t+t+2t=5t=5\ min$

$t=1\ min$

a)

$t_1=2t=2\ min$

b)

$t_2=t=1\ min$

c)

$t_3=2t=2\ min$