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)

$$t_3=2t=2\ min$$