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Answer On Question #61192, Physics / Mechanics - Relativity: Solution

The train travels 1/2 mile in 41 seconds between two stations. It accelerates and decelerates at 8 ft/s^2. Using kinematic equations, the maximum speed is calculated to be 60 mph. It travels at this top speed of 60 mph for a distance of 1672 feet over 11 seconds.

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2K views1 page

Answer On Question #61192, Physics / Mechanics - Relativity: Solution

The train travels 1/2 mile in 41 seconds between two stations. It accelerates and decelerates at 8 ft/s^2. Using kinematic equations, the maximum speed is calculated to be 60 mph. It travels at this top speed of 60 mph for a distance of 1672 feet over 11 seconds.

Uploaded by

Edzel Bautista
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Answer on Question #61192, Physics / Mechanics | Relativity

A train travels between two stations ½ mile apart in a minimum time of 41 sec. If the train
accelerates and decelerates at 8 ft/sec^2, starting from rest at the first station and coming to a
stop at the end of the station, what is its maximum speed in mph? how long does it travel at this
top speed?

Solution:
The mile is an English unit of length of linear measure equal to 5,280 feet.
So, the halfway between two stations is
1 5280 𝑓𝑡
𝑑1 = 𝑚𝑖𝑙𝑒 = = 1320 𝑓𝑡
4 4
Let's say that the train takes t1 time to reach the max. speed v and then it travels at this top
speed distance d2 at time t2.
Use the kinematic equation
𝑎𝑡 2 𝑣𝑡
𝑑1 = 1 + 2
2 2
The time is
𝑡 𝑡 41 𝑠
𝑡1 + 2 = = = 20.5 s
2 2 2
The equation for speed is
𝑣 = 𝑎𝑡1
Thus, substituting in first equation
𝑎𝑡12 𝑎𝑡1 𝑡2
𝑑1 = +
2 2

8𝑡12 8𝑡1 (41 − 2𝑡1 )


1320 = +
2 2

330 = 𝑡12 + 41𝑡1 − 2𝑡12

𝑡12 − 41𝑡1 + 330 = 0

(𝑡1 − 30)(𝑡1 − 11) = 0


The physical solution is
𝑡1 = 11 𝑠
Hence,
𝑣 = 𝑎𝑡1 = 8 ∙ 11 = 88 𝑓𝑡/𝑠
1 Foot per Second = 0.681818 Miles per Hour
Thus,
𝑣 = 88 ∙ 0.681818 = 60 𝑚𝑝ℎ

The distance that it travels at this top speed is


𝑑2 = 𝑣𝑡2 = 𝑣(41 − 2𝑡1 ) = 88(41 − 22) = 1672 𝑓𝑡

Answer: 60 𝑚𝑝ℎ; 1672 𝑓𝑡.

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