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Answer:

The train accelerates at the rate of 20 for some time, until it's just exactly

time to put on the brakes, decelerate at the rate of 100, and come to a

screeching stop after a total distance of exactly 2.7 km.

The speed it reaches while accelerating is exactly the speed it starts decelerating from.

Speed reached while accelerating = (acceleration-1) (Time-1) = .2 time-1

Speed started from to slow down = (acceleration-2) (Time-2) = 1 time-2

The speeds are equal.

.2 time-1 = 1 time-2

time-1 = 5 x time-2

It spends 5 times as long speeding up as it spends slowing down.

The distance it covers speeding up = 1/2 A (5T)-squared

= 0.1 x 25 T-squared = 2.5 T-squared.

The distance it covers slowing down = 1/2 A (T-squared)

= 0.5 T-squared.

Total distance = 2,700 meters.

(2.5 + .5) T-squared = 2,700

T-squared = 2700/3 = 900

T = 30 seconds

The train speeds up for 150 seconds, reaching a speed of 30 meters per sec

and covering 2,250 meters.

It then slows down for 30 seconds, covering 450 meters.

Total time = <u>180 sec</u> = 3 minutes, minimum.

Observation:

This solution is worth more than 5 points.

time to put on the brakes, decelerate at the rate of 100, and come to a

screeching stop after a total distance of exactly 2.7 km.

The speed it reaches while accelerating is exactly the speed it starts decelerating from.

Speed reached while accelerating = (acceleration-1) (Time-1) = .2 time-1

Speed started from to slow down = (acceleration-2) (Time-2) = 1 time-2

The speeds are equal.

.2 time-1 = 1 time-2

time-1 = 5 x time-2

It spends 5 times as long speeding up as it spends slowing down.

The distance it covers speeding up = 1/2 A (5T)-squared

= 0.1 x 25 T-squared = 2.5 T-squared.

The distance it covers slowing down = 1/2 A (T-squared)

= 0.5 T-squared.

Total distance = 2,700 meters.

(2.5 + .5) T-squared = 2,700

T-squared = 2700/3 = 900

T = 30 seconds

The train speeds up for 150 seconds, reaching a speed of 30 meters per sec

and covering 2,250 meters.

It then slows down for 30 seconds, covering 450 meters.

Total time = <u>180 sec</u> = 3 minutes, minimum.

Observation:

This solution is worth more than 5 points.

218

Mary Simon

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