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2 years ago

The graph below describes the journey of a train between two cities.

Mathematics

1 answer:

Veseljchak [2.6K]2 years ago

5 0

Answer:

[A] Acceleration in first 15 min = 200 km/h²

[B] Distance between two cities = 125 km

[C] Average Speed of journey = 62.5 km/hr

Step-by-step explanation:

To Solve:

Acceleration in first 15 min

Distance between two cities

Average speed of journey

Solve:

[A] Work out the acceleration, in km/h?, in the first 15 mins.

Each horizontal block is 1/8 hr = 7.5 min

Each vertical block is 10 km/hr

Time Velocity km/hr

0 Min ( 0 hr) 0

15 Min (1/4 hr) 50

45 Min (3/4 hr) 50

60 MIn ( 1 hr) 100

90 Min ( 3/2 hr) 100

120 Min ( 2hr) 0

Acceleration in first 15 min (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)

= 200 km/h²

Hence, Answer for [A] = 200 km/h²

[B] Work out the distance between the two cities. $60 Velocity (in km/h)

= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

= 25/4 + 25 + 75/4 + 50 + 25

= 125

Distance between two cities = 125 km

[C] Work out the average speed of the train during 20 the journey.

Average Speed of journey = 125/2 = 62.5 km/hr

[RevyBreeze]

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