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The velocity-time graph below shows the journey of a train. How far, in metres (m), did the train travel at a velocity greater than 30 m/s? If your answer is a decimal, give it to 1 d.p​

The velocity-time graph below shows the journey of a train. How far, in metres (m-example-1
User Dvkch
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Answer:

2700 metres

Explanation:

You want to know the number of metres travelled by a train when its velocity is greater than 30 m/s, given the graph of velocity vs. time.

When

The graph shows the velocity is 30 m/s at time = 20 s, rising linearly to 60 m/s at time = 40 s, then falling linearly to 30 m/s at time = 80 s.

The time period of interest is between 20 s and 80 s.

Speed

The average speed on the interval is the average of the minimum and maximum speeds on the interval:

(30 m/s + 60 m/s)/2 = 45 m/s

Distance

The distance traveled is the product of the average speed and the length of time:

d = st

d = (45 m/s)(80 -20 s) = 2700 m

The train travelled 2700 metres at a velocity greater than 30 m/s.

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Additional comment

The area under the curve on the interval [20, 80] can be divided into two trapezoids. The "bases" of each trapezoid are the velocities at the beginning and end of the relevant time interval. So, the area will be ...

1/2(30+60)(20) +1/2(60+30)(40)

= 1/2(30 +60)(20+40) = (45)(60) . . . . as above

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User SagiZiv
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