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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