Distance is the area under the speed graph: a rectangle for a steady speed, a triangle or trapezoid for a steady speed-up. The same holds for any rate: flow into gallons, power into kilowatt-hours.
Opens on Chapter 17’s example: Arturo’s bus from the depot to the first stop: 0 to 30 mph in 20 seconds, 30 mph for 2 minutes, then 30 to 0 in 15 seconds.
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How it works
On a graph of rate against time, each piece is a trapezoid: (starting rate + ending rate) ÷ 2 × time. A steady piece is a rectangle and a speed-up from rest a triangle, half of the rectangle. With speeds in mph and times in seconds, multiply the speed by 5,280 ÷ 3,600 to get feet per second (30 mph is 44 ft/s). A rate below zero (backing up, draining) makes area below the axis: count it as minus for where you end up, and as plus for how far you went in all.
From the book, Chapter 17. Speeding up: 440 feet; steady: 5,280; slowing: 330; total 6,050 feet, about 1.15 miles in 155 seconds. Merging from 30 to 60 mph takes 990 feet. The pump moves 78,000 gallons; the oven uses 2.75 kWh (44¢); the forklift ends 18 feet ahead after driving 42. Every chapter and its calculator →
Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. Functions can be typed as 16t², 6 + 48t − 16t^2, 1000e^(0.05t) or √x; answers are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.
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