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How do you find the total distance of a 2-part trip using the speed vs time graph?
In the classic 'Dumb and Dumber', Lloyd and Harry drive from Nebraska to Aspen on a scooter after Lloyd trades in their van, straight up. How long would it take to drive their scooter, traveling at 40 miles per hour, the 390 mile distance from middle Nebraska to Aspen Colorado?
Summary
- S- start location
- N- the notch point where the sprinter starts going faster
- F- the finish line
- d1- distance between start and the notch point
- d2- distance between notch point and finish
- t- time
- s- speed
- m- meters
- sec-seconds
- Find the total distance

Notes
-
- m- meters
- sec- seconds
- Plot the speed for the start, notch, and finish time points
- Straight lines connect the points since acceleration for each leg is constant
- d1- distance between start and notch
- d2- distance between notch and finish
- If you forget the trapezoid area formula, just break it up into a triangle and rectangle
-
- The area under a speed vs. time graph tells you the distance traveled
-
- d1- distance between start and notch
- b- triangle base
- h- triangle height
- m- meters
-
- d1- distance between the notch and the finish
- b1- the smaller parallel trapezoid base
- b2- the larger parallel trapezoid base
- h- the nonparallel perpendicular trapezoid height
-
- d2- distance between the notch and the finish
- m- meters
-
- d- total distance
- d1- distance between the start and the notch
- d2- distance between the notch and the finish
- m- meters
-
- m- meters
- sec- seconds
- vo- initial velocity
- vf- final velocity
- t- time
- d1- distance for part I, the unknown
-
- m- meters
- sec- seconds
- vo- initial velocity, in this case the initial velocity is the final velocity from part I
- vf- final velocity
- t- time
- d2- distance for part II, the unknown