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Distance Time Graph

Distance Time Graph
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2019-04-17 07:09
FunctionCoordinate GeometryGraphing
This example demonstrates the linear relationship between distance and time through a distance-time graph. It involves core math concepts like function graphs, linear functions, and coordinate geometry. Constructed using commands such as Segment, Function, If, Sequence, Vector, and Midpoint in GeoGebra. Suitable for classroom demonstration or self-review for middle school and above.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Function(((-(x(a) / y(a))) * x) - z(a) / y(a), x(A), x(B)) → f_{AB}
  3. Segment(B, C) → b
  4. If(npart > 1, If[x(B) ≤ x ≤ x(C), ((-(x(b) / y(b))) * x) - z(b) / y(b)], f_{AB}) → f_{BC}
  5. Segment(C, D) → c
  6. If(npart > 2, If[x(C) ≤ x ≤ x(D), ((-(x(c) / y(c))) * x) - z(c) / y(c)], f_{BC}) → f_{CD}
  7. Segment(D, E) → e
  8. If(npart > 3, If[x(D) ≤ x ≤ x(E), ((-(x(e) / y(e))) * x) - z(e) / y(e)], f_{CD}) → f_{DE}
  9. Segment(E, F) → g
  10. If(npart > 4, If[x(E) ≤ x ≤ x(F), ((-(x(g) / y(g))) * x) - z(g) / y(g)], f_{DE}) → f_{EF}
  11. If(t < x(B), f_{AB}, If[t < x(C), f_{BC}, If[t < x(D), f_{CD}, If[t < x(E), f_{DE}, If[t < x(F), f_{EF}, f_{end}]]]]) → f
  12. If(turningback, ((-viewwidth)) / ((2 * carsizefactor)), viewwidth / ((2 * carsizefactor))) → halfcarwidth
  13. Function(((-viewheight)) / 5, 0, 10000) → f_{distanceline}
  14. Sequence((i / journeylinescale, journeylineseparator), i, 0, 10000, 50) → listxaxisticks, {(0, -437), (5, -437), (10, -437), (15, -437), (20, -437), (25, -437), (30, -437), (35, -437), (40, -437), (45, -437), (50, -437), (55, -437), (60, -437), (65, -437), (70, -437), (75, -437), (80, -437), (85, -437), (90, -437), (95, -437), (100, -437), (105, -437), (110, -437), (115, -437), (120, -437), (125, -437), (130, -437), (135, -437), (140, -437), (145, -437), (150, -437), (155, -437), (160, -437), (165, -437), (170, -437), (175, -437), (180, -437), (185, -437), (190, -437), (195, -437), (200, -437), (205, -437), (210, -437), (215, -437), (220, -437), (225, -437), (230, -437), (235, -437), (240, -437), (245, -437), (250, -437), (255, -437), (260, -437), (265, -437), (270, -437), (275, -437), (280, -437), (285, -437), (290, -437), (295, -437), (300, -437), (305, -437), (310, -437), (315, -437), (320, -437), (325, -437), (330, -437), (335, -437), (340, -437), (345, -437), (350, -437), (355, -437), (360, -437), (365, -437), (370, -437), (375, -437), (380, -437), (385, -437), (390, -437), (395, -437), (400, -437), (405, -437), (410, -437), (415, -437), (420, -437), (425, -437), (430, -437), (435, -437), (440, -437), (445, -437), (450, -437), (455, -437), (460, -437), (465, -437), (470, -437), (475, -437), (480, -437), (485, -437), (490, -437), (495, -437), (500, -437), (505, -437), (510, -437), (515, -437), (520, -437), (525, -437), (530, -437), (535, -437), (540, -437), (545, -437), (550, -437), (555, -437), (560, -437), (565, -437), (570, -437), (575, -437), (580, -437), (585, -437), (590, -437), (595, -437), (600, -437), (605, -437), (610, -437), (615, -437), (620, -437), (625, -437), (630, -437), (635, -437), (640, -437), (645, -437), (650, -437), (655, -437), (660, -437), (665, -437), (670, -437), (675, -437), (680, -437), (685, -437), (690, -437), (695, -437), (700, -437), (705, -437), (710, -437), (715, -437), (720, -437), (725, -437), (730, -437), (735, -437), (740, -437), (745, -437), (750, -437), (755, -437), (760, -437), (765, -437), (770, -437), (775, -437), (780, -437), (785, -437), (790, -437), (795, -437), (800, -437), (805, -437), (810, -437), (815, -437), (820, -437), (825, -437), (830, -437), (835, -437), (840, -437), (845, -437), (850, -437), (855, -437), (860, -437), (865, -437), (870, -437), (875, -437), (880, -437), (885, -437), (890, -437), (895, -437), (900, -437), (905, -437), (910, -437), (915, -437), (920, -437), (925, -437), (930, -437), (935, -437), (940, -437), (945, -437), (950, -437), (955, -437), (960, -437), (965, -437), (970, -437), (975, -437), (980, -437), (985, -437), (990, -437), (995, -437), (1000, -437)}
  15. Vector((x(C_2), y(C_2) + (0.05 * viewheight)), C_2) → w
  16. Midpoint(a) → P_{midAB}
  17. Midpoint(b) → P_{midBC}
  18. Midpoint(c) → P_{midCD}
  19. If(t < x(B), abs(y(Q) - y(A)), If[t < x(C), abs(y(B) - y(A)) + abs(y(Q) - y(B)), If[t < x(D), abs(y(B) - y(A)) + abs(y(C) - y(B)) + abs(y(Q) - y(C)), If[t < x(E), abs(y(B) - y(A)) + abs(y(C) - y(B)) + abs(y(D) - y(C)) + abs(y(Q) - y(D)), If[t < x(F), abs(y(B) - y(A)) + abs(y(C) - y(B)) + abs(y(D) - y(C)) + abs(y(E) - y(D)) + abs(y(Q) - y(E)), totaljourneydistance]]]]) → totaldistancetravelled
  20. Sequence(Text[i, (i / journeylinescale - 1.5, journeylineseparator), true, true], i, 0, 10000, 50) → list1, {"0", "50", "100", "150", "200", "250", "300", "350", "400", "450", "500", "550", "600", "650", "700", "750", "800", "850", "900", "950", "1000", "1050", "1100", "1150", "1200", "1250", "1300", "1350", "1400", "1450", "1500", "1550", "1600", "1650", "1700", "1750", "1800", "1850", "1900", "1950", "2000", "2050", "2100", "2150", "2200", "2250", "2300", "2350", "2400", "2450", "2500", "2550", "2600", "2650", "2700", "2750", "2800", "2850", "2900", "2950", "3000", "3050", "3100", "3150", "3200", "3250", "3300", "3350", "3400", "3450", "3500", "3550", "3600", "3650", "3700", "3750", "3800", "3850", "3900", "3950", "4000", "4050", "4100", "4150", "4200", "4250", "4300", "4350", "4400", "4450", "4500", "4550", "4600", "4650", "4700", "4750", "4800", "4850", "4900", "4950", "5000", "5050", "5100", "5150", "5200", "5250", "5300", "5350", "5400", "5450", "5500", "5550", "5600", "5650", "5700", "5750", "5800", "5850", "5900", "5950", "6000", "6050", "6100", "6150", "6200", "6250", "6300", "6350", "6400", "6450", "6500", "6550", "6600", "6650", "6700", "6750", "6800", "6850", "6900", "6950", "7000", "7050", "7100", "7150", "7200", "7250", "7300", "7350", "7400", "7450", "7500", "7550", "7600", "7650", "7700", "7750", "7800", "7850", "7900", "7950", "8000", "8050", "8100", "8150", "8200", "8250", "8300", "8350", "8400", "8450", "8500", "8550", "8600", "8650", "8700", "8750", "8800", "8850", "8900", "8950", "9000", "9050", "9100", "9150", "9200", "9250", "9300", "9350", "9400", "9450", "9500", "9550", "9600", "9650", "9700", "9750", "9800", "9850", "9900", "9950", "10000"}