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X. v ( t ) ( m/s). 120. 20. v f. t (s). t (s). (0,0 ). (0,0). 10. 10. The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 10 seconds. x ( t ) (m). X. v ( t ) ( m/s). 120. 20. v f. t (s). t (s). (0,0 ).

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  2. v(t) (m/s) 120 20 vf t (s) t (s) (0,0) (0,0) 10 10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 10 seconds. x(t) (m)

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  4. v(t) (m/s) 120 20 vf t (s) t (s) (0,0) (0,0) 10 10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 10 seconds. x(t) (m)

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  6. x(t) (m) v(t) (m/s) 200 25 vf 40 t (s) t (s) (0,0) (0,0) 10 10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 10 seconds. Displacement is equal to the area under the (v-t) graph. Area under the (v-t) graph = Area of triangle + Area of rectangle Area = ½ (base)(height) + (base)(height) = ½ (10) (25 - vf) + (10) (vf) Displacement, x = 200 m – 40 m = 160 m from (x-t) graph. 3) Equate the answer of (1) and (2) to get vf=7.0 m/s .

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  8. x(t) (m) v(t) (m/s) 100 t (s) (0,0) 10 vf t (s) (0,0) 10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 10 seconds. 30 Displacement is equal to the area under the (v-t) graph. Area under the (v-t) graph = Area of triangle  Area = ½ (base)(height) = ½ (10) (vf) Displacement, x= 30 m - 100 m = - 70 m from (x-t) graph. 3) Equate the answer of (1) and (2) to find vf= -14.0 m/s.

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  10. v(t) (m/s) 20 20 (0,0) t (s) t (s) (0,0) 20 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 30 seconds. x(t) (m) 10 30 10 30 -1.0 -20 vf

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  12. v(t) (m/s) 20 20 (0,0) t (s) t (s) (0,0) 20 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the velocity of the object at 30 seconds. x(t) (m) 10 30 10 30 -1.0 -20 vf

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  14. The motion of an object along a straight horizontal path is shown by the graphs below. Determine the time tf. v(t) (m/s) x(t) (m) 100 (0,0) 10 t (s) tf 5 -100 (0,0) t (s) tf 5

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  16. The motion of an object along a straight horizontal path is shown by the graphs below. Determine the time tf. v(t) (m/s) x(t) (m) 100 (0,0) 10 t (s) tf 5 -100 (0,0) t (s) tf 5

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  18. v(t) (m/s) a (t) (m/s2) vf 20 t (s) t (s) (0,0) (0,0) 5 5 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. 100 5 10 10

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  20. v(t) (m/s) a (t) (m/s2) vf 20 t (s) t (s) (0,0) (0,0) 5 5 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. 100 5 10 10

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  22. v(t) (m/s) a (t) (m/s2) 30 t (s) t (s) (0,0) (0,0) 5 5 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. Find area under the (a-t) graph Area = Area of Pink Rectangle + Area of Brown Rectangle vf 200 Area=5(30)+5(10) Change in velocity, v = vf – 50 m/s 10 50 Area = 200 m/s 10 10 Change in velocity from (v-t)graph Area under the (a-t) graph = vf – 50 m/s =200 m/s vf = 250 m/s

  23. v(t) (m/s) a (t) (m/s2) 30 t (s) t (s) (0,0) (0,0) 5 5 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. vf=250 200 10 50 10 10 vf = 250 m/s

  24. v(t) (m/s) a (t) (m/s2) 30 t (s) t (s) (0,0) (0,0) 5 5 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. Area under the (v-t) graph is displacement. Area = Area of pink triangle + Area of green triangle + Area of brown rectangle + Area of purple rectangle vf=250 200 10 50 10 10 +(5)(50) +(5)(200) = 1750 m + ½ (5)(150) Area = ½ (5)(50) Thus displacement = 1750 m

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  26. a (t) (m/s2) 2 (0,0) t (s) -10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. Find area under the (a-t) graph v(t) (m/s) Area = Area of Pink Rectangle + Area of Brown Rectangle 100 80 4 Change in velocity, v = vf – 100 m/s Area = 2(–10) + 2(–30) vf -30 t (s) Area = –80 m/s (0,0) 4 2 Change in velocity from (v-t)graph Area under (a-t) graph = vf – 100 m/s = – 80 m/s vf = 20 m/s

  27. a (t) (m/s2) 2 (0,0) t (s) -10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. v(t) (m/s) 100 80 4 vf=20 -30 t (s) (0,0) 4 2 vf = 20 m/s

  28. a (t) (m/s2) 2 (0,0) t (s) -10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. v(t) (m/s) Area under the (v-t) graph is displacement. 100 Area = Area of pink triangle + Area of green rectangle + Area of purple triangle + Area of brown rectangle 80 4 vf=20 -30 t (s) (0,0) 4 2 = 280 m +(2)(20) + (2)(80) Area = ½ (2)(20) +½ (2)(60) Thus displacement = 280 m

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  30. v(t) (m/s) a (t) (m/s2) 5 (0,0) 20 t (s) (0,0) The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object vf t (s) 10 30 -2 10 30

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  32. v(t) (m/s) a (t) (m/s2) 5 (0,0) 20 t (s) (0,0) The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object vf t (s) 10 30 -2 10 30

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  34. v(t) (m/s) a (t) (m/s2) 10 10 (0,0) t (s) t (s) (0,0) 10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. 100 80 tf -4 tf

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  36. v(t) (m/s) a (t) (m/s2) 10 10 (0,0) t (s) t (s) (0,0) 10 The motion of an object along a straight horizontal path is shown by the graphs below. Determine the displacement of the object. 100 80 tf -4 tf

  37. Thank You

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