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Analyzing Velocity and Displacement of an Object Along a Horizontal Path

This analysis investigates the motion of an object along a straight horizontal path using various graphs. By interpreting displacement, velocity, and acceleration graphs, we calculate the velocity of the object at specific time intervals, including 10 seconds and 30 seconds. Furthermore, we demonstrate how to determine displacement using the area under velocity-time graphs and how to find changes in velocity through acceleration-time graphs. This detailed approach aids in understanding kinematics and the relationship between motion variables.

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Analyzing Velocity and Displacement of an Object Along a Horizontal Path

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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

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