Math(F5) Gradient And Area Under A Graph 6.2
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This document discusses finding the area under a graph and using it to determine distance traveled from speed-time graphs. It explains that the area under a graph represents the product of the quantities on the horizontal and vertical axes. For speed-time graphs specifically, the area gives the total distance traveled by calculating the area under pieces of the graph using appropriate formulas for shapes like triangles, rectangles, and trapezoids. Examples are provided of graphs with uniform, linearly increasing, and varying speeds.
Math(F5) Gradient And Area Under A Graph 6.2
- 1. MATHEMATICS FORM 5 CHAPTER 6 GRADIENT AND AREA UNDER A GRAPH
- 2. 6.2 AREA UNDER A GRAPH
- 3. LEARNING OUTCOMES: By the end of this lesson, students will be able to: 1. Find the area under a graph. 2. determine the distance by finding the area under the following types of speed-time graph; a) v = k b) v = kt c) v = kt + h d) a combination of the above
- 4. 6.2 (B) Finding the Area Under a Graph Steps to find the area under a graph: i) Draw one or more dashed lines which are perpendicular to the x- axis. ii) Recognize the shape for the different region. iii) Use suitable formulae to find the areas.
- 5. Example 1 Find the area under the graphs: 6 y x 8 0 6 y x 8 0
- 6. 6.2 (C) Determining the Distance from the Speed-Time Graph a) When the particle travels at a uniform speed: v = k Speed (m/s) Time (s) 30 0 30
- 7. b) When the speed starts from 0 and changes at a fixed rate: v = kt Speed (m/s) Time (s) 24 0 40
- 8. c) When the speed starts from a certain value and changes at a fixed rate; v = kt + h Speed (m/s) Time (s) 40 0 20 20
- 9. d) A combination of the above. When the speed is not consistent, divide the area into several polygons. Find the area of each polygons and sum them up. Speed (m/s) Time (s) 40 10 20 35 C B A
- 10. Summary Quantity represented by the area under a graph is the product of the quantity represented by the horizontal axis and the quantity represented by the vertical axis. Area under a speed-time graph represents the distance traveled