Gradient & area under a graph
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The document explains how to calculate and interpret the gradient and area under a graph, particularly focusing on distance-time and speed-time graphs. It illustrates the concepts through a scenario involving a character named Hanif walking to a canteen and back to his office. Key formulas and graphical representations for calculating speed and understanding motion are also included.
Gradient & area under a graph
- 1. Gradient & Area Under a GraphQuantity Represented by the Gradient of a GraphQuantity Represented by the Area Under a Graph
- 2. Quantity Represented by the Gradient of a GraphRate of change of the quantity on vertical axis with respect to the quantity on the horizontal axisDistance (meter)Time (second)
- 3. Formula to Calculate GradientMethode 1 =Distance (meter)Vertical distanceHorizontal distanceTime (second)
- 4. Formula to Calculate GradientMethod 2 = Distance (meter)Q (x2,y2)P (x1,y1)Time (second)
- 5. Calculating the Speed from the Distance-Time GraphWhen the gradient of a distance-time graph calculated,You are calculating the speedgradient of a distance-time graph = speed
- 6. Distance-Time GraphHanif walk from his office to canteen for some refreshment. After finish his drink, he get back to his office to continue his work.The distance-time graph can be draw according to the story
- 7. Distance-Time GraphHanif travel from his office to canteenHanif take a break at canteenDistance (meter)Hanif go back to his officeTime (second)
- 8. Quantity Represented by the Area Under a GraphArea under a graph is the product of quantity in Y-axis with X-axis.Area under a speed-time graph = distance
- 9. Speed-Time GraphGradient is positive, it is acceleratingspeed ms-1Horizontal, constant speedNegative gradient, decreasing speedTime (s)
- 10. Good LuckEnjoy your study