In today's blog, we attempt to tackle two fairly complex topics in the GCSE course. Firstly, we look at Estimating gradients.Calculating the average gradient from beginning to end does not give a good representation of what is happening in the graph. What can be done is to break the graph down into smaller sections and the average gradient of those are calculated to give a better idea of what is happening. Another method is to find the gradient at specific points on the graph, this involves constructing a series of tangents by eye and calculating the gradient at each point. This is where an estimate comes in because each tangent may vary slightly.
Secondly, we take a look at the area under a curve. The area under a velocity-time graph (most common question) will give you the distance that the object/particle has travelled. You will have to break the graph up into equal widths to give you a triangle and a series of trapezia. Calculate the area of each shape and that will tell the distance travelled.