A car stops at a set of traffic lights, then moves away by the formula: d=3t 2 Draw a table of time and distance for the six seconds after the car moves.

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Presentation transcript:

A car stops at a set of traffic lights, then moves away by the formula: d=3t 2 Draw a table of time and distance for the six seconds after the car moves away. TimeDistance Task One Is the car accelerating? How can you tell?

After 3 seconds a cop pulls the car over. Task Two The driver wants to know if she was speeding or not. Average speed = distance traveled time taken What was her average speed over the first second? The 2 nd and 3 rd seconds? How might we calculate her speed at exactly 3 seconds?

Task Three We need to find out the instantaneous speed of the car at exactly 3 seconds. The following Excel spreadsheet will help: Distance Difference Time Difference

Task Four From the Excel Spreadsheet we can see that the instantaneous speed at t = 3 seconds is 18 m/s. Copy and complete the following table for the instantaneous speed at the given times.

Task Five Complete a time / speed table for the following formulas: d=4t 2 d=5t 2 d=0.5t 2 Repeat for the following cubics: d=t 3 d=3t 3 d=5t 3

Task Six Notation to know: Distance function Speed function f(x) = 3t 2 f ’ (x) = 6t Complete the following table:

Task Seven Further Questions: Can you guess what the speed function would be for the following distance functions: f(x) = 3t f(x) = t 4 f(x) = 6t 5 f(x) = -2t 3 Another name for the speed function is the gradient function. Why do you think this is?