a car stops at a set of traffic lights, then moves away by the formula: d=3t 2 draw a table of time...
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• A car stops at a set of traffic lights, then moves away by the formula: d=3t2
• Draw a table of time and distance for the six seconds after the car moves away.
Time Distance
012...
03
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 2nd and 3rd seconds?
• How might we calculate her speed at exactly 3 seconds?
Task Three
Time Distance3 273.1 28.83
0.1 1.83
Speed 18.3
• 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.
Time Speed 0 1 2 3 …
0
18
Speed Function
Task Five
• Complete a time / speed table for the following formulas:
d=4t2 d=5t2 d=0.5t2
• Repeat for the following cubics:
d=t3 d=3t3 d=5t3
Task Six
• Notation to know:
Distance function Speed function
f(x) = 3t2 f ’(x) = 6t• Complete the following table:
Distance Function
Speed Function
f(x) = 3t2 f ‘(x) = 6t
f(x) = 4t2 …
Task Seven
Further Questions:• Can you guess what the speed function would be
for the following distance functions:• f(x) = 3t• f(x) = t4
• f(x) = 6t5
• f(x) = -2t3
• Another name for the speed function is the gradient function. Why do you think this is?
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