• 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?