Task One
• 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
0
1
2
...
0
3
• Is the car accelerating? How can you tell?
Task Two
• After 3 seconds a cop pulls the car over.
• 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
• We need to find out the instantaneous speed of
the car at exactly 3 seconds.
• The following Excel spreadsheet will help:
Time
Difference
Time
3
3.1
Distance
27
28.83
0.1
1.83
Speed
18.3
Distance
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
0
1
2
3
…
Speed Function
Speed
0
18
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
f(x) = 3t
2
f(x) = 4t
…
2
Speed Function
‘
f (x) = 6t
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?