Year 9 Science · Unit 4 · Lesson 12
Challenge Worksheet
Learning Goals
Read the graph — Stopping distances on NSW roads
The stacked bar chart shows thinking distance (lighter) and braking distance (darker) at four speeds. Study it, then answer the questions.
Data: Transport for NSW (2023). Speeding: It's not worth the risk.
(a) By how many times does total stopping distance increase when speed doubles from 50 km/h to 100 km/h? Show your calculation.
(b) Convert 100 km/h to m/s. Show your working.
(c) The graph shows that braking distance increases much faster than thinking distance as speed increases. Explain why braking distance grows faster than speed, using the idea that kinetic energy increases with the square of speed (KE ∝ v²).
Policy scenario
The NSW Government is considering lowering the urban speed limit from 50 km/h to 40 km/h. Proponents argue the change will save lives; opponents argue it will significantly slow down commutes. Use the speed formula and stopping distance data to evaluate both sides of the argument.
(a) Using the stopping distance data from the graph, estimate the total stopping distance at 40 km/h. (Hint: thinking distance scales roughly with speed; braking distance scales with speed squared. At 50 km/h, thinking = 14 m, braking = 13 m.) Calculate approximate values at 40 km/h and compare to 50 km/h. Show reasoning.
(b) Calculate how much longer a 5 km commute would take at 40 km/h compared to 50 km/h. Give your answer in minutes and seconds. Show all working. (Use t = d ÷ v; convert units carefully.)
(c) Using your calculations from (a) and (b), evaluate whether the safety benefit of lowering the speed limit to 40 km/h justifies the extra travel time cost. State your conclusion and support it with at least two pieces of quantitative evidence from your working above.
Wrap Up
In one sentence, what was the main idea of this lesson?