Total marks: 100 · Duration: 2 hours 30 minutes
Instructions to candidates
- This paper consists of SIX compulsory questions in two sections. Answer ALL questions.
- Section A has THREE structured questions worth 55 marks. Question 1 is a data analysis question worth 25 marks; do NOT spend more than 30 minutes on it.
- Section B has THREE extended response questions worth 15 marks each (45 marks).
- In the January 2027 sitting this paper is "hybrid": you read the questions on screen and write your answers in the answer booklet. Graph paper is provided in the booklet.
- A silent, non-programmable calculator may be used. Show all working and give units with your answers.
- Where needed, use: speed of light c = 3.00 × 10⁸ m s⁻¹; speed of sound in air = 340 m s⁻¹; specific heat capacity of water = 4200 J kg⁻¹ °C⁻¹.
Paper
Section A — Structured Questions (55 marks)
Question 1 (data analysis)
A student investigates the motion of a trolley released from rest on a straight ramp 2.00 m long, with one end raised 0.40 m above the bench. She releases the trolley from rest at the top and times how long it takes to reach the bottom. She repeats the run three times and obtains 2.2 s, 2.0 s and 2.1 s.
She then releases the trolley from rest at different distances s from the bottom of the ramp and records the mean time t for each. Her results are shown in the table; two values of t² have been left blank.
| Distance s / m | Mean time t / s | t² / s² |
|---|---|---|
| 0.40 | 0.94 | 0.88 |
| 0.80 | 1.33 | |
| 1.20 | 1.63 | 2.66 |
| 1.60 | 1.88 | |
| 2.00 | 2.10 | 4.41 |
(a) Calculate the mean of her three times for the full 2.00 m ramp. (1 mark)
(b) Using your answer to (a), calculate the average speed of the trolley down the full ramp. (2 marks)
(c) Copy and complete the table by calculating t² for the distances 0.80 m and 1.60 m. (2 marks)
(d) On graph paper in your answer booklet, plot a graph of s (vertical axis) against t² (horizontal axis) and draw the line of best fit. (4 marks)
(e) Determine the gradient of your line, showing the values you used. (2 marks)
(f) For an object starting from rest with uniform acceleration a, s = ½ a t². Use your gradient to find the acceleration of the trolley. (2 marks)
(g) Calculate the speed of the trolley as it reaches the bottom of the 2.00 m ramp, and show that it is about twice the average speed found in (b). (2 marks)
(h) Explain, in terms of forces, why the trolley accelerates down the ramp. (2 marks)
(i) Suggest ONE reason why the student timed each run three times. (1 mark)
(j) Plan and design an experiment to investigate how the height of the raised end of the ramp affects the acceleration of the trolley. Your answer should include:
(i) a hypothesis (1 mark)
(ii) the method, including the apparatus you would use (3 marks)
(iii) TWO variables you would keep constant (1 mark)
(iv) a results table with suitable headings (1 mark)
(v) the results you would expect if your hypothesis is correct (1 mark)
Total 25 marks
Question 2
A home has a 230 V mains supply. Each circuit has a live wire (brown), a neutral wire (blue) and an earth wire (green and yellow). Two appliances are connected: a kettle rated 230 V, 2000 W and a lamp rated 230 V, 60 W.
(a) (i) State the purpose of the earth wire. (1 mark)
(ii) Explain why the fuse is always placed in the live wire and not in the neutral wire. (2 marks)
(b) Calculate the current drawn by the kettle when operating at its rated power. (2 marks)
(c) Fuses are available in ratings of 3 A, 5 A, 10 A and 13 A. State which fuse should be fitted to the kettle, giving a reason for your answer. (2 marks)
(d) The kettle heats 1.5 kg of water from 28 °C to 100 °C. Calculate the minimum energy required. (3 marks)
(e) Calculate the shortest time in which the kettle could supply this energy. (2 marks)
(f) The lamp is used for 5 hours every day. Calculate the cost of running it for 30 days if electricity costs $0.80 per kilowatt-hour. (3 marks)
Total 15 marks
Question 3
(a) (i) What is meant by the electromagnetic spectrum? (2 marks)
(ii) Name TWO regions of the electromagnetic spectrum that have higher frequencies than visible light. (2 marks)
(iii) State TWO properties shared by all electromagnetic waves. (2 marks)
(b) Red light from a lamp has a wavelength of 6.56 × 10⁻⁷ m. Calculate its frequency. (2 marks)
(c) A group of students stand at a distance from Gros Piton in Saint Lucia and shout towards the mountain. They hear an echo 4.0 seconds after shouting.
(i) What is an echo? (1 mark)
(ii) Calculate the distance between the students and Gros Piton. (3 marks)
(iii) Suggest TWO reasons why the echo sounds quieter than the original shout. (2 marks)
(d) Explain why sound cannot travel through a vacuum although light can. (1 mark)
Total 15 marks
Section B — Extended Response (45 marks)
Question 4
Several countries generate electricity from nuclear fission.
(a) Describe the process by which energy is released in a nuclear fission reactor. In your answer, include:
- the nuclear reaction that takes place
- the role of neutrons in sustaining the reaction
- how the energy released is converted to electrical energy. (8 marks)
(b) In one fission of a uranium-235 nucleus, the total mass of the products is 3.2 × 10⁻²⁸ kg less than the mass of the reactants.
(i) Calculate the energy released in one fission. (2 marks)
(ii) Calculate how many fissions must occur each second to produce a power of 1.0 MW. (2 marks)
(c) (i) Explain the purpose of the control rods in a reactor. (2 marks)
(ii) Explain why spent fuel from a reactor must be stored securely for a very long time. (1 mark)
Total 15 marks
Question 5
Several Caribbean nations are exploring renewable energy such as geothermal, solar and wind power. The table compares two methods of generating electricity.
| Feature | Nuclear fission | Geothermal |
|---|---|---|
| Fuel source | Uranium-235 | Heat from the Earth's interior |
| CO₂ emissions during operation | Very low | Very low |
| Energy output per kg of fuel | Very high | Not applicable |
| Initial construction cost | Very high | Moderate |
| Risk of catastrophic accident | Low, but serious if it occurs | Very low |
| Waste disposal issues | Significant (radioactive) | Minimal |
(a) Describe the energy conversions that take place in a geothermal power station, from the hot rock to the electricity supplied. (4 marks)
(b) Evaluate the use of nuclear fission compared with geothermal energy for generating electricity in a Caribbean country. Consider environmental impacts, economic factors, safety and suitability for the region, and make a justified recommendation for a country such as Saint Lucia or Dominica. (11 marks)
Total 15 marks
Question 6
Electricity from a power station reaches homes through a transmission network.
(a) Describe how a simple a.c. generator produces an alternating electromotive force (e.m.f.). (4 marks)
(b) State Faraday's law of electromagnetic induction, and give TWO ways of increasing the e.m.f. induced in a generator. (3 marks)
(c) At the power station a transformer steps up the voltage from 11 kV to 132 kV. Its primary coil has 500 turns. Calculate the number of turns on the secondary coil. (2 marks)
(d) Explain why electrical energy is transmitted at a high voltage. (3 marks)
(e) A power of 2.0 MW is sent along cables with a total resistance of 5.0 Ω. Calculate the power lost as heat in the cables when the transmission voltage is 132 kV. (3 marks)
Total 15 marks