This set mixes the five lessons of integrated physical reasoning: energy and motion, waves, thermal transfer, circuits, and nuclear or space evidence. All data are invented for practice, and the questions are original.
Cover the answers, attempt each question on paper, then open the worked solution. Use g = 10 N/kg where gravity is involved. Log each wrong answer in the mistake log and retest queue.
Starter questions
Question 1. A 3.0 kg box is lifted onto a shelf 5.0 m above the floor. Find its gravitational potential energy gain.
Show answer
GPE = mgh = 3.0 × 10 × 5.0 = 150 J.
Question 2. A 0.20 kg ball moves at 10 m/s. Find its kinetic energy.
Show answer
KE = ½mv² = ½ × 0.20 × 10² = 0.10 × 100 = 10 J.
Question 3. A wave has a frequency of 50 Hz and a wavelength of 6.0 m. Find its speed.
Show answer
v = f × λ = 50 × 6.0 = 300 m/s.
Question 4. (a) Name the process by which thermal energy reaches Earth from the Sun. (b) The handle of a metal spoon left in hot soup becomes warm. Explain this using particles.
Show answer
(a) Radiation, because the energy travels as infrared and other waves through space, which has no particles. (b) The particles of the spoon in the soup gain energy and vibrate harder. They pass energy to neighbouring particles by collisions, and free electrons in the metal carry energy along the spoon, so the handle warms by conduction.
Core questions
Question 5. A 9.0 V cell is connected to a 2.0 Ω resistor and a 4.0 Ω resistor in series. Find the current and the potential difference across the 4.0 Ω resistor.
Show answer
R = 2.0 + 4.0 = 6.0 Ω. I = 9.0 ÷ 6.0 = 1.5 A. V across 4.0 Ω = 1.5 × 4.0 = 6.0 V. The other resistor takes 1.5 × 2.0 = 3.0 V, and 6.0 + 3.0 = 9.0 V.
Question 6. The corrected count rate of a sample falls from 480 counts/min to 60 counts/min in 9.0 h. Find its half-life.
Show answer
480 → 240 → 120 → 60 is 3 halvings. 9.0 ÷ 3 = 3.0 h.
Question 7. A 0.50 kg ball is dropped from 3.2 m. Ignoring air resistance, find its speed just before landing and its kinetic energy then.
Show answer
GPE lost = 0.50 × 10 × 3.2 = 16 J. This equals the kinetic energy: 16 J. Then ½ × 0.50 × v² = 16, so v² = 64 and v = 8.0 m/s. Check: v² = 2gh = 2 × 10 × 3.2 = 64.
Question 8. In a ripple tank, 20 waves pass a marker in 8.0 s. Five wavelengths measure 20 cm. (a) Find the frequency and the speed. (b) The ripples enter shallow water where the speed is 0.060 m/s. Find the new wavelength.
Show answer
(a) f = 20 ÷ 8.0 = 2.5 Hz. λ = 20 ÷ 5 = 4.0 cm = 0.040 m. v = 2.5 × 0.040 = 0.10 m/s. (b) Frequency stays 2.5 Hz, so λ = v ÷ f = 0.060 ÷ 2.5 = 0.024 m = 2.4 cm. The wavelength is shorter because the wave is slower.
Harder questions
Question 9. A 12 V supply is connected across two lamps in parallel, of resistance 6.0 Ω and 12 Ω. (a) Find the current in each lamp and the total current. (b) The 12 Ω lamp is removed. State and explain what happens to the current in the 6.0 Ω lamp and the total power.
Show answer
(a) 12 ÷ 6.0 = 2.0 A and 12 ÷ 12 = 1.0 A. Total = 3.0 A. (b) Each branch is connected directly across the supply, so the potential difference across the 6.0 Ω lamp is still 12 V and its current stays 2.0 A. The total current falls from 3.0 A to 2.0 A, so the total power falls from 12 × 3.0 = 36 W to 12 × 2.0 = 24 W.
Question 10. A 1200 kg car travelling at 15 m/s brakes with a constant force of 6000 N. How far does it travel before stopping? Explain what happens to its kinetic energy.
Show answer
KE = ½ × 1200 × 15² = 600 × 225 = 135 000 J. Work done = force × distance, so 6000 × d = 135 000 and d = 22.5 m. The kinetic energy is transferred to thermal energy in the brakes, tyres and road, and then to the surroundings. Check: 6000 × 22.5 = 135 000 J.
Question 11. A planet moves in a circular orbit of radius 2.3 × 10¹¹ m with a period of 5.9 × 10⁷ s. Find its orbital speed to 2 significant figures. Use π = 3.14.
Show answer
v = 2πr ÷ T = (2 × 3.14 × 2.3 × 10¹¹) ÷ (5.9 × 10⁷) = 1.444 × 10¹² ÷ 5.9 × 10⁷ = 2.45 × 10⁴, so 2.4 × 10⁴ m/s. The value is about 24 km/s.
If you got these wrong
Match each kind of error to the lesson that fixes it.
| What went wrong | Go to |
|---|---|
| Energy not carried across stages, a missing ½, or unit slips with mass | Combine energy and motion in a staged problem |
| Frequency and wavelength mixed up, or the wrong quantity said to change | Interpret a wave observation and a numerical relationship |
| Process named without particles, or a cooling pattern left unexplained | Connect thermal transfer with particle behaviour |
| Series and parallel confused, or a current or power not followed through | Explain a circuit change using more than one quantity |
| Background ignored, half-lives miscounted, or orbit speed mishandled | Relate a nuclear or space model to supplied evidence |
Try the scientific investigation critic when a mistake is about judging an experiment rather than calculating. Retest each weak skill with a new question a few days later.
If a mistake keeps returning after the lesson, it usually has a reason behind it, and our teachers can find it in online one-to-one Co-ordinated Sciences tuition.