Physics Numericals Step by Step: A Method for Class 9 to 11

Last updated 10 October 2026. Worked examples are at FBISE Class 9 to 11 level. Symbols may differ slightly from your textbook (u and v or vi and vf); use your book's notation.

#Why do students lose marks in physics numericals?

Students usually lose marks in physics numericals for missing units, skipped steps and wrong unit conversions, not for hard physics. FBISE written sections reward working: Section B and C questions on the SSC-II Physics model paper carry 3 marks or more each, and the HSSC-II model paper includes numericals like orbital speed and capacitive reactance in its short questions. A neat method protects those marks, and it is one of the easy-mark habits in our guide on how to aim for 95% in FBISE Class 10.

#What is the five-line method to solve physics numericals step by step?

The five-line method is a fixed layout that you use for every numerical:

1. Given: each quantity with its symbol, value and SI unit.
2. Required: the quantity you need, with its symbol.
3. Formula: the equation that links them.
4. Substitution: values with units put into the formula.
5. Answer: the result with its SI unit, boxed or underlined.

Add a sixth step in your head: check. Is the size sensible? Is the unit right? A car moving at 2,000 m/s is a sign something went wrong.

#Which SI units do you need to know?

You need the SI unit of every quantity you use, because mixing units is the fastest way to a wrong answer.

Common conversions: 1 km = 1000 m; 1 g = 0.001 kg; 1 cm = 0.01 m; 1 hour = 3600 s. To convert km/h to m/s, divide by 3.6 (so 72 km/h = 20 m/s).

#Worked example 1 (Class 9): How do you use the equations of motion?

Question: A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. Find its final velocity and the distance covered.

Given: vi = 0 m/s (starts from rest), a = 2 m/s², t = 5 s
Required: vf = ?, S = ?

Formula 1: vf = vi + at
Substitution: vf = 0 + (2 m/s²)(5 s)
Answer: vf = 10 m/s

Formula 2: S = vi t + ½ a t²
Substitution: S = 0 + ½ (2 m/s²)(5 s)² = ½ × 2 × 25
Answer: S = 25 m

Check: 2aS = vf² − vi² gives 2 × 2 × 25 = 100, and 10² − 0² = 100. It matches.

#Worked example 2 (Class 9): How do you handle unit conversion?

Question: A car moving at 72 km/h brakes and stops uniformly in 4 s. Find its deceleration and stopping distance.

Given: vi = 72 km/h = 72 ÷ 3.6 = 20 m/s, vf = 0 m/s, t = 4 s
Required: a = ?, S = ?

Formula: a = (vf − vi) / t
Substitution: a = (0 − 20 m/s) / 4 s
Answer: a = −5 m/s² (the minus sign means deceleration of 5 m/s²)

Formula: S = ((vi + vf) / 2) × t
Substitution: S = ((20 + 0) / 2) × 4 = 10 × 4
Answer: S = 40 m

If you had used 72 instead of 20, you would get a deceleration of 18 "units" and a distance of 144 "units", both wrong. Convert first, always.

#Worked example 3 (Class 9): How do you solve force questions?

Question: A 1200 kg car accelerates at 2.5 m/s². What net force acts on it? If friction is 600 N, what force must the engine provide?

Given: m = 1200 kg, a = 2.5 m/s², friction f = 600 N
Required: F(net) = ?, F(engine) = ?

Formula: F = ma
Substitution: F = (1200 kg)(2.5 m/s²)
Answer: F(net) = 3000 N

The engine must overcome friction and still provide the net force:
F(engine) = F(net) + f = 3000 N + 600 N = 3600 N

#Worked example 4 (Class 9): How do you find work and power?

Question: A 50 kg student climbs stairs 6 m high in 12 s. Find the work done against gravity and the power. Take g = 9.8 m/s².

Given: m = 50 kg, h = 6 m, t = 12 s, g = 9.8 m/s²
Required: W = ?, P = ?

Formula: W = mgh
Substitution: W = (50 kg)(9.8 m/s²)(6 m)
Answer: W = 2940 J

Formula: P = W / t
Substitution: P = 2940 J / 12 s
Answer: P = 245 W

#Worked example 5 (Class 10): How do you solve series and parallel circuits?

Question: Resistors of 4 Ω and 6 Ω are connected to a 12 V battery. Find the current (a) in series and (b) in parallel.

(a) Series
Formula: R(eq) = R₁ + R₂ = 4 Ω + 6 Ω = 10 Ω
Formula: I = V / R
Substitution: I = 12 V / 10 Ω
Answer: I = 1.2 A
Check: voltage across 4 Ω = 1.2 × 4 = 4.8 V; across 6 Ω = 1.2 × 6 = 7.2 V; total 12 V. Correct.

(b) Parallel
Formula: 1/R(eq) = 1/R₁ + 1/R₂ = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
So: R(eq) = 12/5 = 2.4 Ω
Substitution: I = 12 V / 2.4 Ω
Answer: I = 5 A

Check: the parallel resistance (2.4 Ω) is smaller than the smallest resistor (4 Ω), as it should be.

#Worked example 6 (Class 10): How do you use the wave equation?

Question: A sound wave of frequency 170 Hz travels in air at 340 m/s. Find its wavelength.

Given: f = 170 Hz, v = 340 m/s
Required: λ = ?
Formula: v = fλ, so λ = v / f
Substitution: λ = 340 m/s / 170 Hz
Answer: λ = 2 m

#Worked example 7 (Class 11): How do you solve projectile motion?

Question: A ball is thrown at 20 m/s at 30° above the horizontal from level ground. Find its time of flight, maximum height and horizontal range. Take g = 9.8 m/s² and ignore air resistance.

Given: v₀ = 20 m/s, θ = 30°, g = 9.8 m/s²; sin 30° = 0.5, sin 60° ≈ 0.866
Required: T = ?, H = ?, R = ?

Time of flight: T = 2v₀ sin θ / g = (2 × 20 × 0.5) / 9.8 = 20 / 9.8
Answer: T ≈ 2.04 s

Maximum height: H = v₀² sin²θ / 2g = (400 × 0.25) / 19.6 = 100 / 19.6
Answer: H ≈ 5.10 m

Range: R = v₀² sin 2θ / g = (400 × 0.866) / 9.8 = 346.4 / 9.8
Answer: R ≈ 35.3 m

Check: a launch at 60° would give the same range, since sin 120° = sin 60°. That symmetry is a nice way to test your answer.

#How do you get faster at physics numericals?

You get faster at physics numericals by doing a few every day, not twenty the night before the paper. A simple progression works:

1. One-formula questions until you can do them without looking at notes.
2. Two-step questions where you find an in-between quantity first (like a in example 2).
3. Mixed sets from different chapters, so you practise choosing the formula.
4. Timed past paper sections in the last two months (see how to use past papers).

Keep a formula sheet with every formula, what each symbol means and its unit. Write it from memory once a week. With the new 50% MCQ pattern, Class 9 and 11 papers also contain scenario-based MCQs that need quick calculations (SSC-I Physics model paper), so speed matters more than before. The FBISE paper pattern guide has the details.

#Can seeing the physics help with numericals?

Yes. Many numerical mistakes come from not picturing what is happening, such as forgetting that a ball thrown up slows down. Qurricular is a board exam prep app for Pakistani students from Class 9 to A Level, and its free physics lab lets you launch projectiles and change gravity and friction, so you can see why the numbers come out the way they do. Its AI study partner, Ryder, can also walk you through a numerical step by step at your class level.