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Physics numericals are graded heavily on method, not just the final number — examiners want to see the right formula chosen, the right values substituted, and the right units carried through. Unlike pure math problems, physics numericals also test whether you understand what each quantity physically means, since that's what tells you which formula applies in the first place. These 15 examples span the four topics that dominate Matric and FSc physics papers: kinematics, force, work & energy, and basic electricity.

A Simple Method for Any Numerical

Almost every physics numerical can be approached the same way, regardless of topic:

• Step 1 — List what's given. Write down every value provided, with correct units (5 m/s, 3 s, 10 kg, etc).
• Step 2 — Identify what's being asked. Underline the actual quantity the question wants (acceleration? distance? force?).
• Step 3 — Choose the formula that connects them. Look at which known quantities and the unknown quantity appear together in one equation.
• Step 4 — Substitute carefully, keeping units consistent. Convert km/h to m/s, grams to kg, etc. before substituting — mixed units are one of the most common sources of wrong answers.
• Step 5 — Solve and sanity-check the answer. Does the magnitude make sense? A car accelerating at 400 m/s² is almost certainly a calculation error, not a real answer.

Kinematics (Examples 1–5)

1. A car starts from rest and reaches 20 m/s in 5 s. Find its acceleration.
a = (v−u)/t = (20−0)/5 = 4 m/s².

2. A ball is dropped and falls for 3 s. Find its velocity (g = 10 m/s²).
v = u + gt = 0 + 10(3) = 30 m/s.

3. A car travels at 15 m/s for 8 s. Find the distance covered.
s = vt = 15 × 8 = 120 m.

4. A body accelerates from 5 m/s to 15 m/s over 40 m. Find the acceleration.
Using v² = u² + 2as: 225 = 25 + 2a(40) → 200 = 80a → a = 2.5 m/s².

5. A stone is thrown upward at 20 m/s. Find the time to reach maximum height (g = 10 m/s²).
At max height, v=0. t = (v−u)/(−g) = (0−20)/(−10) = 2 s.

Force & Newton's Laws (Examples 6–9)

6. Find the force needed to accelerate a 10 kg object at 3 m/s².
F = ma = 10 × 3 = 30 N.

7. A 5 kg object experiences a net force of 20 N. Find its acceleration.
a = F/m = 20/5 = 4 m/s².

8. Two forces, 8 N and 6 N, act in opposite directions on an object. Find the net force.
Net force = 8 − 6 = 2 N (in the direction of the larger force).

9. A 2 kg object rests on a table. Find the normal force (g = 10 m/s²).
Weight = mg = 2 × 10 = 20 N. Normal force = 20 N (balances weight).

Work & Energy (Examples 10–12)

10. Find the work done lifting a 4 kg object 2 m (g = 10 m/s²).
W = mgh = 4 × 10 × 2 = 80 J.

11. Find the kinetic energy of a 3 kg object moving at 6 m/s.
KE = ½mv² = 0.5 × 3 × 36 = 54 J.

12. A machine does 500 J of work in 10 s. Find its power.
P = W/t = 500/10 = 50 W.

Electricity (Examples 13–15)

13. Find the current through a 10 Ω resistor with 5 V across it.
I = V/R = 5/10 = 0.5 A.

14. Find the resistance if a 12 V source drives 3 A through a circuit.
R = V/I = 12/3 = 4 Ω.

15. Find the power dissipated by a resistor carrying 2 A at 6 V.
P = VI = 6 × 2 = 12 W.

Common Mistakes Students Make

• Not converting units before substituting. Speeds given in km/h must be converted to m/s (divide by 3.6) before use in most kinematics formulas — forgetting this gives an answer that's wrong by a factor of 3.6.
• Sign confusion with direction. In problems involving deceleration or a ball thrown upward, treating "up" and "down" (or acceleration and deceleration) with inconsistent signs is a very common source of errors, as seen in example 5.
• Forgetting g = 10 m/s² vs 9.8 m/s². Different textbooks and boards use slightly different values for gravitational acceleration — always use the value your specific board/paper specifies, since it changes the final answer.
• Confusing mass and weight. Mass (kg) and weight (N, calculated as mg) are different quantities. Using mass directly in a formula that requires weight (or vice versa) is a very common numerical error.
• Not showing the formula before substituting numbers. Even if the final answer is correct, most marking schemes give a portion of marks specifically for writing the correct formula — skipping straight to numbers can cost marks even with a right answer.

Frequently Asked Questions

Which kinematics equation should I use when I don't know the time?
Use v² = u² + 2as, since it relates initial velocity, final velocity, acceleration, and displacement without needing time at all — exactly as shown in example 4.

Why does electricity use different formulas (V=IR, P=VI) for what seems like the same idea?
Each formula highlights a different relationship: V=IR (Ohm's Law) connects voltage, current, and resistance, while P=VI connects power to voltage and current. Depending on which two quantities you're given, one formula will directly solve the problem faster than the other.

How much working should I show for full marks?
As a rule, always write the formula first, then the substitution step with units, then the final answer with correct units and appropriate significant figures — skipping any of these three stages is where partial marks are usually lost.

Double-Check Your Numbers

Use Calvo's scientific calculator to verify each step — small unit or sign errors are the most common way marks are lost in physics numericals, so it's worth checking your arithmetic separately from your method. Recomputing the final substitution step alone (once you're confident in the formula and setup) is usually enough to catch an arithmetic slip.

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