Mechanics

Vectors

Scalars vs vectors, resultants, and components in 1D and 2D.

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Grade 10 · Physical Sciences (Physics) · Mechanics

Physics is Physical Sciences Paper 1.

The paper
Grade 10 Paper 1 starts from vectors, motion in one dimension, energy, and electrostatics.
Working
Write the formula as it appears on the data sheet, substitute with units, then the answer with the unit and the direction if it is a vector. A positive direction you chose must be stated when the sign matters.
The relation
R = √(Rx² + Ry²). Resultant magnitude
How a marker reads it
State both magnitude AND direction. A number alone is a scalar, not a displacement.

Paper 1 is 150 marks. The data sheet is allowed. A formula copied wrong cannot be saved by a tidy final number.

Diagram

Worked example

A learner walks 40 m east then 30 m north. Find the resultant displacement.

Before any working — hunt first

Given

Numbers and units already in the sentence: 40 m · 30 m. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: the resultant displacement. Circle that word — that is the missing variable.

Find

We are required to find: the resultant displacement. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write R = √(Rx² + Ry²) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives the resultant displacement.

Simplified approach

This is a 3-4-5 triangle. Resultant is 50 m at tan⁻¹(30/40) north of east.

Culture note

Walking from a spaza to the taxi rank then north to school in Soweto is this two-leg displacement.

Formulas

R=Rx²+Ry²

Resultant magnitude

How to hunt the missing letter

Do not start by naming the letters. First hunt the missing one: copy every number you can see (Given). The letter with no number is Missing. The asking word is Find. The formula that still contains that letter is what you Calculate.

How to hunt: (1) Underline every number and its unit — those are Given. (2) Circle the asking word — find, calculate, how far, what is. That word names Find. (3) The letter the asking word names, which has no number yet, is Missing. (4) Write the formula with empty letters. Cross out every given letter. The letter still standing is what you Calculate.

Rx, Ry
components
How you spot this in the sentence
When the sentence names the components, that letter is Rx, Ry. Copy the number next to it into Given. If the sentence never names it, Rx, Ry is Missing. The east-west and north-south pieces of a vector. Rx = R cos θ, Ry = R sin θ.
Example:A 10 N force at 30° to x: Rx = 10 cos 30°, Ry = 10 sin 30°.
R
resultant
How you spot this in the sentence
When the sentence names the resultant, that letter is R. Copy the number next to it into Given. If the sentence never names it, R is Missing. One vector that replaces the lot. R = √(Rx² + Ry²).
Example:Rx=3, Ry=4→R=5 (a 3-4-5 triangle).

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

List the five, then pick the equation that still has the missing letter
How:Write a column: v_i, v_f, a, Δt, Δx. Tick every one that has a number. The unticked letter is Missing. Choose the SUVAT line that does not need a letter you do not have — do not start from the formula you remember first.
When to use it:Any constant-acceleration question that names times, speeds or distances.
Use g = 9,8 unless the paper says take g = 10
How:Copy g from the data sheet onto your given column first. If the instruction line says “take g = 10”, write that. Otherwise 9,8 m·s⁻². Using 10 when the paper did not say so loses the accuracy mark even if the method is right.
When to use it:Free fall, projectiles, weight, and gravitational potential energy.
State “mechanical energy is conserved” in words before you substitute
How:The method mark sits in the sentence, not in the algebra. Write: mechanical energy conserved because no non-conservative work (or friction is neglected). Then E_k + E_p at A = E_k + E_p at B. Then substitute.
When to use it:Any conservation question, rollers, pendulums, or falling masses.

Step 1 / 5

Sketch

East 40 m, north 30 m, right angle.

Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

Walk 40 m east then 30 m north. Resultant displacement?

4. Step-by-step working

01
Magnitude
R=40²+30²=50 m.
50 m
02
Direction
θ = tan⁻¹(30/40)=36.9° N of E.
36.9° N of E

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Walk 40 m east then 30 m north. Resultant displacement?

Before any working — hunt first

Given

Numbers and units already in the sentence: 40 m · 30 m. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: Resultant displacement. Circle that word — that is the missing variable.

Find

We are required to find: Resultant displacement. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write 50 m with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Resultant displacement.

In other words — as if you have never seen this before

If you have never seen this before: R = √(Rx²+Ry²). Direction tan⁻¹(Ry/Rx) north of east. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

Rx=40 m, Ry=30 m.

3. Which method — and why this one?

R = √(Rx²+Ry²). Direction tan⁻¹(Ry/Rx) north of east.

4. Step-by-step working

01 / 05
Magnitude
R=40²+30²=50 m.
50 m
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Direction
θ = tan⁻¹(30/40)=36.9° N of E.
36.9° N of E
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
50 m at 36.9° north of east
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

50 m at 36.9° north of east

Copy onto your answer sheet — in this order

Formula: 50 m

Answer: 50 m at 36.9° north of east

6. Check it like a marker

A displacement needs magnitude AND direction. East-then-north is a right angle.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

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Motion in one dimension

Physical Sciences — Physics

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