Lesson 1: Kinematic Motion & Vectors | PHY 2.4

Lesson at a Glance | He Tirohanga Whakamua

Do NowDistance vs Displacement: 400m track run10 min

Vector QuantitiesScalar vs Vector, vector addition & components15 min

Kinematic EquationsSelecting & solving the 4 motion equations15 min

Portfolio EntryWrite Section 1: Kinematic Motion & Vector Calculation Guide10 min

Exit CalculationSolve stopping distance for a car braking at

5 {ms}^{- 2}

5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

The fundamental distinction between Scalar (magnitude only: distance, speed) and Vector quantities (magnitude + direction: displacement, velocity, acceleration).
How to select and rearrange the 4 NCEA Level 2 kinematic equations:
1) $v_{f} = v_{i} + a t$
2) $d = v_{i} t + \frac{1}{2} a t^{2}$
3) $v_{f}^{2} = v_{i}^{2} + 2 a d$
4) $d = \frac{v_{i} + v_{f}}{2} t$
How to interpret slope and area on Displacement-Time and Velocity-Time graphs.

Students will demonstrate

By solving 3 multi-step kinematic acceleration calculations with vector directions.
By completing Section 1 of their Level 2 Physics Mechanics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Vector Displacement Prompt:

"An athlete runs 1 full 400-metre lap around an oval track in 50 seconds, stopping at the exact starting line. What is their average speed, and what is their average velocity?"

Unpack: Average speed is $\frac{total distance}{time} = \frac{400 m}{50 s} = 8.0 {ms}^{- 1}$ . But because they ended at their starting point, their total displacement ( $Δ d$ ) is 0 metres! Therefore, their average velocity is $0.0 {ms}^{- 1}$ . Vectors require direction and net change in position.

The 4 Kinematic Equations (15 min)

1. $v_{f} = v_{i} + a t$

Relates initial velocity ( $v_{i}$ ), final velocity ( $v_{f}$ ), acceleration ( $a$ ), and time ( $t$ ). No displacement ( $d$ ).

2. $d = v_{i} t + \frac{1}{2} a t^{2}$

Relates displacement ( $d$ ), initial velocity ( $v_{i}$ ), acceleration ( $a$ ), and time ( $t$ ). No final velocity ( $v_{f}$ ).

3. $v_{f}^{2} = v_{i}^{2} + 2 a d$

Relates initial & final velocity, acceleration, and displacement. No time ( $t$ ). Ideal for stopping distance!

4. $d = \frac{v_{i} + v_{f}}{2} t$

Uses average velocity to find displacement when acceleration ( $a$ ) is uniform but unknown.

Scalar and Vector Quantities (15 min)

1. Scalars carry size only

Distance, speed, time and mass are scalars: a number and a unit, nothing more. Run one lap of a 400 m track and the distance is 400 m.

2. Vectors carry size and direction

Displacement, velocity, acceleration and force are vectors. Run that same lap and the displacement is $0$ m, because you finished where you started. Add vectors head-to-tail, or by components; never just add the numbers. Two 3 N forces give 6 N only if they point the same way.

Do this now: for your 400 m lap, state distance, displacement, average speed and average velocity. Two of the four are zero, and being able to say which is the difference between Achieved and Merit here.

📁 Physics Mechanics Portfolio — Section 1: Kinematic Motion & Vectors

Students open their Level 2 Physics Portfolio and complete Section 1:

Section 1 Requirements:

1. Scalar vs Vector Definition Table: Compare Distance vs Displacement, Speed vs Velocity, and Acceleration with SI units and vector notation.

2. Kinematic Solver Grid: Solve 3 physics scenarios (e.g. car braking from $25 {ms}^{- 1}$ to a stop at $- 4 {ms}^{- 2}$ , vertical ball drop) showing variable list, formula selection, and working.

3. Excellence Graph Interpretation: 1-paragraph explanation of why the area under a Velocity-Time graph represents displacement while the gradient represents acceleration.

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 1 correctly selects v_f^2 = v_i^2 + 2ad to calculate stopping distance without needing time, stating final displacement with direction."

Teacher Planning & NCEA Alignment

NCEA Level 2 Physics Alignment (6 Credits External):

Kinematic Motion: Demonstrate understanding of linear motion, velocity, acceleration, and kinematic equations.
Vector Quantities: Distinguish scalar and vector quantities and interpret motion graphs.

Vocabulary: Kinematics, scalar, vector, displacement, velocity, acceleration, uniform motion, initial velocity ( $v_{i}$ ), final velocity ( $v_{f}$ ).

Same concept, shorter route: the Guided Viewing & Problem Practice version of this unit covers it in Kinematics, Vectors and Projectile Motion. That route is a compact viewing-and-practice sequence; this one builds the concept over ten sections with a formative portfolio.

Lesson 1: Kinematic Motion Vectors & Kinematic Equations