Mechanics
What the Exam Tests
Mechanics is the first of the five modules of the official physics syllabus and the one with the most listed topics: kinematics (displacement, velocity, acceleration, uniformly accelerated motion, free fall), Newton's laws and their applications, momentum, impulse and the conservation of momentum, work, energy and the conservation of mechanical energy, circular motion and universal gravitation, and simple harmonic motion and mechanical waves. The last of these is taught in the Optics & Waves module: the course section Mechanical Vibrations & Simple Harmonic Motion (with nodes and antinodes in Standing Waves & Resonance) and the practice lesson Vibrations & Waves.
Every question is single-answer multiple choice, set in Chinese or English. Questions can ask you to read a v–t or x–t graph, resolve the forces on a block on an incline, analyse connected bodies, a projectile or a collision, follow energy along a track, or compare satellites in different orbits. Chinese textbook problems take g = 10 m/s² unless they say otherwise.
In our mock papers Mechanics gets 18 of the 48 questions, the largest share, because it lists the most topics. The CSCA publishes the topics but not how many questions each gets, so this split is our own reading of the syllabus.
What is Kinematics?
Kinematics is the study of motion without worrying about what causes it. We describe how objects move using four key quantities: displacement (Δx), velocity (v), acceleration (a), and time (t).
Displacement vs. Distance
Distance is the total path length traveled and is always positive. Displacement is the change in position from start to finish — it has both magnitude and direction. If you walk 3 m east then 3 m west, your distance is 6 m but your displacement is 0 m.
Speed vs. Velocity
Speed is how fast you move (scalar). Velocity is speed with a direction (vector). Average velocity = Δx / Δt. Instantaneous velocity is the velocity at a single moment.
Acceleration
Acceleration tells us how quickly velocity changes: a = Δv / Δt. Acceleration in the same direction as the velocity means speeding up; acceleration opposite to the velocity means slowing down. The sign of a alone does not tell you: a = −2 m/s² speeds up an object that is already moving in the negative direction. (位移 displacement, 速度 velocity, 加速度 acceleration, 匀变速直线运动 uniformly accelerated linear motion.) On Earth, gravity provides a constant downward acceleration of g ≈ 9.8 m/s². Many problems say “g 取 10 m/s²” (take g = 10 m/s²) to keep the arithmetic simple, so always use the value the question gives.
The Five Kinematic Equations (Constant Acceleration)
- v = v₀ + at — final velocity from initial velocity
- Δx = v₀t + ½at² — displacement from initial velocity and time
- v² = v₀² + 2aΔx — velocity and displacement without time
- Δx = ½(v₀ + v)t — displacement from average velocity
- Δx = vt − ½at² — displacement from final velocity
Two results that follow from these are used constantly in Chinese textbook problems (for example ticker-tape / 打点计时器 questions): the velocity at the middle moment of an interval equals the average velocity over it, v(t/2) = (v₀ + v)/2 = Δx/t; and the displacements in successive equal time intervals T differ by a constant, x₂ − x₁ = aT². Starting from rest, the distances covered in the 1st, 2nd, 3rd … equal intervals are in the ratio 1 : 3 : 5 : …
Free Fall
An object in free fall has only gravity acting on it. Near Earth’s surface a = −g = −9.8 m/s² (taking upward as positive). A ball thrown straight up slows by 9.8 m/s every second, stops at the top, then speeds up on the way down at the same rate.
Graphs of Motion
Position–time graphs: the slope gives velocity. Velocity–time graphs: the slope gives acceleration and the area under the curve gives displacement. Reading x–t and v–t graphs is a standard textbook question type, so practise it.
Problem-Solving Strategy
1) List knowns and unknowns. 2) Pick the equation containing exactly one unknown. 3) Substitute and solve. 4) Check units and the sign of your answer.
Key takeaway: Kinematics describes motion using displacement, velocity, acceleration, and time. Master the five kinematic equations for constant acceleration — they are the backbone of mechanics.
Key Formulas
- v = v₀ + at
- Δx = v₀t + ½at²
- v² = v₀² + 2aΔx
- Δx = ½(v₀ + v)t
- Free fall (自由落体运动): v = gt, h = ½gt², g ≈ 9.8 m/s² downward (often taken as 10 m/s²)
Worked Example 1
Example 1: A car accelerates from rest at 3 m/s² for 8 seconds. How far does it travel?
Step 1: Knowns: v₀ = 0 m/s, a = 3 m/s², t = 8 s
Step 2: Equation: Δx = v₀t + ½at²
Step 3: Δx = 0 + ½(3)(64) = 96 m
Answer: 96 m
Worked Example 2
Example 2: A ball is thrown up at 20 m/s. Maximum height? (g = 9.8 m/s²)
Step 1: At top: v = 0. v₀ = 20, a = −9.8
Step 2: v² = v₀² + 2aΔx → 0 = 400 − 19.6Δx
Step 3: Δx = 400/19.6 ≈ 20.4 m
Answer: 20.4 m
Worked Example 3
Example 3: A train at 30 m/s brakes at 2 m/s². Time to stop?
Step 1: v = v₀ + at → 0 = 30 − 2t → t = 15 s
Answer: 15 seconds
Exam tip: No time variable? Use v² = v₀² + 2aΔx.
Exam tip: Define positive direction first. Sign errors are the top mistake.
Exam tip: Graph skills: slope of x-t = v, slope of v-t = a, area under v-t = displacement.
Common mistake: Forgetting that a = −g when upward is taken as positive. g itself is always the positive number 9.8 (or 10) m/s²; the minus sign belongs to the acceleration.
Common mistake: Confusing distance and displacement in round-trip problems.
Common mistake: Applying kinematic equations when acceleration is not constant.
Try This Yourself
Module Summary
Open and read all sections to complete this module