Kinematics is the foundation of every IB Physics paper. Topic A.1 sets up the language — scalars vs vectors, displacement, velocity, acceleration — and the toolkit (SUVAT, motion graphs, projectiles) that you will reuse in every later mechanics topic, from forces and momentum to circular motion and rigid bodies. The new IB syllabus stays SL/HL-shared here, but examiners regularly hide multi-step traps inside what looks like a simple SUVAT or projectile problem: an air-resistance flag, a height mismatch, a "speed at the apex" question, or a graph where the gradient suddenly changes sign.
This cheatsheet condenses every formula, trick and trap from Topic A.1 Kinematics into one page you can revise from. It covers scalars and vectors, the four SUVAT equations, motion graphs (gradients and areas), 2-D projectile motion with and without air resistance, and the qualitative description of fluid resistance and terminal velocity. Scroll to the bottom for the printable PDF and the full Photon Academy library (notes, tutorials, marked solutions).
§1 — Scalars, Vectors & Definitions A.1
Scalars vs vectors
- Scalar quantities: distance, speed, time, mass, energy.
- Vector quantities: displacement, velocity, acceleration, force.
Distance vs displacement
- Displacement $\vec{s} = \vec{r}_f - \vec{r}_i$ — change in position (vector, can be negative).
- Distance — total path length, always $\geq 0$.
Average vs instantaneous
| Quantity | Average | Instantaneous (gradient) |
|---|---|---|
| Velocity | $\bar{v} = \dfrac{\Delta s}{\Delta t}$ | $v = \dfrac{ds}{dt}$ — gradient of $s$–$t$ |
| Acceleration | $\bar{a} = \dfrac{\Delta v}{\Delta t}$ | $a = \dfrac{dv}{dt}$ — gradient of $v$–$t$ |
§2 — SUVAT Equations (Uniform Acceleration) A.1
Variable list (SI units)
- $s$ — displacement (m)
- $u$ — initial velocity (m s⁻¹)
- $v$ — final velocity (m s⁻¹)
- $a$ — acceleration (m s⁻²)
- $t$ — time (s)
Choosing the right SUVAT
| Variable NOT given / asked | Use |
|---|---|
| $s$ | $v = u + at$ |
| $v$ | $s = ut + \tfrac{1}{2}at^2$ |
| $u$ | $v^2 = u^2 + 2as$ |
| $a$ | $s = \tfrac{1}{2}(u + v)t$ |
| $t$ | $v^2 = u^2 + 2as$ |
§3 — Motion Graphs A.1
| Graph | Gradient gives | Area under gives |
|---|---|---|
| $s$–$t$ | $v$ (velocity) | — |
| $v$–$t$ | $a$ (acceleration) | $s$ (displacement) |
| $a$–$t$ | — | $\Delta v$ (change in velocity) |
Shape clues: a curved $s$–$t$ graph means non-uniform velocity; a straight $v$–$t$ line means uniform acceleration; a horizontal $a$–$t$ line means constant acceleration (SUVAT applies).
§4 — Projectile Motion (No Air Resistance) A.1
Resolve into independent components. Horizontal motion is uniform; vertical motion has constant acceleration $g$ downward.
| Horizontal (constant $v$) | Vertical (constant $a = g$ down) |
|---|---|
| $v_x = u\cos\theta$ | $v_y = u\sin\theta - gt$ |
| $x = u\cos\theta \cdot t$ | $y = u\sin\theta \cdot t - \tfrac{1}{2}gt^2$ |
Useful results (launch height = landing height only)
§5 — Fluid Resistance & Terminal Velocity A.1
Projectile WITH air resistance — qualitative
Compared to the ideal (no-drag) case:
- Range decreases.
- Max height decreases.
- Time of flight decreases.
- Trajectory is not symmetric — the descent is steeper than the ascent.
- Landing speed is less than launch speed.
- Drag opposes the velocity vector, so its direction changes throughout the flight.
Terminal velocity (free fall)
Drag $= mg$ ⇒ net force $= 0$ ⇒ acceleration $= 0$. The object falls at constant terminal speed $v_T$.
§6 — Exam Attack Plan A.1 — All sections
When you see this in the question — reach for that:
| Question trigger | Reach for |
|---|---|
| "Constant acceleration", numerical motion problem | Pick the right SUVAT (table above) — list $u, v, a, s, t$ first |
| Free fall, dropped object, ball thrown up | SUVAT with $a = -g$ (taking up as positive) |
| Velocity from a position-time graph | Gradient (tangent) — not chord |
| Displacement from a velocity-time graph | Area under curve (signed) |
| "Distance travelled" on a $v$–$t$ graph | Sum of $|$areas$|$ — count negative areas as positive |
| 2-D projectile, flat ground | Range / max-height formulas; check launch = landing height |
| Projectile from a cliff or onto a higher platform | Resolve into components; SUVAT vertically and horizontally |
| "Speed at the highest point" | $u\cos\theta$ — not zero |
| Air resistance / drag mentioned | Qualitative description only — do NOT apply SUVAT |
| "Terminal velocity" | Drag $= mg$ ⇒ $a = 0$ ⇒ constant speed |
Worked Example — IB-Style Projectile from a Cliff
Question (HL Paper 2 style — 6 marks)
A stone is launched from the top of a 25 m vertical cliff with initial speed 18 m s⁻¹ at an angle of 35° above the horizontal. Air resistance is negligible. Take $g = 9.81$ m s⁻². Calculate (a) the time the stone takes to reach the sea below, and (b) its horizontal range from the base of the cliff.
Solution
- Resolve the launch velocity. Take up as positive.
$u_x = 18\cos 35° = 14.74$ m s⁻¹; $\;u_y = 18\sin 35° = 10.32$ m s⁻¹. (M1) - For vertical motion use $s_y = u_y t - \tfrac{1}{2}g t^2$ with $s_y = -25$ m (sea is 25 m below launch):
$-25 = 10.32\,t - 4.905\,t^2$. (M1) - Rearrange: $4.905\,t^2 - 10.32\,t - 25 = 0$. Apply the quadratic formula:
$t = \dfrac{10.32 \pm \sqrt{10.32^2 + 4(4.905)(25)}}{2(4.905)} = \dfrac{10.32 \pm 24.36}{9.81}$. (A1) - Take the positive root: $t = \dfrac{10.32 + 24.36}{9.81} = 3.54$ s. (A1) [part (a)]
- Horizontal range: $x = u_x \cdot t = 14.74 \times 3.54 = 52.1$ m. (M1)(A1) [part (b)]
Examiner's note: Using the flat-ground range formula here would give $R = 18^2 \sin 70° / 9.81 = 31.0$ m — completely wrong, because launch height $\neq$ landing height. Whenever the projectile starts and finishes at different heights, you must split into components and use SUVAT vertically. Sign convention matters: $s_y = -25$, not $+25$.
Common Student Questions
When can I use SUVAT in IB Physics?
What is the difference between distance and displacement?
What is the speed of a projectile at its highest point?
When can I use the range formula $R = u^2 \sin 2\theta / g$?
How does air resistance change projectile motion?
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