Kinematics (Copy)
KINEMATICS — O LEVEL & IGCSE ADDITIONAL MATHEMATICS FORMULA SHEET + COMMON MISTAKES
| Topic | Formula / Rule | Common Mistake |
|---|---|---|
| Distance | Total path travelled | Mixing with displacement |
| Displacement | Straight-line change in position | Ignoring direction |
| Speed | speed = distance/time | Using displacement |
| Velocity | velocity = displacement/time | Ignoring direction |
| Acceleration | acceleration = change in velocity/time | Using speed instead |
| Deceleration | Negative acceleration | Treating separately |
| Uniform Velocity | Constant velocity | Assuming acceleration exists |
| Uniform Acceleration | Constant acceleration | Using changing formulas |
| First Equation of Motion | v = u + at | Mixing u and v |
| Second Equation of Motion | s = ut + 1/2 at² | Forgetting 1/2 |
| Third Equation of Motion | v² = u² + 2as | Wrong sign |
| Fourth Equation of Motion | s = (u + v)t/2 | Forgetting average velocity |
| Initial Velocity | u | Mixing with final velocity |
| Final Velocity | v | Reversing symbols |
| Acceleration Symbol | a | Using s |
| Time Symbol | t | Mixing with displacement |
| Displacement Symbol | s | Using distance always |
| Velocity-Time Graph Gradient | Acceleration | Thinking it is velocity |
| Velocity-Time Graph Area | Displacement | Using gradient instead |
| Distance-Time Graph Gradient | Speed/velocity | Using area |
| Horizontal Velocity-Time Graph | Constant velocity | Saying acceleration exists |
| Horizontal Distance-Time Graph | Stationary object | Saying moving |
| Positive Acceleration | Velocity increasing | Ignoring sign |
| Negative Acceleration | Velocity decreasing | Calling positive |
| Free Fall Acceleration | g ≈ 9.8 m/s² | Using wrong sign |
| Upward Motion | Acceleration downward | Using positive g upward |
| Downward Motion | Velocity increases downward | Wrong direction signs |
| Maximum Height | v = 0 at top | Forgetting condition |
| Stopping Distance | Final velocity v = 0 | Using moving equations |
| Average Velocity | (u + v)/2 | Using average speed |
| Motion in Opposite Direction | Use negative signs carefully | Ignoring direction |
| Units | Keep consistent units | Mixing km/h and m/s |
| Conversion | 1 m/s = 3.6 km/h | Multiplying wrong way |
| Instantaneous Velocity | ds/dt | Using average formula |
| Instantaneous Acceleration | dv/dt | Using displacement formula |
| Displacement from Velocity | ∫v dt | Differentiating instead |
| Velocity from Acceleration | ∫a dt | Differentiating instead |
| Acceleration from Velocity | dv/dt | Using v/t directly |
| Velocity from Position | ds/dt | Using displacement only |
| Relative Velocity | Difference of velocities | Adding wrongly |
| Projectile Motion | Horizontal and vertical independent | Mixing motions |
| Vertical Motion | Use SUVAT equations | Using horizontal equations |
| Rest Condition | u = 0 or v = 0 depending on question | Using both incorrectly |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
QUICK SUVAT FORMULAS TABLE
| Formula | Expression |
|---|---|
| First Equation | v = u + at |
| Second Equation | s = ut + 1/2 at² |
| Third Equation | v² = u² + 2as |
| Fourth Equation | s = (u + v)t/2 |
QUICK SYMBOLS TABLE
| Symbol | Meaning |
|---|---|
| u | Initial velocity |
| v | Final velocity |
| a | Acceleration |
| t | Time |
| s | Displacement |
QUICK GRAPH RULES TABLE
| Graph | Meaning |
|---|---|
| Gradient of distance-time graph | Speed/velocity |
| Gradient of velocity-time graph | Acceleration |
| Area under velocity-time graph | Displacement |
| Horizontal distance-time graph | Stationary |
| Horizontal velocity-time graph | Constant velocity |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
QUICK PROJECTILE MOTION RULES
| Situation | Rule |
|---|---|
| Maximum height | v = 0 vertically |
| Gravity | g ≈ 9.8 m/s² downward |
| Horizontal motion | Constant velocity |
| Vertical motion | Constant acceleration |
QUICK CALCULUS KINEMATICS RULES
| Formula | Meaning |
|---|---|
| v = ds/dt | Velocity |
| a = dv/dt | Acceleration |
| s = ∫v dt | Displacement |
| v = ∫a dt | Velocity from acceleration |
UNIT CONVERSION TABLE
| Conversion | Result |
|---|---|
| m/s → km/h | × 3.6 |
| km/h → m/s | ÷ 3.6 |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
EXAM HACKS
| Situation | Fast Trick |
|---|---|
| Constant acceleration | Use SUVAT |
| Missing time | Use v² = u² + 2as |
| Velocity-time graph | Area = displacement |
| Distance-time graph | Gradient = speed |
| Maximum height | Set v = 0 |
| Free fall | Use g downward |
| Opposite direction | Use negative signs |
| Calculus question | Differentiate/integrate carefully |
| Unit conversion | Convert before solving |
| Rest condition | Velocity becomes zero |
MOST COMMON LOSSES OF MARKS
| Mistake | Why Marks Are Lost |
|---|---|
| Mixing distance and displacement | Wrong formula usage |
| Wrong sign for acceleration | Entire answer incorrect |
| Forgetting 1/2 in SUVAT | Formula marks lost |
| Using inconsistent units | Numerical errors |
| Wrong graph interpretation | Method lost |
| Ignoring direction | Sign errors |
| Reversing u and v | Wrong calculations |
| Using wrong SUVAT formula | Unnecessary algebra |
| Forgetting v = 0 at maximum height | Incorrect solution |
| Calculator rounding too early | Accuracy lost |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.