Motion Graphs
Year 10 (IGCSE) 🚀 Forces & Motion Interpret and draw distance-time and velocity-time graphs.
📈 Distance-Time and Displacement-Time Graphs
Motion graphs give us a powerful way to analyse movement without complex equations.
| 📊 Graph shape | 🏃 Motion described | 📐 Gradient |
|---|---|---|
| Horizontal line | Stationary (not moving) | 0 → speed = 0 |
| Straight line (slope up) | Constant speed | = speed (m/s) |
| Steeper slope | Faster constant speed | Larger = faster |
| Curve (getting steeper) | Accelerating | Increasing |
| Curve (getting shallower) | Decelerating | Decreasing |
📈 Gradient of d-t graph
$$\text{Speed} = \text{gradient} = \frac{\Delta d}{\Delta t}$$📊 Velocity-Time Graphs
Velocity-time (v-t) graphs show how velocity changes with time. They reveal both acceleration and distance.
| 📊 Graph feature | 🔍 What it tells us |
|---|---|
| Gradient of v-t graph | Acceleration (m/s²) |
| Area under v-t graph | Distance (displacement) travelled |
| Horizontal line | Constant velocity (zero acceleration) |
| Sloping line upward | Uniform acceleration |
| Sloping line downward | Deceleration (negative acceleration) |
📊 v-t graph relationships
$$a = \frac{\Delta v}{\Delta t} \qquad d = \text{area under graph} = \frac{1}{2}(u+v)t$$🔢 SUVAT Equations
For uniform acceleration, five equations link the five variables: s, u, v, a, t.
🔢 SUVAT Equations
$$v = u + at \qquad s = ut + \frac{1}{2}at^2$$
$$v^2 = u^2 + 2as \qquad s = \frac{(u+v)}{2} \cdot t$$| 📝 Symbol | 📖 Meaning | 📏 Unit |
|---|---|---|
| s | Displacement | m |
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | s |
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📈 SUVAT & Motion Graph Calculator
Velocity–Time Graph & Equations of Motion