Unit 1 · 1.3 — Representing Motion

Everything to learn here

• Concept: On a position-time (x-t) graph, the instantaneous slope represents instantaneous velocity
• Concept: On a position-time (x-t) graph, a constant slope indicates constant velocity, and a curving slope indicates acceleration
• Concept: On a velocity-time (v-t) graph, the instantaneous slope represents instantaneous acceleration
• Concept: On a velocity-time (v-t) graph, the area bounded by the curve and the time axis represents the displacement (delta x)
• Concept: On an acceleration-time (a-t) graph, the area bounded by the curve and the time axis represents the change in velocity (delta v)
• Equation: $$\Delta x=\int vdt\text{(Displacement as the area under a v-t graph)}$$
• Equation: $$\Delta v=\int adt\text{(Change in velocity as the area under an a-t graph)}$$
• Vocabulary: Motion Diagram — A visual representation mapping an object's position at equal time intervals to indicate velocity and acceleration
• Vocabulary: Qualitative Graph — A sketch showing key behavioral features (increasing/decreasing, zero crossings) without requiring exact numerical scaling
• Vocabulary: Quantitative Graph — A plot requiring scaled, labeled axes with correct SI units and precisely plotted data points
• Skill: Translation Between Representations — Sketching corresponding x-t, v-t, and a-t graphs by evaluating slopes and ensuring areas logically align
• Skill: Data Analysis — Calculating displacement by finding the geometric area of triangles and rectangles under a v-t graph
• Skill: FRQ Task Verb "Plot" — Draw data points accurately on a provided grid, ensuring the chosen scale spreads the data across the entire grid and axes are labeled with units
• Equation: $$v=v0+at,x=x0+v0t+0.5a{t}^2,and{v}^2=v{0}^2+2a\text{(delta x)}$$

Practice problems for this topic are coming — generated and validated by our AI pipeline, aligned to these exact items.