Visualize Velocity: The v-t Graph Secret

Struggling with velocity-time graphs? What if you could 'see' the displacement directly on the graph?

Subject: mechanics • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

The area under a velocity-time (v-t) graph represents the displacement of an object. Remember: Displacement = Area under v-t curve. This works because velocity is the rate of change of displacement with respect to time ($v = \frac{\Delta x}{\Delta t}$), so $\Delta x = v \Delta t$. On a graph, $v \Delta t$ is simply the area of a rectangle (or other shape) under the curve. For non-constant velocity, think of it as summing many tiny rectangles.

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