Visualize Velocity: Motion Graph Trick

Struggling with motion graphs? Did you know the area under a velocity-time graph gives you the displacement? Let's unlock this secret!

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

The Trick

The area under a velocity-time (v-t) graph represents the displacement of the object. Why? Velocity is the rate of change of displacement ($v = \frac{\Delta x}{\Delta t}$). Therefore, $\Delta x = v \Delta t$. On the graph, $v \Delta t$ represents the area of a rectangle with height 'v' and width '$\Delta t$'. For non-constant velocity, you integrate the velocity function, which geometrically gives you the area.

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