For a velocity-versus-time graph, the displacement is the area under the curve.

For the three regions, we can visualize their area from the figure below.

We see that region A is in the shape of a triangle while regions B and C are in the shapes of trapezium.

The area of a triangle is given by:

$\overline{){\mathbf{A}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{b}}{\mathbf{h}}}$, where b is the base and h is the perpendicular height.

A person on horseback moves according to the velocity-versus-time graph shown below. (The vertical axis is marked in increments of 2 m/s and the horizontal axis is marked in increments of 5 s.) Find the displacement of the person for each of the segments A, B, and C individually, as well as the whole trip represented by the graph.

m (A)

m (B)

m (C)

m (whole trip)

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