Calculating Displacement from Velocity-Time Graphs Video Lessons

Concept

# Problem: 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)

###### FREE Expert Solution

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.

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###### Problem Details

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)