Velocity time graph part two

There is another important feature of a velocity-time graph.

The area under the curve gives the displacement.

The area under the curve is this shaded area

Velocity is defined as follows:

We can rearrange this equation to make displacement the subject

To find the shaded area we can work out the areas of the three shapes outlined in red below

There are two triangles and a rectangle.

The two triangles are the same area because they have the same base and height. They are congruent.

The area of each triangle is

Notice that in calculating the area we are multiplying time and velocity. According to our formula, this gives displacement. The displacement given by the first triangle is 150m. This displacement is positive and this tells us that the direction is east. The displacement shown by the first triangle is 150m east.

The area of the rectangle is

The area under the curve is

The displacement of the journey is 3300m east.