8. Calculating Distance from
the Area Under the Curve

Success Criteria

Your learning has been successful if you can do the following:

Define acceleration and its units.
Calculate acceleration from speed and time measurements.

Vocabulary

Learn these so you can communicate this concept well.

Average speed: Calculated by the total distance travelled divided by the total time taken for the journey.
Gradient / slope: How steep a line on a graph is.
Speed: How fast an object is moving.
Velocity: Similar to speed, but also tells us the direction in which an object is moving. It includes both speed and direction of motion.

Lesson 4: Hei Mahi (Do Now)

Do Now:

Collect and complete this small 'Do Now'. Then glue into your SciPAD page 11. Use your commonsense when glueing - don't glue straight on-top of words!

Lesson 4: Exit Task

Find some space on page 15 of your PESS1.2 SciPAD,
and answer the following questions:

What does each letter in CUTLASS stand for?

How do we calculate distance using a Speed-Time Graph?

Distance travelled by a moving object can be calculated from its speed-time graph of motion. This is done by funding the are of the shape(s) beneath the graph.

The graph below shows the speed-time graph of a moving object.

For calculating the total distance travelled by this object in 30 seconds, you need to calculate the total area beneath the line. Reason: distance = speed x time. For convenience, you can divide this into three areas, two triangles (A and C) and a rectangle (B).

Remember from Lessons 1-3 that:

This can be rearranged as:

On a speed-time graph, this is the same calculation as the area under the line on the graph.

Summarising the Speed-Time Graph

Consider the following speed-time graph for a road grader (heavy-duty machine) going up and down a section of straight road.

In summary:

The speed of an object at different times can be plotted on a speed-time graph.
The vertical axis is used for speed, while the horizontal axis is used for time.
Positive speeds indicate movement in one direction, while negative speeds indicate movement in the opposite direction.
The size of the slope gives the acceleration. The greater the slope, the greater the acceleration.
A negative acceleration = deceleration = slowing down.
The area between the graph line and the time axis gives the distance travelled.
The area above the time axis indicates the distance travelled in one direction.
The area below the time axis indicates the distance travelled in the opposite direction.

Tasks & Homework

Task 1: PESS1.2 SciPAD

Page 14 - Calculating Speed from a Distance-Time Graph

Page 15 - New Zealand Secondary Schools Rally Team

Homework:

Access your own copy of this homework task on Microsoft Teams.

Remember, to calculate the distance travelled:

Split the graph into simple shapes, then find the area of each shape and add them together.
Area of a rectangle = width x height
Area of a triangle = 1/2 base x height