Topic 3: Graphs – Sample Activity

Context
Annabel was being monitered as she was driving through Kampala city to her workplace. She was followed by a traffic officer who kept recording her movements for an hour and a half and he plotted it on a graph. An unknown person, however, had reported Annabel for speeding on this journey.

Support
The safety driving rules in Uganda provides speed guidelines as follows:
1. Driving in urban places should not exceed 50 km/h.
2. Driving in rural places should not exceed 80 km/h. Driving on highways should not exceed 100 km/h.

Task
As a traffic inspector, prepare a written report on safe driving regarding Annabel’s journey to present to court.

Miscellaneous activities
1. In each case, sketch a speed-time graph and find the distance travelled.
(a) A car travels at a steady speed of 65 mph for 3 hours.

(b) A car decelerates steadily from a speed of 54 mph until it stops 4 seconds later.
(c) A car accelerates steadily from 12 ms1 to 24 ms1 over a period of 6 seconds.
(d) A car decelerates steadily from 108 kph to 63 kph over a period of 8 seconds
2. In each of the following:
(a) draw a speed-time graph on graph paper.
(b) describe what happens during the given time interval.
(c) estimate the distance travelled to the nearest metre.

Case 1

Topic Summary
In this topic, you have learnt that:
1. a graph is a visual representation of a relationship between, but not restricted to, two variables.
2. a graph commonly consists of two axes called the x-axis (horizontal) and y-axis (vertical). Each axis corresponds to one variable. The axes are labelled with different names.
3. a line graph shows points plotted on a graph.
4. a distance-time graph measures how far two objects are from each other. Often these graphs are used to show the journey that someone makes from one place to another and back.
5. a velocity-time graph (or speed-time graph) is a way of visually expressing a journey.