Distance-Time Graphs: Bob's Journey Analysis

1. Drawing distance-time graphs

2. You can record the distances that an object travels and the time taken to travel those distances. • The distance and time are measured from where and when the object started. • You can plot this data on a distance–time graph. Time is usually plotted on the x-axis and distance on the y-axis.

3. Bob remembers that he left a light on so runs back covering the 300 m home in 2 minutes. • Bob goes for a walk from his house to a local shop to buy a paper. You can plot his journey on a distance–time graph as follows. • It takes them 5 minutes to buy the paper. 300 Distance from house (m) 150 0 2 4 6 8 10 12 14 • Bob walks 150 m from his house towards the newsagents for 2 minutes. Time (minutes) • Bob and his friend walk on together talking. They travel the remaining 150 m in 4 minutes. • He meets a friend and stops on the pavement talking for 1 minute.

4. You can tell how fast something is moving by looking at the slope of the line. • If an object moves faster, it goes a greater distance for a given time and the slope of the line is steeper. If an object goes slower, it moves a smaller distance for a given time and the slope is less steep. • We call the slope the gradient of the graph. • The gradient of a distance–time graph represents speed. • If a distance–time graph has a straight slope, this tells you that the object is moving at a constant speed. • Where the line in a distance–time graph is horizontal, the object has not moved any distance – it is stationary.

5. You can interpret what happened by looking at the slope of the graph. • Bob was stationary while he was talking with his friend (part b) and while he was waiting to buy his paper (part d). • d 300 Distance from house (m) • c • b 150 • e • a 0 2 4 6 8 10 12 14 • Bob walked quicker by himself than with his friend. The gradient for part a is greater than for part c. Time (minutes) • Bob was travelling in the opposite direction in part e because the gradient is negative.