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Chapter Overview
Learning Goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Travel graphs show distance travelled on the $y$-axis against time on the $x$-axis. They can be used to determine the speed and direction of motion.
Travel graphs have a series of line segments that join together to represent a journey. An example travel graph is given below. It shows a journey to a supermarket and back, with a small stop on the way to the shop.
The graph can be broken into its separate straight line segments:
If the graph is going up, then the direction is away from the starting position. If the graph is going down, then the direction is toward the starting position. If the graph is flat, then motion has stopped.
Travel graphs give you enough information to calculate the speed of the motion.
The speed of a segment is calculated by finding the gradient of the line segment. Gradient is calculated with the formula:
$m=\frac{\text{change in }y}{\text{change in }x}$
Note: If a line segment has a negative gradient, ignore the negative sign for the speed. The negative just means that motion is back towards the starting position.
Given that each line segment is either a diagonal line or a flat line, finding the gradient is straightforward: for diagonal lines, just use the coordinates of the top and bottom of the line; for flat lines, the gradient, and hence speed, is zero.
Note: The straight line means that the speed is constant.
Alternatively, use:
$\text{speed}=\frac{\text{distance}}{\text{time}}$
Note: The unit of speed will the unit of distance divided by the unit of time.
In the first ten minutes of the walker's journey, how fast do they travel?
In the first ten minutes, the walker has travelled one kilometre. Hence their speed is:
$\frac{1\text{ km}}{10\text{ mins}}=0.1\text{ km per minute} = \underline{100\text{ m per minute}}$
How fast did they walk on their way back home? Use the same graph above again.
Use the final $15$ minutes of the journey; the graph is going down, hence the direction is back toward the starting location. In this time, the walker travels $1.6\text{ km}.$ Hence their speed (rounded to three significant figures) was:
$\frac{1.6\text{ km}}{15\text{ mins}}=0.107\text{ km per minute} = \underline{107\text{ m per minute}}$
Travel graphs show distance travelled on the $y$-axis against time on the $x$-axis. They can be used to determine the speed and direction of motion.
Travel graphs have a series of line segments that join together to represent a journey. An example travel graph is given below. It shows a journey to a supermarket and back, with a small stop on the way to the shop.
The graph can be broken into its separate straight line segments:
If the graph is going up, then the direction is away from the starting position. If the graph is going down, then the direction is toward the starting position. If the graph is flat, then motion has stopped.
Travel graphs give you enough information to calculate the speed of the motion.
The speed of a segment is calculated by finding the gradient of the line segment. Gradient is calculated with the formula:
$m=\frac{\text{change in }y}{\text{change in }x}$
Note: If a line segment has a negative gradient, ignore the negative sign for the speed. The negative just means that motion is back towards the starting position.
Given that each line segment is either a diagonal line or a flat line, finding the gradient is straightforward: for diagonal lines, just use the coordinates of the top and bottom of the line; for flat lines, the gradient, and hence speed, is zero.
Note: The straight line means that the speed is constant.
Alternatively, use:
$\text{speed}=\frac{\text{distance}}{\text{time}}$
Note: The unit of speed will the unit of distance divided by the unit of time.
In the first ten minutes of the walker's journey, how fast do they travel?
In the first ten minutes, the walker has travelled one kilometre. Hence their speed is:
$\frac{1\text{ km}}{10\text{ mins}}=0.1\text{ km per minute} = \underline{100\text{ m per minute}}$
How fast did they walk on their way back home? Use the same graph above again.
Use the final $15$ minutes of the journey; the graph is going down, hence the direction is back toward the starting location. In this time, the walker travels $1.6\text{ km}.$ Hence their speed (rounded to three significant figures) was:
$\frac{1.6\text{ km}}{15\text{ mins}}=0.107\text{ km per minute} = \underline{107\text{ m per minute}}$
FAQs
Question: What do the different directions of the graph mean in a travel graph?
Answer: If the graph is going up, then the direction is away from the starting position. If the graph is going down, then the direction is toward the starting position. If the graph is flat, then motion has stopped.
Question: How do you work out speed on a travel graph?
Answer: The speed of a segment is calculated by finding the gradient of the line segment.
Question: What does a travel graphs look like?
Answer: Travel graphs are have a series of line segments that join together to represent some journey.
Theory
Exercises
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