What are the key learning points about distance-time graphs?
Interpreting distance – time graphs.
Recognising that the In a graph, the gradient is the steepness of the line. The greater the gradient, the greater the rate of change. of a distance-time graph is the speed
What do distance-time graphs show?
A distance-time graph shows how the distance travelled by an object changes over time and can be used to calculate the speed of the object.
A horizontal line on a A graph with distance travelled plotted on the vertical axis against time taken on the horizontal axis. shows that the object is Not moving, stopped, at rest (speed = 0 m/s). (not moving because the distance does not change).
A sloping line on a distance-time graph shows that the object is moving.
Key fact
In a distance-time graph, the slope or In a graph, the gradient is the steepness of the line. The greater the gradient, the greater the rate of change. of the line is equal to the speed of the object.
The steeper the line (and the greater the gradient) the faster the object is moving.
How to calculate the gradient of a distance-time graph
To calculate the gradient of a straight-line graph:
- Choose two points on the line that are far apart.
- Using a ruler, draw a right-angled triangle from one point to the other.
- Use the y-axis scale to work out the height or rise of the triangle.
- Use the x-axis scale to work out the width or run of the triangle.
Gradient = \(\frac{change~in~y}{change~in~x}\)
But this is often easier to remember as:
Gradient = \(\frac{rise}{run}\)
How much do you know about distance-time graphs?
See how much you know about distance-time graphs by answering the questions below.
Example question
Calculate the speed of the object represented by the green line in the graph, from 0 to 3 s.
Answer
A right-angled triangle is drawn using two far apart points – in this case using the points on the green line at 0 seconds and 3 seconds.
Rise = 6 m.
Run = 3 s.
Gradient = \(\frac{rise}{run}\)
Gradient = \(\frac{6}{3}\)
Gradient = 2 m/s.
The speed of the object represented by the green line in the graph is 2 m/s.
Question
Calculate the average speed of the object represented by the purple line in the graph, from 0 to 2 s.
Draw a right-angled triangle between the points on the purple line at 0 seconds and 2 seconds.
Rise = 10 m.
Run = 2 s.
Gradient = \(\frac{rise}{run}\)
Gradient = \(\frac{10}{2}\)
Gradient = 5 m/s.
Speed = gradient of distance-time graph = 5 m/s.
The speed of the object represented by the purple line in the graph is 5 m/s.
Question
Calculate the average speed of the object represented by the green line in the graph, from 0 to 10 s.
Answer
The slope of the green line changes over the 10 seconds and so to work out the average speed use:
Average speed = \(\frac{distance}{time}\)
Distance = 7 m.
Time = 10 s.
Average speed = \(\frac{7}{10}\)
Average speed = 0.7 m/s.
The average speed of the object represented by the green line, from 0 to 10 s is 0.7 m/s.
Question
Look at this distance-time graph and answer the following questions.
Question
How far did the vehicle travel in the first 4 seconds?
Answer
Go to 4 seconds on the x-axis.
Go vertically up until you meet the line of the graph.
Then trace across horizontally until you meet the y-axis.
The reading on the y-axis equals the distance travelled by the car in the first 4 s.
The distance travelled by the car in the first 4 seconds = 30 m.
Question
What was the speed of the vehicle over the first 4 seconds?
Answer
Draw a right-angled triangle between the points on the line at 0 seconds and 4 seconds.
Rise = 30 m.
Run = 4 s.
Gradient = \(\frac{rise}{run}\)
Gradient = \(\frac{30}{4}\)
Gradient = 7.5 m/s.
Speed = gradient of distance-time graph = 7. 5 m/s.
The speed of the car over the first 4 seconds = 7. 5 m/s.
Question
How long was the vehicle stationary?
Answer
The distance moved remains at 30 m between 4 and 8 seconds. The vehicle was stationary for a total of 4 seconds.
Question
What was the average speed of the vehicle over the journey?
Answer
The slope of the line changes over the 10 seconds and so to work out the average speed for the entire journey use:
Average speed = \(\frac{distance}{time}\)
Distance = 40 m.
Time = 10 s.
Average speed = \(\frac{40}{10}\)
Average speed = 4 m/s.
The average speed of the car over the entire journey = 4 m/s.
Summary
Key points
- The slope or gradient of the line of a distance-time graph is equal to the speed of the object.
- The steeper the line (and the greater the gradient) the faster the object is moving.
- Gradient = \(\frac{rise}{run}\)
How much do you know about distance-time graphs?
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