Distance-time graphs
Learning Objective:
Can you explain how to interpret a
distance time graph?
Starter
Key Terms:
Distance
Time
Graph
Gradient /Slope
speed
Acceleration
Where do you need Distance
vsTime
• https://www.youtube.com/watch?v=yGVgKJTJkQo
Distance-time graphs
Learning Objective:
Can you explain how to interpret a distance time graph?
Success Criteria:
Level 1-2:
Interpret distance–time graphs
Level 2:
Calculate speed using a distance–time graph
Level 3:
Define acceleration.
I will be using enquiry processes to:
present data in a distance–time graph.
Journey to the Bus Stop
Every morning Tom walks along a straight road from his
home to a bus stop, a distance of 160 meters.
The graph shows his journey on one particular day.
Review - Speed
Speed:
- The measure of how fast/slow something moves a particular distance over a
given amount of time.
- It can then be calculated using the following formula:
- speed=distance/time
Distance-time graphs
How do you graph speed?
Graphs are always set up the same way:
Y - axis
X- axis
Distance - Time Graphs
On a distance time graph, the distance will always be the dependent variable on
the y- axis.Y - axis
X- axis
Time is the independent variable and will always be placed on the x-axis.
Lines on the Graphs
The lines on the graphs can tell you many different things. For example:
The slope of a line (steepness) can tell you speed.
If the slope is steep (more vertical) then the speed is fast.
If the slope is flatter (more horizontal) then the speed is slow.
If the line is completely flat or horizontal then the object has no speed or is
stopped.
Examples of distance-time graphs
FAST
STOPPED
SLOW
Leaving and coming back:
1.The bell goes and Homer stops work and runs
Homer 250m to his car, this takes him 5 minutes.
2. Homer drives for 10 minutes but only gets 2000m before
he needs to stop for a doughnut.
3. He sits in his parked car and spends 5 minutes eating the
doughnut.
4. Finally he starts the engine and drives for 5 minutes,
1000m back home.
3500
Distance 3000
travelled 2500
(m)
2000
1500
1000
500
0
5
10
15
20
25
0
Time taken (mins)
1. Bart sprints 100m through school which takes a
Bart minute.
2. He then jumps on his skateboard and takes 4 minutes to
dodge his way 500m through a crowd of people.
3. Bart jumps off at Apu’s and looks around for 10 minutes
4. Finally he jumps back on his skateboard and travels 750m
back in a record time of 4 minutes!
1400
Distance 1200
travelled 1000
(m)
800
600
400
200
0
0 2 4
6 8 10 12 14 16 18 20
Time taken (mins)
Marge
1. Marge sets off carefully from her shopping trip,
driving 1500m in 10 minutes
2. She then realises she might be late so speeds up, covering
the next 1000m in 2 ½ minutes before reaching traffic lights
3. She waits at the lights for 5 minutes.
4. She drives 500m home, this takes 5 minutes.
3500
Distance 3000
travelled 2500
(m)
2000
1500
1000
500
0
0
5
10
15
20
25
Time taken (mins)
Distance-time graphs
Grade D/C
Distance-Time graphs
Date
LO To interpret distance-time graphs
Find the gradient of the highlighted lines
Gradient (m) = change in y
change in x
Gradient (m) = 12 = 6
2
>>> EXT Find the gradient of the line on the red tile
KEY WORDS: gradient, axis, units, constant
3)
Gradient (m) = change in y
change in x
4)
Gradient (m) = change in y
change in x
1)
Gradient (m) = change in y
change in x
2)
Gradient (m) = change in y
change in x
>>> EXT
5)
Gradient (m) = change in y
change in x
Speed = distance
time
Speed = 12 miles
2 hours
Speed = 6 mph
The steeper the gradient the faster the speed
Speed = distance
time
How can you use a distance-time graph to find
the speed?
The gradient of a distance-time graph represents
the speed
Determining Speed from a graph
s=d/t
1. Think of the graph in sections divided
by each line segment
2. Then determine the total distance for
the line segment you are looking at.
3. Then determine the total time for that
segment.
4. Finally, use the equation to determine
speed of the line segment.
Example: the object traveled a total distance of 25 m for the first segment. It took
the object 20 seconds. s=d/t s=25/20 s= 1.25 m/s
Practice
Calculate the speed for last line segment:
1.
2.
3.
4.
Distance traveled = 25 m
Time = 10 sec
v=d/t 25/10
2.50 m/sec
Was the object moving faster or slower than when
they started?
Lisa
1. Lisa sees the time and spends 5 minutes packing
her saxophone away. Its then a 5 minute walk to her
bike 300m away.
2. She then cycles on a flat 800 metres in 5 minutes.
3. At this point she reaches a hill and slows down, travelling
the next 300 metres in 3 minutes, before reaching home.
1600
1400
Distance 1200
travelled 1000
(m)
800
600
400
200
0
0 2 4
6 8 10 12 14 16 18 20
Time taken (mins)
Bart the daredevil
The table shows how long it took Bart to cover a few
distances before Homer came to the rescue.
Plot a distance-time graph to show Bart as he accelerates
(gets faster). How would you describe the graph?
Distance Time
travelled Taken
(m)
(s)
5
8
7.5
6
10
4
12.5
3
Distance travelled (m)
Bart the daredevil
40
35
30
25
20
15
10
5
0
0
4
8
12
16
20
Time taken (secs)
24
Distance-time graphs
Question 1
Which graph shows the object travelling at a faster speed?
A
B
Question 2
Which part of the graph shows that the object is stationary?
A
B
C
Question 3
Which line shows an object that is accelerating?
A
B
Question 4
How far did object A travel?
50 metres
100 miles
100 metres
Question 5
What was the speed of object A?
200 m/s
5 m/s
0.2 m/s
Question 6
Which part of the graph shows that the object is returning to the start?
B
C
A
A
B
C
Question 7
Which parts of the graph shows that the object is travelling at a
constant speed?
B
C
A
A+B
B+C
A+C
Question 8
How long was the cyclist stationary for?
B
C
A
80s
40s
220s
Homework
title
Learning Objective:
Success Criteria:
Matching activity
F-3
Matching activity
G-8
Matching activity
A-7
Matching activity
C-9
Matching activity
H-4
Matching activity
B-6