Distance-time graphs
Distance-time graphs show how distance changes as time goes on.
● The gradient of a distance-time graph is the speed of the body.
The gradient might be different for different sections of the graph so you cannot simply calculate speed
using 𝑠𝑝𝑒𝑒𝑑 =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
as you normally would.
𝑡𝑖𝑚𝑒
In a distance-time graph like this a horizontal line means the distance is not changing as time goes on. That
means the object is not moving; it is stationary.
If the line is diagonal, that means the distance is changing so the object is moving.
1. If we want to know the speed from 0 to 3.0 seconds, we calculate the gradient of that section.
𝛥𝑦
𝛥𝑑
30−0
30
𝑣 = 𝛥𝑥 = 𝛥𝑡 = 3.0−0 = 3.0 = 10 𝑚/𝑠
2. If we want to know the speed from 5.0 to 7.0 seconds, we calculate the gradient of that section
𝛥𝑦
𝛥𝑑
70−30
40
𝑣 = 𝛥𝑥 = 𝛥𝑡 = 7.0−5.0 = 2.0 = 20 𝑚/𝑠
3. If we want to know the speed from 8.0 to 10.0 seconds, we calculate the gradient of that section
𝛥𝑦
𝛥𝑑
80−70
10
𝑣 = 𝛥𝑥 = 𝛥𝑡 = 10.0−8.0 = 2.0 = 5.0 𝑚/𝑠
The fastest section is from 5.0 to 7.0 seconds. We can also see that the line is steepest there.
Distance-time graph questions
Use the following distance-time graph to answer the following questions.
1. Calculate the speed from 0.0 to 2.0 seconds.
2. State the speed from 2.0 to 4.0 seconds.
3. Calculate the speed from 4.0 to 6.0 seconds.
4. State the speed from 6.0 to 8.0 seconds.
5. Calculate the speed from 8.0 to 10.0 seconds.
6. Use the total distance travelled divided by the total time taken to calculate the average speed.
Speed-time graphs
Speed-time graphs show how the speed of an object changes as time goes on.
● The gradient of a speed-time graph is acceleration.
● The area under a speed-time graph is the distance travelled.
The gradient might be different for different sections of the graph so you cannot simply use 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑠𝑝𝑒𝑒𝑑
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑝𝑒𝑒𝑑
but you can use 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 .
𝑡𝑖𝑚𝑒
A diagonal line pointing upwards means that the speed is increasing. We call this accelerating.
A horizontal line means the speed is constant. This does not mean the object is stationary unless the
horizontal line is at speed = 0.
A diagonal line pointing downwards means that the speed is decreasing. We call this decelerating.
1. If we want to know the acceleration from 0.0 to 3.0 seconds, we calculate the gradient for that section
using
𝑎=
𝛥𝑦 𝛥𝑣
60 − 0
60
=
=
=
= 20 𝑚/𝑠 2
𝛥𝑥 𝛥𝑡 3.0 − 0.0 3.0
If we want to know the distance travelled from 0.0 to 3.0 seconds, we calculate the area under the graph for
that section. That is the area of a triangle so we use
1
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 = 𝑎𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 = 0.5 × 3.0 × 60 = 90 𝑚
2
2. The acceleration from 3.0 to 5.0 seconds is 0 because the speed doesn't change.
The distance travelled from 3.0 to 5.0 seconds is the area of a rectangle.
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 = 𝑎𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 = (5.0 − 3.0) × (60 − 0) = 2.0 × 60 = 120 𝑚
3. If we want to calculate the deceleration from 5.0 to 6.0 seconds, we calculate the gradient for that section
using
𝑎=
𝛥𝑦 𝛥𝑣
60 − 0
60
=
=
=
= 60 𝑚/𝑠 2
𝛥𝑥 𝛥𝑡 6.0 − 5.0 1.0
The distance travelled from 5.0 to 6.0 seconds is the area of a triangle.
1
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 = 𝑎𝑟𝑒𝑎 = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 = 0.5 × (6.0 − 5.0) × (60 − 0) = 30 𝑚
2
4. The object is stationary from 6.0 to 7.0 seconds. This section has 0 area so the distance travelled is 0.
Speed-time graphs questions
Use this speed-time graph to answer the following questions
1. Calculate the acceleration from 0 to 2.0 seconds
2. Calculate the distance travelled from 0 to 2.0 seconds
3. State the acceleration from 2.0 to 4.0 seconds
4. Calculate the distance travelled from 2.0 to 4.0 seconds
5. Calculate the deceleration from 4.0 to 5.0 seconds.
6. Calculate the distance travelled from 4.0 to 5.0 seconds.
7. Describe the motion from 5.0 to 7.0 seconds.
8. Calculate the distance travelled from 7.0 to 8.0 seconds.
9. Calculate the deceleration from 8.0 to 10.0 seconds.
10. Calculate the distance travelled from 8.0 to 10.0 seconds.