About Speed-Time Graph
A Speed-Time Graph plots the speed of an object against its time.
In this revision note, you will learn how to find distance in Speed-Time Graph.
You will also learn other applications like:
- Finding Acceleration
- Find Average Speed
- Important Definitions
- Relationships between Speed-Time, Distance-Time, and Acceleration-Time Graphs
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How to Find Distance in Speed-Time Graph
The diagram below shows a speed-time graph of a car. A straight line indicates a constant speed for a length of time. In order to calculate distance traveled, you’ll need to consider the horizontal axis and vertical axis as length and breadth. By treating this shape as an area, you can easily calculate distance traveled.
For Example:
Distance travelled, from 0 s to 10 s
= 1/2 x 10 x 20
= 100 m
Distance travelled, from 10 s to 25 s
= 15 x 20
= 300 m
Distance travelled, from 25 s to 30 s
= 1/2 x 5 x 20
= 50 m
Total Distance = 100 + 300 + 50
= 450 m
Example of Finding Average Speed in Speed-Time Graph
In order to determine the average speed over a length of period, you’ll need the total distance covered and the total time taken.
Average Speed = Total distance travelled ÷ Total time taken
= 450 m ÷ 30 s
= 15 m/s
How to Find Acceleration in Speed-Time Graph
The gradient of the speed-time graph gives the acceleration.
Example of Finding Acceleration in Speed‒Time Graph
For first 10 s, Acceleration,
a = 20 m/s ÷ 10 s
= 2 m/s2 (acceleration)
For last 5s,
a = (0 – 20 m/s) ÷ 5 s
= –4 m/s2 (retardation or deceleration)
Important Definitions of Kinematics
Initial = at the beginning t = 0
Instantaneously at rest v = 0
Stationary v = 0
Constant velocity a = 0
1. Velocity is the rate of change of displacement or distance in a particular direction with respect to time. (Can be Negative → Going in Negative Direction)
2. Speed is the rate of change of distance. (Cannot be Negative)
3. Average speed
4. Acceleration is the rate of change of velocity with respect to time.
About Distance-time Graphs
The diagram shows a distance-time graph of a car travelling from City A to City B.
(1) Positive (+) gradient indicates car travelling away from City A to City B.
(2) Zero gradient indicate car is at rest and not moving.
(3) Negative (‒) gradient indicates car is returning towards City A.
At any given time, calculating speed is done by finding the gradient of the graph.
Example of Distance-Time Graph
Find speed and average speed from distance‒time graph
From time, t = 2 h to 3 h,
Speed = 20 km ÷ 1 h
= 20 km/h
(Note: total time taken includes rest time)
For the whole journey,
Relationship of Distance-Time Graph, Speed-Time Graph, and Acceleration-Time Graph
Here are some different graphs that all show an object moving. Depending on the distance moved across the entire journey, and the type of graph, calculating distance is done through different methods.
Sketching of distance-time and acceleration–time graphs from speed-time graph
Given the following speed-time graph, sketch the corresponding distance-time and
acceleration–time graph.
The area under a speed‒time graph gives the distance travelled
At t = 20 s, d1 = 1/2 × 20 × 30 = 300 m
At t = 45 s, d2 = 300 + 23 × 30 = 1050 m
At t = 50 s , d3 = 1050 + 1/2 × 5 × 30 = 1125 m
Using the information above, we can now sketch the distance-time graph.
The gradient of a speed-time graph gives acceleration.
At t = 0 to 20 s, a1 = (30 – 0) / (20 – 0) = 1.5 m/s 2
At t = 20 to 45 s, a2 = (30 – 30) / (45 – 25) = 0 m/s 2
At t = 45 to 50 s , a3 = (0 – 30) / (50 – 45) = – 6 m/s2
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