YOU ARE LEARNING:
Velocity/Time Graphs
Velocity/Time Graphs
Velocity/time graphs show you the direction and speed of a moving object.
This is a velocity/time graph. What does it have in common to a distance/time graph?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
So both V-T graphs and D-T graphs have time as their independent variable.
They differ in their dependent variables.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
Let's try reading this graph.
What was this object's velocity after 10 seconds?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
So at time = 10 seconds, the object was travelling at 15m/s.
This information is given by the point (10,15).
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
What was this object's velocity after 20 seconds?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
True or false? This object was moving faster after 20 seconds than after 10 seconds.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
After 10 seconds the object was moving with a velocity of 15m/s, and after 20 seconds it was moving with a velocity of 30m/s . That means that this object was...
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
So this is a velocity/time graph that shows an accelerating object.
The further out on the x-axis you go, the higher the velocity (m/s) gets.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
What is the acceleration of this object?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
Horizontal Lines
How would you describe the motion of this particular object?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/gX9vtIOQo6HZMEPy6L82.png)
What is the slope, and thus the acceleration, of this object?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/gX9vtIOQo6HZMEPy6L82.png)
So this is a velocity/time graph that shows an object that is moving at constant speed - it has acceleration of 0m/s2
No matter when the object's velocity was measured, it was unchanged. It stayed at 40m/s.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/gX9vtIOQo6HZMEPy6L82.png)
Positive Gradients
What is the change in velocity here from 10 seconds to 20 seconds?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/bgNWVNQE6v59DGyG1Vkw.png)
So at 10 seconds, the velocity is 35 m/s, and at 20 seconds the velocity is 50 m/s. What is the acceleration in m/s2 over the course of those 10 seconds?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/bgNWVNQE6v59DGyG1Vkw.png)
Between 10 and 20 seconds, the acceleration of the object is 1.5 m/s2. Is that the same between 30 seconds and 40 seconds? Answer yes or no.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/bgNWVNQE6v59DGyG1Vkw.png)
True or false? This object is moving at constant speed.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/bgNWVNQE6v59DGyG1Vkw.png)
True or false? This object is speeding up at a constant rate.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/bgNWVNQE6v59DGyG1Vkw.png)
So, a velocity/time graph with a positive gradient shows an object with a constant (unchanging) acceleration.
We call this uniform acceleration.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/bgNWVNQE6v59DGyG1Vkw.png)
Negative Gradients
How was the velocity of this object changing over time?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
So this object was...
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
So this is a velocity/time graph that shows an object that is slowing down or decelerating.
The further out on the x-axis you go, the lower the velocity (m/s) gets.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
What kind of acceleration does this object have?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
Calculate the acceleration of this object.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
So a negative gradient shows negative acceleration. Is this uniform acceleration?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
So, a velocity/time graph with a constant negative acceleration...
shows the motion of an object with uniform deceleration.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/szzspPxT7m8OkyGYJ3VP.png)
Curved Lines
Is the gradient the same at all points on this graph?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/KAekVwemTp2OA6HXqbxS.png)
Was this object speeding up at a constant rate?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/KAekVwemTp2OA6HXqbxS.png)
This curved line shows that the object was speeding up faster and faster
The further out the x-axis you go, the steeper the graph gets, so the larger its acceleration gets.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/KAekVwemTp2OA6HXqbxS.png)
The green line shows an object that is...
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/w3n87BaDRl643DQMOqmF.png)
The green line shows an object which is still speeding up, but at a lower and lower rate
If a curve flattens out in a velocity/time graph, that just means that the object is going towards constant speed. It does not mean the object stops moving!
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/w3n87BaDRl643DQMOqmF.png)
Are these examples of uniform acceleration?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/w3n87BaDRl643DQMOqmF.png)
So curved lines on a velocity/time graph show...
non-uniform acceleration.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/w3n87BaDRl643DQMOqmF.png)
Summary!
A velocity/time graph has velocity on the y-axis and time on the x-axis.
The gradient in a velocity/time graph is the same as acceleration a=ΔtΔv , with units m/s2
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/uQ2urZphTHyqTvaabuW3.png)
A horizontal line means the object is moving at a constant speed
This is because it has no gradient, and thus no acceleration.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/gX9vtIOQo6HZMEPy6L82.png)
A constant positive gradient means...
the object has a positive uniform acceleration.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/VemXm6HRQd2pPbQRZEDP.png)
A constant negative gradient means...
the object has a uniform deceleration.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/FpaYbAFdS0qSIOLWJVus.png)
A line that curves upwards means the object is speeding up faster and faster.
Its acceleration is increasing, so it is non-uniform.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/KAekVwemTp2OA6HXqbxS.png)
A line that flattens out means the object is still speeding up, but doing so at a slower and slower rate
Its acceleration is decreasing, so it is non-uniform.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/72mq4d4wQueb57o8zmDs.png)