__Speed, velocity and acceleration__

**Speed and distance-time graphs**

Speed is measured in metres per second (m/s) or kilometres per hour (km/h). If an athlete runs with a speed of 5 m/s, she will cover 5 metres in one second and 10 metres in two seconds. An athlete with a faster speed of 8m/s will travel further, 8m in each second, and will take less time to complete his journey.

This video shows a working example of speed calculation and talks about constant speed.

**Direction of travel**

There are two ways of looking at a journey:

- You can say that the distance you travel can only increase or stay the same, and then the speed is always a positive number.
- You can consider the direction you travel, so that if you travel towards school, that is a positive distance and when you travel in the opposite direction that is a negative distance. Sometimes, distance in a given direction is called displacement.
- You only need to know the term ‘displacement’ for Edexcel.

Quantities that have a magnitude and direction are called vectors.

Velocity is a vector, because velocity is speed in a given direction.

Example : A boy walks in a positive direction and then back again with a constant speed of 2 m/s, so he walks with a velocity of +2 m/s and then with a velocity of –2m/s.

**Distance–time graphs**

- a horizontal line means the object is stopped
- a straight line sloping upwards means it has a steady speed.

****The steepness, or gradient, of the line shows the speed:

- a steeper gradient means a higher speed
- a curved line means the speed is changing.

- A negative distance is in the opposite direction to a positive distance.
- A straight line sloping downwards means it has a steady speed, and a steady velocity in the negative direction.

Between 30 s and 50 s the cyclist stopped. The graph has a steeper gradient between 50 s and 70 s than between 0 s and 20 s – the cyclist was travelling at a greater speed.

To calculate a speed from a graph, work out the gradient of the straight line section as shown above in Fig. 9.1:

**Average speed and instantaneous speed**

You can calculate the average speed of the cyclist for the total journey in Fig 9.1 above using:

**Velocity–time and speed–time graphs**

- A positive slope (gradient) means that the speed is increasing – the object is accelerating.
- A horizontal line means that the object is travelling at a steady speed.
- A negative slope (gradient) means the speed is decreasing – negative acceleration.
- A curved slope means that the acceleration is changing – the object has non-uniform acceleration.

*Check carefully whether a graph is a speed-time graph or a distance-time graph.*

**Graphs, acceleration and distance**