Motion and speed

In a nutshell

The speed of an object tells you how fast it is travelling. By looking at the relationship between distance and time, you can find out the speed of an object and sometimes even the way in which the speed of the object is changing. 

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Equations

Variable definitions 

Speed calculations

You can find the average speed of the object if you know the distance it has travelled and the time it took for the object to travel that far.

​$$speed = \frac{distance}{time}$$

​$$s = \frac{d}{t}$$​​

If you need to calculate the distance travelled instead, you can rearrange this equation to make distance the subject. Or if you need to find the time taken to travel a certain distance, you can rearrange for time. 

Example

A car travels at a speed of $$3 \space m/s$$ for a total of $$10 \space seconds$$​. How far has the car travelled in metres? 

Begin by writing out the quantities you been given:

​$$speed = 3 \space m/s$$​​

​$$time = 10 \space s$$​​

Rearrange the equation to find distance travelled: 

$$distance = speed \times time$$​​

Substitute the values into the equation:

​$$distance = 3 \times 10$$

The distance travelled by the car is $$\underline{30 \space m}$$​. 

Distance-time graphs

A distance-time graph shows you how the speed of an object changes over time. Distance is plotted on the $$x$$-axis and time is plotted on the $$y$$-axis. The slope, also called the gradient, tells you the speed of the object. The shape of the distance-time graph can also tell you about how the motion of the object is changing.

A Distance B Time

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