Calculating Speed

Definition of Speed

Speed is a scalar quantity, meaning it has only magnitude and no direction. It tells us how fast an object is moving, without considering which way it is going.

Speed is defined as the distance travelled per unit time. The standard unit for speed in physics is metres per second (m/s).

Speed Formula

The formula to calculate speed is:

Speed = $$\frac{\text{distance}}{\text{time}}$$

Where:

• Distance is how far the object has travelled (in metres, m)
• Time is how long the journey took (in seconds, s)

If the units are different, you must convert them before calculating speed. For example, if distance is in kilometres and time in hours, convert to metres and seconds for standard SI units.

For instance, if a cyclist travels 1500 metres in 300 seconds, the speed is:

$\text{Speed} = \frac{1500}{300} = 5 \text{ m/s}$

Calculating Speed from Graphs

Distance-time graphs are useful for finding speed. On these graphs:

• The horizontal axis (x-axis) shows time (seconds)
• The vertical axis (y-axis) shows distance (metres)

The gradient (slope) of the line on a distance-time graph represents speed.

You calculate the gradient by choosing two points on the line and using:

Speed = $$\frac{\text{change in distance}}{\text{change in time}}$$

Different shapes on the graph mean different types of motion:

• Steep straight line: high constant speed
• Shallow straight line: low constant speed
• Flat horizontal line: stationary (speed = 0)
• Curved line: changing speed (acceleration or deceleration, but this is covered in other topics)

For example, if the line rises 100 metres over 20 seconds, the speed is:

$\text{Speed} = \frac{100}{20} = 5 \text{ m/s}$

Practical Measurement of Speed

To measure speed practically, follow these steps:

1. Measure the distance the object will travel using a metre ruler or tape measure. Be as accurate as possible.
2. Use a stopwatch to measure the time taken for the object to travel that distance.
3. Calculate the speed using the formula $\text{speed} = \frac{\text{distance}}{\text{time}}$.

For example, if a toy car travels 2 metres in 4 seconds, its speed is:

$\text{Speed} = \frac{2}{4} = 0.5 \text{ m/s}$