Speed and velocity refer to the motion of an object. Distance-time and velocity-time graphs can be a useful way of analysing motion.

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Distance is a measure of how far an object moves. Distance refers only to how far an object moves - it does not include an object's direction. This means that distance is a scalar quantity. Smaller distances can be measured with a ruler, a tape measure or a trundle wheel. Larger distances can be measured with GPS or aerial photography.

Speed is the rate of change of distance - it is the distance travelled per unit time. Like distance, speed is also a scalar quantity, as it does not refer to direction. To measure speed in the laboratory, a distance value and a time value are needed. The time value can be measured accurately with light gates, although a stopwatch can also be used.

To calculate speed, use the equation:

\[speed = \frac{distance}{time}\]

This is when:

- speed is measured in metres per second (m/s)
- distance is measured in metres (m)
- time is measured in seconds (s)

A toy car rolls down a ramp. The car takes 0.4 s to complete the final 30 cm of the ramp. Calculate the speed of the car as it rolls down the final 30 cm of the ramp.

**First convert the distance from centimetres to metres:**

30 cm = 0.3 m

**Then substitute the values into the equation:**

\[speed = \frac{distance}{time}\]

\[speed = 0.3 \div 0.4\]

\[speed = 0.75~m/s\]