 1. Units of distance
2. Units of speed
3. Units of acceleration
4. Proving units
5. Errors in measurement

The main SI unit for measuring distance is metre and the symbol used for it is m. Other common units (and their symbols) used for measuring distance are millimetres (mm), centimetres (cm) and kilometres (km). The main SI unit for measuring speed is metres per second, given as m/s or ms⁻¹. An alternative unit for speed would be kilometres per hour, given as km/h or kmh⁻¹. Speed is a compound quantity, as it is made up of both distance and time, therefore to convert between units of speed both distance and time must be converted separately. The SI unit for measuring acceleration is metres per second squared, given by m/s² or ms⁻². An alternative unit that can be used is km/h² or kmh⁻². Just like speed, acceleration is a compound quantity made up of distance and time, therefore when converting between units of acceleration, the units for distance and time must be converted separately. The equations of speed and acceleration can be used to prove the units used for distance, speed and acceleration. Speed and acceleration are both compound quantities, therefore by using the units of the separate quantities that make up their equations, their units can be found. During experiments, random errors may occur which will affect precision and cause values of measurements to be different from the real values. Random errors can be reduced by repeating a process at least three times and calculating the mean, or by using computers to take measurements to reduce human error by, for example, eliminating the reaction time.

Systematic errors may also occur due to a faulty experimental method, which affects the accuracy of the measurements obtained, as it will make the values be either too great or too small by the same amount every time. Systematic errors can be reduced by calibrating apparatus and taking measurements at eye level to avoid parallax error.

Uncertainties can be calculated to find the range in which the true value of a reading (usually from an apparatus, electronic) or measurement (usually manual) is expected to lie.

uncertainty in a reading = ±(half the smallest division)
uncertainty in a measurement = ±(at least 1 smallest division)

When adding and subtracting data, the absolute uncertainties can be added, whereas when multiplying and dividing the data, the percentage uncertainties can be added. # 1

Find the main SI units of speed using the speed equation.

Using speed = distance/time and measuring distance in m and time in s, speed = m/s.

m/s # 2

Convert 5 m/s to km/h. Give your answer in an exact form.

5 m/s = (5/1000) × 3600 s = 18 km/h

18 km/h # 3

Convert 8.5 m/s² to km/h².

8.5 m/s² = 8.5/1000 × 3600² km/h² = 110160 km/h²

110160 km/h² # 4

A runner runs 14.2 metres in 2 seconds. Find the speed of the runner in km/h.

speed = distance/time
speed = 14.2/2 m/s = 7.1 m/s
speed = (7.1/1000)/(1/3600) km/h = 25.56 km/h

25.56 km/h # 5

Give 16.4 km/h² in m/s² to 3 significant figures.

16.4 km/h² = (16.4 × 1000)/3600² m/s² = 0.00127 m/s² (to 3 significant figures)

0.00127 m/s² End of page