Introduction


Mass, length, and time are three of the most fundamental physical quantities. They are called base quantities. You will already have met their units – kilograms, metres, and seconds. The sizes of 1 kg, 1 m, and 1 s are set by international definition.

Mass, length, and time are called base quantities. They are just three of the possible base quantities used in the SI (Système International) system of measurement.



Derived quantities are defined as combinations of the base quantities listed above. For example, speed and

velocity

An object's velocity states both the speed and direction of motion relative to a fixed reference point.velocity are derived quantities and are both combinations of length and time.



The units for derived quantities are combinations of the units of the corresponding base quantities.





Sometimes the size of derived quantities is stated in non-standard units, but this is equally acceptable as there will always be derived equivalents.

It is easy to match the weightlifting record because there is only one answer in kilograms. Matching the 100 m and 200 m times is also quite straightforward, as we would naturally expect the time for the 200 m to be larger because the distance is greater. Matching the javelin and the discus distances is not quite so easy as their magnitudes are similar.

Humans have a natural perception of time, distance, and mass because we relate new circumstances to our existing experience. When quantities are of a similar size scientific methods involving accurate measurements are needed to distinguish between them.

To compare how quickly objects are moving we can determine their average speeds. Average speed is defined as



The blue and green balls in Fig.4 have similar speeds. To be certain which is moving faster, you will need to measure the time taken to complete a certain distance and then calculate their average speeds. The stopwatch in Fig.4 can be used for this purpose.



Simply comparing the times in the previous question is not sufficient to decide which is moving faster, the distance travelled must also be taken into account. However, we can use the definition of average speed to make a direct comparison.

Finding an average speed involves accurately measuring the time to travel a known distance. Measuring distances with a ruler is sufficiently accurate if the distance is more than a few centimetres, but measuring short time intervals accurately by manually starting and stopping a stopwatch is more difficult. To overcome this problem you can use a system of light gates like that shown in Fig.5.

• When the card on the trolley interrupts the light beam at A the electronic timing system starts.
  
  
• Timing continues until the card interrupts the light beam at B.
  
  
• The clock within the computer measures the time interval between the start and stop signals very accurately.
  
  

Repeat the experiment shown in Fig.5 and record the time the trolley takes to travel from A to B on each occasion in the following table.





To determine the average speed of the trolley as it travels from A to B in each experiment you would measure the distance between A and B and calculate the average speed using the equation,

You will have noticed that the trolley in Fig.5 gets faster as it rolls down the slope. The trolley is accelerating and travels faster past B than past A. The method outlined above determines the average speed between A and B.

The speed of a rolling trolley can be measured at different places along the runway with a single light gate as shown in Fig.6.

Start the experiment and note the following points:

• When the front edge of card on the trolley interrupts the light beam the electronic timing system starts.
  
  
• Timing continues while the card is interrupting the beam.
  
  
• Timing stops when the beam is reformed.
  
  

The clock within the computer measures the time taken for the card to pass through the light beam. During this measured time interval the trolley travels a distance equal to the length of the card. With these quantities we can calculate the average speed during this short time interval.



If the time interval is short the calculated average speed will be close to the speed of the trolley at the instant timing began. The instantaneous speed of a moving object is defined as the average speed over a very short time interval.

In Fig.6 you can move the light gate by clicking on the green spot and dragging it to another position. Measure the interrupt times for the light gate positioned at each of the lines A to E. Record your measurements in the table below.





The speed of a lorry is determined from the time taken for the rotation of one of its wheels. The distance travelled during each rotation is equal to the wheel's circumference so even at moderately low speeds the time for each revolution is short. Speedometers are widely regarded as showing instantaneous speeds.



A tachograph is a record of the instantaneous speed of a vehicle over a period of time. The instantaneous speed varies but if the total distance travelled during a 24 hr period is known the average speed can be calculated.

Summary


Speed is a derived quantity which is defined in terms of the base quantities distance and time.

The average speed of a moving object is defined as



In laboratory experiments average speeds are determined using either one or two light gates.

The average speed over a very short time interval is called the instantaneous speed.

Tachograph charts record instantaneous speeds over extended periods.