Define the following:
Position, displacement, distance; speed, velocity; acceleration, magnitude of acceleration; relative velocity (in 1 dimension).
Position – describes the location of an object
Distance – describes how far something has moved
Displacement – describes how far something has moved, in a specific direction
Speed – describes a change in distance in a specific amount of time
Velocity - describes speed in a specific direction
Acceleration – describes a change in velocity
Magnitude of acceleration – describes the size of the acceleration (i.e. without a direction)
Relative velocity (in 1 dimension) – describing the velocity of one particle relative to another. For example – when driving at 30mph and another car overtakes, doing 10 mph faster – so its real speed is 40mph, but relative to your vehicle it is travelling at 10mph.
The key is getting the difference between a vector quantity (such as velocity and acceleration) and a scalar quantity (such as speed or distance).
Students need to experiment with descriptions of journeys, or describing their location in order to clarify the difference between them.
Like other aspects of mathematics the distinctions become easier as the course develops – so at the start the teacher often has to labour the point rather a lot, but this should become clearer in the student’s mind as more of the course is covered.
The rest of the mechanics course is going to take these concepts further – at this stage it is probably enough to try to seek clarity.
The students have met speed & distance at GCSE and even back in Key Stage 3 – so they should be able to understand these general concepts.
Trying to think about the A-level version, about velocity rather than speed, should help them see the connection with previous work – but helping them see the advanced nature of vectors.