Forces and Motion

Average and instantaneous values

Teaching Guidance for 14-16 Supporting Physics Teaching

Differences and similarities

Wrong Track: We covered 15 kilometre on our ride in 2 hours so we must have been travelling at 7.5 kilometre / hour.

Right Lines: The average speed is calculated from distanceduration. But it's possible that you weren't travelling at that speed for very much of the journey at all. If you made a movie clip of your cycle computer, showing your current speed, it's likely that for most frames it wouldn't be showing 7.5 kilometre / hour.

Making intelligent choices

Thinking about the learning

Dividing the distance covered during the journey (kilometre) by the duration of the journey (hour) will give an average speed:durationspeedaverage = distance

This global value can't be allowed to become confused with the values shown on the measuring instruments carried on the journey, which will show the values at a particular time, not over the whole duration of the journey.

Such right-now representations are true at an instant (so have no necessary connections to the history of the journey up to that instant). Here are some examples: resultant forces, velocities, accelerations, instantaneous speed, and positions.

Thinking about the teaching

You'll need to think about how to refer to measurements that represent an average for a whole journey, or for a significant interval during that journey.

You'll also need to think how to refer to values that represent a right-now value, for a particular clock time, at that instant.

Here are some suggestions, for thoughtful adaptation to your own practice and situation.

Resultant forces, forces, velocities, accelerations and positions are right-now representations, and so are true at an instant (no history). The clock reading is always a series of instants.

So time is always timeinstantaneous. t stands for this, and only this. Some instant, defined by a clock reading. A unique now-ness. So:

vinstantaneous is a longer way of writing v.

sinstantaneous is a longer way of writing s.

ainstantaneous is a longer way of writing a.

Finstantaneous is a longer way of writing F.

If we want to deal with them as averages (we'd suggest avoiding this until post-16 studies, if possible) we'd extend the conventions – for example – like this:

vaverage; saverage; aaverage.

appears in the relation F=ma a=dv/dt a=-(w^2)x
is used in analyses relating to Terminal Velocity
can be represented by Motion Graphs
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