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## 'Motion Sensor' printed from http://nrich.maths.org/

This turned out to be a popular problem and
we had lots of correct solutions - well done to everybody.
Emily and Kaia from Stoke-By-Nayland School
and Josh from Maungatapere School were first in with well-explained
answers.
The person was moving quickest at the point where the graph's
slope or gradient, either up or down, is steepest.

Between 9 seconds and 12 seconds they walked 4 metres, so a
reasonable estimate for the speed can be found dividing the
distance by the time.

4 metres in 3 seconds gives an average of around 1.3 m/s

Average speeds for other parts of the motion can be estimated in
a similar way to give approximate speeds of 0.6 m/s, 0.5 m/s, then
the 1.3 m/s (fastest) and finally 0.25 m/s

Nearly everyone went on to give the lowest
speed as the final part of the motion - that's around
0.25 m/s . But see what Alice from Montreal thinks :
The lowest speed must be zero.

If the person switches direction, say they were going forwards
and then go backwards, or the other way round, then there was an
instant when they stopped.

Even if it was almost no time at all there was still a point in the
motion when the speed, just for that moment, must have been
zero.

In this question that happened three times :

At around 9 seconds, 12 seconds and 16 seconds, the person
switched between motion forwards and motion backwards.

That's pretty good thinking, Alice!