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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

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Escalator

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

Motion Sensor

Stage: 4 Challenge Level: Challenge Level:1

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!