Motion Sensor
Problem
A motion sensor collects data. At regular intervals it records the distance between itself and an object. If that object is moving towards, or away from, the sensor the distance data will change.
For 20 seconds a motion sensor is collecting data as a person moves backwards and forwards in front of it.
Here's the distance-time graph for that movement. Can you describe the person's motion? (the units are metres and seconds)
When was the person moving quickest? Calculate an estimate for this speed.
What was their lowest speed and when was this?
Getting Started
From the graph values you probably have an estimated speed in metres per second, how many metres would that be in an hour?
How many miles to how many kilometres?
Can you carry on thinking like that until you have mph?
Student Solutions
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!Teachers' Resources
This problem rests on the student visualising the motion from a graphical expression of the distance-time data.
Asking for a result in units other than those given on a graph scale involves a little problem solving but mostly relies on an ability to see the same quality (speed) expressed in more than one way (m/s or mph)