THE SPEED PROBLEM
Analysis
 
1. A CAR JOURNEY

A car goes on a journey, which you can see illustrated in the graph below. The distance travelled is expressed in kilometres and the time in minutes.
1.- Change the time values and look at the different distances covered, in kilometres.

Use the coloured arrow keys to the right of the word 'time'. You can enter any value between 0 and 64 minutes. Decimal values are rounded to the nearest whole number.

Use the Init button to restore the initial values.

2.- If you draw the graph in your exercise book and make a note of the distances covered and the time taken to do so you should be able to answer the following questions:

¿How far has the car travelled?

How long has the journey taken?

When was the car stationary?

What was the car's average speed?

If you take away the time when the car was stationary, what was the car's average speed?

What was the average speed between every two stops?

When was the car travelling the fastest?
2. THE AVERAGE SPEED

The average speed travelled between two points in time t1 and t2 can be expressed as follows:
 

Each section of the graph representing the car's journey can be analysed in more detail. The following Descartes window gives the average speed during a certain time interval. The time values can be written to two decimal places.

 
2.- Change the start and finish times of the time interval in order to work out the car's average speed between these times:[0,10], [10,17], [17,18], [18,32], [32,42], [42,50], [50,52] y [52,64]. Compare these results to the ones you got earlier.

3.- Work out the car's average speed during different intervals within the time interval [0,10]. Does the car travel at a constant speed during this time interval? Find other intervals on the journey when the car's speed was constant. Is there any connection with the fact that the graph is a straight line? 

4.- Work out the average speed for different sub-intervals within the time interval [10,17].

Increase the scale and move the axes to see the section of the graph in question more clearly.

Use the Init button to restore the initial values.

5.- What change in speed is there? Work out which other intervals during the journey involve a change in speed. Is there a connection between the change in speed and the shape of the graph?
6.- As you know, the speedometer in a car measures the speed that the car is travelling at any particular moment. In other words, rather than measure the car's speed over a time interval it tells us the car's speed at that instant, known as the instantaneous speed. Can you work out the speed of the car after 15 minutes? Give an approximate value.

 
       
           
  Miguel García Reyes
 
Spanish Ministry of Education. Year 2001
 
 

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