Friday, May 4, 2012

Calculus Speed trap

Catching speeders from our math class

Instead of using a worksheet, or pseudo-context question from a textbook you can show how related rates can be used to estimate the speed of a car from our classroom window.

1)      I used the Distmeasure app to determine the distance my classroom window is from the road.

2)      A student extended his arm and followed a car with arm until it hit a 45 degree angle.  Different students timed how long it took and we averaged the times.  [This will allow us to calculate the average rate of change of his arm in radians/second] in our class this took 4.6 seconds, as the following:

3)      Perform the calculations below
Since we know that student stopped at 45 degrees we can use the special triangle of 45/45/90 to substitute into the above formula.

We can then deduce that car is speeding through the school zone.

4)      Talk about the limitations of this activity, and how accurate this is.


  1. It is the most important topic which has a great role in research work of mathematics.Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

  2. cool! sounds like a fun party trick too.

  3. Nice exercise in math, but, for the final conclusion, more initial info should be stated first. Even assuming that the process yielded correct results, without stating the speed limit, one cannot know if the deduction is correct. Note that 40km/hr is a mere 25mph. Also, the time of day is important, as the speed limit is generally lower only for certain times of day.

  4. Why does your speed in the final answer not match the speed found by dividing the distance the car has traveled, which would be the same 32 m since it's a 45-45-90 triangle, by the time of 4.6 sec? 10.9 m/s vs 6.9 m/s.

    1. This is really late, like 4 years late. You're right, there is an error in the original post. The issue is that the change in the angle is not constant. At the beginning it changes rapidly and less rapidly as time goes on. This method could be used to find the change in your angle using the fact that you know the change in X.

  5. This seems to not need calculus, since the distance the car travels is known, 32m, and constant.