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Physics IA -motion

Extracts from this document...



Of A Hot Wheels Radar Gun



Title: The accuracy of a Radar Gun

Aim: To investigate the accuracy of a “hot wheels” radar gun.

Theory: Radar guns are, in their most simple form, radio transmitters and receivers. They send out a radio signal, and then receive the same signal back as it bounces off the objects. However, the radar beam is different when it comes back, and from that difference the radar gun can calculate vehicle speed.The gun uses the Doppler Effect to calculate the speed of the object in the beam's path. Using a comparison of frequency shift between received images instead of the frequency shift between sent and received frequencies creates what is known as moving radar, the radar must be stationary to measure speed.

By utilizing a number of different equations, it is thought that the accuracy of a Hot Wheels Radar Gun will be found. The equations that will be used are as follows:

  • Constant Velocity = distance (m)/time(s)
  • Instantaneous Velocity = small distance (m)/small time (s)
  • Conversion fromm/s to km/h = V × 60² / 1000
  • Uncertainty = limit of reading/2
  • Percentage Uncertainty = (uncertainty/value) × 100.
  • Percentage Deviation =( Exp Value – Accepted Value) / Accepted Value   X  100%


  • Hot wheels radar gun
  • Video recording device (mobile phone)
  • Markers (shoes)
  • Car


  • Chalk  
  • Measuring Tape

Diagram: The set up for the radar gun experiment








  1. A distance of 10m was measured out and marked with chalk.
  2. Three markers were used to mark out the distances of 0m, 5m, and 10m.
  3. The radar guns settings were changed to 1:1 and km/h.
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Distance Travelled

Velocity on Speedometer (Expected Value)

± 5

R.G. Velocity

± 0.5

Time taken according to V.D. (seconds)    ± 0.005













Table 3:

Calculating and finding uncertainties:

To find the uncertainty of a measurement one must simply find the limit of reading for the instrument being used and half it. The limit of reading is equal to the smallest graduation of the scale of an instrument. E.g. it can be seen above that the “time taken according to V.D.” table has an uncertainty of 0.005 seconds. This is because the smallest graduation in time shown on virtual dub is 0.01 seconds, hence 0.01/2 = 0.005.

Converting into percentage uncertainties:

When viewing the results of percentage accuracy the uncertainty must also be in percentage form. The following formula can be utilized to find this, percentage uncertainty = (uncertainty/value) × 100.

After finding the percentage uncertainty, one is able to find a more accurate uncertainty for the “I.V. km/h"

Finding velocity and Accuracy

To be able to compare the R.G. velocity to the instantaneous velocity one must first know the following components, time and distance. The formula, V= s/t gives you the velocity in m/s; however it then needs to be converted into km/h. This is done by multiplying the value by 60², then dividing by 1000, like so: value in km/h = m/s value × 60² ÷1000.

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The data that was accumulated shows that the radar gun has an average accuracy of 93.473% ± 1 for velocities that range approx. 20km/h-40km/h. After observing the tables and graphs it can be seen that velocity is inversely proportional to the accuracy of the radar gun, hence the accuracy decreases as the velocity increases. It was also gathered that the gradient of an “accuracy vs I.V.” decreases as the velocity increases, again another inverse relationship. The average accuracy was found to be 6.527% off 100% accuracy, which is a reasonable outcome, depending on the way one looks at it. In summation, this experiment was an overall success as the aim to find the accuracy of a Hot Wheels Radar Gun was met, and much was learned about the components that make up aspects of physics such as constant velocity, instantaneous velocity, etc.


In relation to the possible errors that may have occurred, if this experiment were to be repeated, the following modifications would be made.

  • Measure the velocity of the car with a more accurate device. This would in turn cause the final uncertainty to be smaller and the accuracy higher.
  • A larger space to conduct the experiment. An area such as an airport run way would be ideal for this experiment as it would give ample time for the driver to reach and maintain a constant velocity.
  • More care should be taken in both the recording and calculating process of data to reduce error.
  • Prac should take place in doors, to avoid environmental factors that may contribute to a higher error.
  • Rounding should be kept to a bare minimum in order to accumulate the most accurate data.

        Riki Nagoya                                                           21/04/08                                                            Mr Marshall

...read more.

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