Is there a more accurate way to determine speed? I am asking because this has to do with an accident reconstruction where my son was killed. The investigators are trying to conclude his speed prior to impact and I want to know if this is the only way to determine speed.
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$\begingroup$ My deepest sympathies. Even if your son or another driver was speeding, that does not mean that his/their speeding was the only factor that led to your tragedy. Some locations the law recognizes this and apportions responsibility proportionately. You may need to consult local experts that are aware of your situation and the laws in your location $\endgroup$– DaleCommented May 17, 2023 at 15:27
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$\begingroup$ Thank you for your reply $\endgroup$– Dayle SuzanneCommented May 17, 2023 at 17:06
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3 Answers
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I'm very sorry for your loss.
The definition of the average speed of an object as it passes between two points is the distance $d$ between them divided by the time $t$ it took to get from one to the other. This is only an average, which means that the actual speed could have varied a bit during that time interval, but it would have to average out to $d/t$.
Trained investigators can also use indirect evidence, such as skid marks on the road and the nature of the damage or injuries which occur during the crash, to make more specific and detailed inferences about the speeds involved.
If you have questions about any conclusions that professional investigators have reached, it would be best to discuss it with them or to retain another professional to evaluate the situation independently. As a general rule, physicists tend to focus on the fundamental principles at play in a given situation, but if you have a problem with your pipes then you want a plumber, not an expert in fluid dynamics. If you are concerned about things such as legal or ethical liability or the validity of some expert testimony, a group of (well-meaning) quasi-anonymous physicists is unlikely to be your best source for specific information.
answered May 17, 2023 at 14:24
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In this case, it would not be about the fundamental calculation such as d/t, but the tell tale clues and their incorporation into the calculation. Fuzzy data, so to speak. There is difficulty of measuring t since the event has already passed and the measurement of d needs to be in the correct direction (for example an odometer won't measure something like sideways skid). So to really rely on d/t after the fact, you would need something like a video recording.
Also mentioned in the other answer is that even with d/t, how long an time interval you are observing matters. Average speed for longer intervals approaching actual speed for a point in time as you shorten the intervals. Average speed being the one speed where if it was held constant over the same time interval, it would result in the same distance traveled as the real world case being examined, which could have varied to be both above and below the average speed over that same time. This does not bode well if one is interested in a speed at a point in time where rapid, unpredictable changes in speed (i.e. braking) or curves (i.e. swerving) are involved.
All that means is that although d/t is the most accurate way, it also relies on information that probably is no longer available. If the interest is the actual speed prior to impact then d/t can't really be used without lots of instrumentation already present. Even video would require lots of objects/features to serve as distance benchmarks in the footage in this case.
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$d/t$ is the average speed. Consider a simple case: if someone needs to brake for $t=2 \, s$ to finally immobilize the car and during that time he/her travels a distance $d=22 \, m$, $d/t$ would average into $\approx 40 \, km/h$. However, the initial speed (at the moment accident is most likely realized) would be Higher than that. If the car loses speed under a constant rate up until fully stopping, that speed would be around double that value or $\approx 80 \,km/h$.
However, the problem is to know how speed was lost (deceleration). That constant loosing speed condition may be inappropriate in some cases as many factors like road, tires, brakes and whether conditions affect it. Therefore, no simple solution to get the exact initial speed was in your specific case.
NOTE: I’m not an accident expert, so please talk to the experts and try to understand the methodology used.
