When discussing the motion of an Olympic sprinter for something like the hundred meter dash, one often talks about the maximum speed of the sprinters in the race. However, have you ever wondered what the acceleration is for one of those sprinters, and how long it takes to reach their maximum speed? Approximately two months ago, Usain Bolt, an Olympic runner from Jamaica, set the world record for the 100 meter dash in a time of 9.58 seconds!
Usain Bolt sets new record
To put that in perspective, that’s an average speed of 10.43 m/s. However, we all know that that was not his maximum speed during the race. It has been thought that sprinters typically reach their top speed at around 50-60 meters; Bolt reached his top speed at the distance of 60-80 meters, at which point he was running at the incredible rate of 12.42 m/s (27.79 mph). Assuming that he slowed a little bit in the next twenty meters, we can assume that he ran the final forty meters of the race at a somewhat constant speed of around 12 m/s. Therefore, he took 3.33 seconds on the final forty meters, meaning that it took him 6.25 seconds to accelerate from 0 to approximately 28 mph. By using one of our acceleration equations [A = 2(X final)/(t^2)], we are able to determine that Bolt’s acceleration, assuming that it was constant, was an average of 3.072 m/s/s.
This is pretty incredible to imagine, as his acceleration is somewhat close to that of the 2000 Honda moped’s 0-30 mph acceleration time of 5 seconds. On top of that, Bolt was able to accelerate to around 30 mph in about 41 seconds less than a fully loaded school bus! It will be interesting to see the sprinters of the future, and their ability to sprint at mind-boggling speeds. But for now, Usain Bolt’s time of 9.58 seconds in the 100 meter dash will do!
October 22nd, 2009 at 10:02 pm
Wow, he can accelerate as fast as my car! That is incredible. I found it very intereting how you broke down his race and found the average speed and acceleration for the first 60 meters. I wonder how close to a constant acceleration he had. Or would his rate of acceleration decrease as he approached his top speed?
October 23rd, 2009 at 3:18 pm
that is pretty fast..BUT! i really still think he coulda gone faster though..at the end it seemed like he slowed down..since he knows he’s winning anyways..but wow..amazing..
October 23rd, 2009 at 8:02 pm
I remember watching this before…and I was amazed at Bolt’s time. Even more amazing is the highest speed you calculated for his run…almost 28mph! I wonder how his rate of acceleration compares to the other runners here (when some start off too fast, or slower and then accelerate more rapidly) as well as to other races Bolt has completed. Does he always reach his max 60-80 meters? Does he usually accelerate at this rate, or does he usually run longer at a constant speed?
October 25th, 2009 at 11:02 am
@powerrangerlightspeed I don’t know if he chose to slow down- these guys are motivated by winning AND records. I think they give everything they got every time.
October 26th, 2009 at 2:29 pm
I was curious about the advantages Usain Bolt has over his competitors and I found this interesting article: http://www.telegraph.co.uk/sponsored/sport/sportslife/6416543/Athletics-what-makes-Usain-Bolt-the-fastest-man-on-the-planet.html
October 26th, 2009 at 6:28 pm
I think that Usain Bolt is an incredible sprinter, but even more incredible is how long he actually accelerates. If he doesn’t actually reach his top speed until about 60-80 meters down the track, that means he is increasing his speed the entire time. My only question would be, Does the amount of leverage that he uses on his body affect how fast he accelerates?