How Long Does a Sprinter Accelerate Before Reaching Top Speed?

  • Thread starter Cliborpimus
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In summary, the question asks for the time at which the sprinter stops accelerating and the distance he covers before reaching his top speed. The relevant equations involve six variables: Vf (final velocity), Vi (initial velocity), a (acceleration), t (time), Xf (final position), and Xi (initial position). The sprinter's final velocity (13.4m/s) and final position (200m) are known, and the question is asking for the time (t) and the distance (Xi) when the sprinter stops accelerating. The equations that can be used to solve this problem are Vf=Vi+at and Xf=Xi+Vit+(1/2)at^2.
  • #1
Cliborpimus

Homework Statement


The sprinter completes 200m in 19.3sec. When the starting pistol fires he accelerates constantly until he reaches his top speed of 13.4m/s. He then holds speed till the 200m point. At what time did he stop accelerating and how many meters did he cover before reaching top speed.

Homework Equations



Vf=Vi+ at
Xf=Xi+(1/2)(Vi+Vf)t
Xf=Xi+Vi t + (1/2)at^2
Vf^2=Vi^2 +2a (Xf-Xi)

The Attempt at a Solution



I know I have solved something like this before but it's been about 4 years since I've been in school and just can't seem to remember. I feel no matter what I do I am always short a variable. I have tried breaking it down into two different problems but I just can't seem to get it.
 
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  • #2
Cliborpimus said:

Homework Statement


The sprinter completes 200m in 19.3sec. When the starting pistol fires he accelerates constantly until he reaches his top speed of 13.4m/s. He then holds speed till the 200m point. At what time did he stop accelerating and how many meters did he cover before reaching top speed.

Homework Equations



Vf=Vi+ at
Xf=Xi+(1/2)(Vi+Vf)t
Xf=Xi+Vi t + (1/2)at^2
Vf^2=Vi^2 +2a (Xf-Xi)

The Attempt at a Solution



I know I have solved something like this before but it's been about 4 years since I've been in school and just can't seem to remember. I feel no matter what I do I am always short a variable. I have tried breaking it down into two different problems but I just can't seem to get it.
Your standard relevant equations involve six variables. Which of these are known from the question, and which do you have to find?
 

What is the definition of "Sprinter reaches top speed"?

The term "sprinter reaches top speed" refers to the point in a sprint race where a runner has reached their maximum velocity. At this point, the runner is moving at their fastest speed and cannot accelerate any further. This is typically towards the end of the race, as sprinters gradually build up their speed throughout the race.

What factors contribute to a sprinter reaching top speed?

There are several factors that contribute to a sprinter reaching top speed. These include the runner's physical abilities, such as their muscle strength, power, and explosiveness. Technique, experience, and training also play a crucial role in a sprinter's ability to reach top speed. Additionally, external factors such as weather conditions and track surface can impact a sprinter's performance.

How does a sprinter's top speed compare to their average speed?

A sprinter's top speed is significantly faster than their average speed. During a sprint race, a runner will gradually increase their speed until they reach their top speed, which is typically maintained for a short period before gradually slowing down at the finish line. On the other hand, a sprinter's average speed is the overall pace they maintain throughout the race, which includes the slower start and the faster top speed.

Can a sprinter improve their top speed?

Yes, a sprinter can improve their top speed through proper training and technique. By focusing on exercises that develop muscle strength, power, and explosiveness, a sprinter can increase their maximum velocity. Additionally, working on their technique and form can also help a sprinter reach their top speed more efficiently.

How is a sprinter's top speed measured?

A sprinter's top speed is typically measured using a speed gun or a timing system that records their time over a set distance, such as 100 meters. In addition, coaches and trainers may also use video analysis to assess a runner's top speed and identify areas for improvement. Ultimately, a sprinter's top speed is determined by their ability to reach and maintain their maximum velocity during a race.

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