How Long Does a Sprinter Accelerate Before Reaching Top Speed?

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SUMMARY

The discussion focuses on calculating the acceleration time and distance covered by a sprinter who completes 200 meters in 19.3 seconds, reaching a top speed of 13.4 m/s. The relevant kinematic equations provided include Vf = Vi + at, Xf = Xi + (1/2)(Vi + Vf)t, and Vf² = Vi² + 2a(Xf - Xi). Participants emphasize the challenge of solving for unknown variables, particularly when attempting to break the problem into two segments: acceleration and constant speed. The key takeaway is the necessity of identifying known variables to effectively utilize the equations.

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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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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?
 

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