Calculating Acceleration and Time in a 100 m Sprint Race

[arvin369]

Homework Statement

The title of “Fastest human” traditionally goes to the record holder of the 100 m race, which world-class sprinters can run in approximately ten seconds. Typically a sprinter accelerates quickly from rest to their maximum speed, after which their speed gradually tapers off towards the finish.

We can reasonably model a particular 100 m race for a runner by a constant (high) acceleration phase from rest to a maximum speed 11.9 m/s in t₁ seconds, followed by a constant (low) negative acceleration phase from 11.9 m/s to a final speed 11.0 m/s in a final total time of 10.30 seconds.

A) What is the time of the first phase?
B) What is the acceleration of the first phase?
C) What is the acceleration of the second phase?

Homework Equations

x(t) = x₀ + v₀t + 1/2at²
v(t) = v₀ + at

The Attempt at a Solution

So there are multiple variables that are unknown so I attempted eliminating a few with substitutions. Didn't work out too well. I may have eliminated it wrong. I have no idea what to do I have tried everything. Please give me hints on how to solve this, I don't want an answer or a direct way to do it. Just aim me in the right direction please. Thanks!

 

[fzero]

As you've stated the problem, you haven't quite explained what quantities you want to derive. It'd be a good idea to write down the equations for each phase (x(t₁), v(t₁), etc.) and identify which parameters are known and which need to be solved for. Don't plug numbers in until the end of the problem, or you'll just complicate the algebra.