How far does he run during the acceleration phase?

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    Acceleration Phase
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Homework Help Overview

The problem involves a sprinter accelerating from rest to a top speed with a specified acceleration, followed by running a fixed distance at that top speed. The total distance of the race is given, along with the total time taken to complete it.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting up equations of motion for both the acceleration phase and the constant speed phase. There are attempts to express distance and speed in terms of time variables, but some participants express confusion about the setup and calculations.

Discussion Status

There is an ongoing exploration of the problem with various approaches being suggested. Some participants are attempting to clarify the equations needed for both phases of motion, while others are seeking assistance with the setup and calculations. No consensus has been reached, and confusion remains regarding the application of the equations.

Contextual Notes

Participants are working within the constraints of the total race distance and time, and there is a focus on correctly applying the equations of motion. Some participants express uncertainty about what values to use in their calculations.

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If anyone could help it would be greatly appreciated! A sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.50 m/s2. After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is one hundred meters long. If the total race is run in 17.00 s, how far does he run during the acceleration phase?
 
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well I'd start by setting up the equations of motion in two parts: the accelaration phase and the constant speed phase:
ie: for 0<t<t(a) s(t) = 3.5/2 * t^2 [t(a) is the time they stop accelarating]..
do the same for the constant speed (its a bit more complicated) and using your known values see what you can do
 
hey i tried doing that but cannot seem to come up with the right answer. any ideas?
 
well, when you are done accelerating what is your speed? (using t(a) as a variable) and how far have you gone? (again using t(a) and the 1st equation)
 
i don't know i keep getting confused on what to plug in where. any chance on getting help setting up the equations?
 
something like this
0<t<t(a) s(t)=3.5/2 t^2
t(a)<t<t(f) s(t) = [3.5*t(a)]*[t-t(a)] + 3.5/2*t(a)^2
 

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