How Far Does a Sprinter Run During Acceleration in a 100m Dash?

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AI Thread Summary
In the 100m dash, a sprinter accelerates at 2.68 m/s² from rest before reaching a constant speed for the remainder of the race, which lasts 12.0 seconds. The equations used to calculate the distance during the acceleration phase include d1 = 1/2 * 2.68 m/s² * t² and d2 = vt, where v is the top speed. The initial attempt to solve the problem involved combining these equations and using the quadratic formula, but the results were incorrect. After some reflection, the individual resolved their errors in the calculations. The discussion highlights the importance of correctly applying physics equations to determine the distance covered during acceleration.
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Homework Statement


In the 100 m dash a sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 2.68 m/s2. After reaching top speed, he runs remainder of race with constant velocity. If total race is run in 12.0s, how far does he run during the acceleration phase?



Homework Equations


d1= 1/2*2.68 m/s2*t2
d2= vt = 2.68 m/s2*t*12.0s - t



The Attempt at a Solution


Not knowing if the above equations are correct I tried d1+d2=100m.
I multiplied everything, moved the 100m to the other side and tried the quadratic formula. I don't think I came out with the correct answer. I got approx. t= 3.5 or t= about 18. Any suggestions
 
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Nevermind. I've finally figured out my errors.
 

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