Calculate the Sprinter's Final Speed at the Finish Line

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To calculate the sprinter's final speed at the finish line, the problem involves determining the distance covered during the initial acceleration phase of 3.40 seconds and the subsequent constant speed phase of 6.60 seconds. The sprinter accelerates with a positive, nonzero acceleration for the first 3.40 seconds and maintains a constant speed for the remaining 6.60 seconds to complete the 100-meter dash in 10 seconds. The solution requires applying kinematic equations to find both the acceleration and the final speed. The discussion emphasizes the need to analyze the two phases of the sprint to derive the necessary values. Ultimately, the sprinter's speed at the finish line can be calculated using these principles.
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Homework Statement



A sprinter can accelerate with constant acceleration for 3.40 s before reaching top speed. He can run the 100-meter dash in 10 s.

What is his speed as he crosses the finish line? (in m/s)

Homework Equations



kinematic equations

The Attempt at a Solution



a (acceleration) is positive and nonzero for the first 3.40 s

a is zero for the last 6.60 s
 
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What is the distance covered in the first 3.40s? What is the distance covered in the last 6.60s ?
 
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