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# The running event known as the $100 \mathrm{~m}$ dash consists of three stages. In the first, the runner accelerates to the maximum speed, which usually occurs at the $50 \mathrm{~m}$ to $70 \mathrm{~m}$ mark. That speed is then maintained until the last $10 \mathrm{~m}$, when the runner slows. Consider three parts of the record-setting run by Usain Bolt in the 2008 Olympics: (a) from $10 \mathrm{~m}$ to $20 \mathrm{~m}$, elapsed time of $1.02 \mathrm{~s}$, (b) from $50 \mathrm{~m}$ to $60 \mathrm{~m}$, elapsed time of $0.82 \mathrm{~s}$, and (c) from $90 \mathrm{~m}$ to $100 \mathrm{~m}$, elapsed time of $0.90 \mathrm{~s}$. What was the average velocity for each part?

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What is the average velocity for a 100-meter dash of parts:

$a)$ 10-20 m, where $\Delta t_a=1.02$ s.

$b)$ 50-60 m, where $\Delta t_b=0.82$ s.

$c)$ 90-100 m, where $\Delta t_c=0.9$ s.

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