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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?

Solution

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Givens

• $x_a=x_b=x_c=x=10\ \text{m}$ - the distances travelled in each part of the race
• $t_a=1.02\ \text{s}$ - the time it takes in part a)
• $t_b=0.82\ \text{s}$ - the time it takes in part b)
• $t_c=0.9\ \text{s}$ - the time it takes in part c)

Required

• $v_a$, $v_b$, $v_c$ - the average velocities in parts a), b) and c), respectively

How can we use the definition of the average velocity in order to solve this problem?

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