Question

A 97-kg sprinter wishes to accelerate from rest to a speed of 13 m/s in a distance of 22 m. What coefficient of static friction is required between the sprinter's shoes and the track?

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Knowns{\large \textbf{Knowns}}

The maximum static friction\textbf{maximum static friction} is directly proportional to the normal force:

fs,max=μsN\begin{gather*} f_{s,max} = \mu_s N\tag{1} \end{gather*}

Where μs\mu_s is the coefficient of static friction.

From velocity-position\textbf{velocity-position} kinematic equation, the relation between the initial speed, final speed, acceleration and the change in position is:

vf2=vi2+2aΔx\begin{gather*} v_f^2 = v_i^2 + 2a\Delta x\tag{2} \end{gather*}

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