Uniform accelerated motion (UAM) equations, a.k.a. "kinematics equations":

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

Kinetic friction:

$\overline{){{\mathbf{f}}}_{{\mathbf{k}}}{\mathbf{=}}{{\mathbf{\mu}}}_{{\mathbf{k}}}{\mathbf{N}}{\mathbf{=}}{{\mathbf{\mu}}}_{{\mathbf{k}}}{\mathbf{m}}{\mathbf{g}}}$

Newton's second law:

$\overline{){\mathbf{\Sigma}}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

For the tire at low pressure:

- a = ?
- Δx = 18.6 m
- v
_{0}= 3.80 m/s - v
_{f}= 3.80/2 = 1.90 m/s - Δt = ?

v_{f}^{2} = v_{0}^{2} + 2aΔx

Two bicycle tires are set rolling with the same initial speed of 3.80 m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes 18.6m ; the other is at 105 psi and goes 92.6m . Assume that the net horizontal force is due to rolling friction only.

What is the coefficient of rolling friction (μk) for the tire under low pressure?

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