Percent kinematics

A runner completes a 12km race with an average velocity (\(\overline { { v }_{ total } }\)) of \(4\text{ m/s}\). She does this in a certain amount of time, and after running for the first 16% of this time, her average velocity is \(8\text{ m/s}\) when she reaches a checkpoint. Afterwards, she continues running for the same amount of time again. By the end of this time, she covers the first 50% of the race's distance.

Using the information given, calculate the runner's average velocity, \(\overline { { v }_{ mid } }\), from the checkpoint up to this halfway point. Express your answer as the percent decrease from \(\overline { { v }_{ mid } }\) to \(\overline { { v }_{ total } }\).

Details and Assumptions

Do not calculate the average velocity as time-weighted; use the following formula: \[\overline { v } =\frac { \Delta x }{ \Delta t } =\frac { { x }_{ f }-{ x }_{ i } }{ { t }_{ f }-{ t }_{ i } }\] Treat all acceleration as constant; there is no need for calculus.

Picture credits: F5 St. Patrick’s Day Dash by Erika Schultz, The Seattle Times

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