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# Answer to Question #109456 in Mechanics | Relativity for Patricia

Question #109456
Explain how it is possible for a small child and a large football player to have the same momentum. If the small child and the large football player were running side-by-side (same velocity) which would take more force to stop? Why?
1
2020-04-15T10:25:07-0400

What is momentum? It is mass times velocity. Therefore, at low velocity an adult footballer may have the same momentum as a not so heavy child running at a full speed:

"p=m_fv_f=m_cv_c."

On the other hand, momentum can be expressed as

"p=\\frac{F}{t},\\\\\n\\space\\\\\nt=\\frac{F}{p}."

The force that makes the footballer and the child stop is the force of friction. Assume that the coefficient of kinetic friction is the same for both:

"F=f=\\mu mg."

Substitute this to the previous equation with force and expand the momentum:

"t=\\frac{\\mu mg}{mv}=\\frac{\\mu g}{v}."

Therefore, for the same speed it may theoretically take the same time for them to stop.

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