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Скорость есть первая производная от пути:
![s(t)= dfrac{5t+1}{t+2}
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v(t)= s'(t)=dfrac{(5t+1)'(t+2)-(5t+1)(t+2)'}{(t+2)^2} = dfrac{5(t+2)-(5t+1)}{(t+2)^2} =
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= dfrac{5t+10-5t-1}{(t+2)^2} =dfrac{9}{(t+2)^2}
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v(7)= dfrac{9}{(7+2)^2} = dfrac{9}{81} = dfrac{1}{9} (m/s)](https://tex.z-dn.net/?f=s%28t%29%3D++dfrac%7B5t%2B1%7D%7Bt%2B2%7D+%0A%5C%0Av%28t%29%3D+s%27%28t%29%3Ddfrac%7B%285t%2B1%29%27%28t%2B2%29-%285t%2B1%29%28t%2B2%29%27%7D%7B%28t%2B2%29%5E2%7D+%3D+dfrac%7B5%28t%2B2%29-%285t%2B1%29%7D%7B%28t%2B2%29%5E2%7D+%3D%0A%5C%0A%3D+dfrac%7B5t%2B10-5t-1%7D%7B%28t%2B2%29%5E2%7D+%3Ddfrac%7B9%7D%7B%28t%2B2%29%5E2%7D+%0A%5C%0Av%287%29%3D+dfrac%7B9%7D%7B%287%2B2%29%5E2%7D+%3D+dfrac%7B9%7D%7B81%7D+%3D+dfrac%7B1%7D%7B9%7D+%28m%2Fs%29 "s(t)= dfrac{5t+1}{t+2}
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v(t)= s'(t)=dfrac{(5t+1)'(t+2)-(5t+1)(t+2)'}{(t+2)^2} = dfrac{5(t+2)-(5t+1)}{(t+2)^2} =
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= dfrac{5t+10-5t-1}{(t+2)^2} =dfrac{9}{(t+2)^2}
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v(7)= dfrac{9}{(7+2)^2} = dfrac{9}{81} = dfrac{1}{9} (m/s)")
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