# The position of a particle as it moves along a straight line is given by s(t)=(t^2-5)(3t+4). Find the velocity of the particle as a function of time.

The position of a particle as it moves along a straight line is given by $s\left(t\right)=\left({t}^{2}-5\right)\left(3t+4\right)$ Find the velocity of the particle as a function of time.
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Lamar Esparza
Given $s\left(t\right)=\left({t}^{2}-5\right)\left(3t+4\right)\phantom{\rule{0ex}{0ex}}\frac{ds}{dt}=v\phantom{\rule{0ex}{0ex}}v\left(t\right)=\frac{d}{dt}\left({t}^{2}-5\right)\left(3t+4\right)+\left({t}^{2}-5\right)\frac{d}{dt}\left(3t+4\right)\phantom{\rule{0ex}{0ex}}=\left(2t-0\right)\left(3t+4\right)+\left({t}^{2}-5\right)\left(3\right)\phantom{\rule{0ex}{0ex}}=6{t}^{2}+8t+3{t}^{2}-15\phantom{\rule{0ex}{0ex}}v\left(t\right)=9{t}^{2}+8t-15$