Notes: suppose that the position of a particle as a function of time (in seconds) is given by the formula s(t)=6.5+4t^2-t^4,t>0 the time at which the...

Tuesday, 18 October 2016

suppose that the position of a particle as a function of time (in seconds) is given by the formula s(t)=6.5+4t^2-t^4,t>0 the time at which the...

The position
function is given as $\displaystyle{s}{\left({t}\right)}={6.5}+{4}{{t}}^{{2}}-{{t}}^{{4}}$ for t>0

The velocity function is
the first derivative of the position function, and the acceleration function is the derivative
of the velocity function (or the second derivative of the position function.)

$\displaystyle{v}{\left({t}\right)}={s}'{\left({t}\right)}={8}{t}-{4}{{t}}^{{3}}$

$\displaystyle{a}{\left({t}\right)}={v}'{\left({t}\right)}={s}''{\left({t}\right)}={8}-{12}{{t}}^{{2}}$

(a) The velocity is zero when $\displaystyle{8}{t}-{4}{{t}}^{{3}}={0}$

$\displaystyle{4}{t}{\left({2}-{{t}}^{{2}}\right)}={0}=\Rightarrow$
4t=0,2-t^2=0 $\displaystyle{\sin{{c}}}{e}{t}>{0}{w}{e}{h}{a}{v}{e}$ t=sqrt(2)~~1.41