The time when the particle is at rest is at 1.63 s or 3.36 s.
The velocity is positive at when the time of motion is at [tex]0<t<1.63 \ s \ \ or \ \ t> 3.36 \ s[/tex].
The total distance traveled in the first 10 seconds is 847 m.
The time when the particle is at rest is calculated as follows;
s(t) = 2t³ - 15t² + 33t + 17
[tex]v = \frac{ds}{dt} = 6t^2 -30t + 33\\\\at \ rest, \ v = 0\\\\6t^2 - 30t + 33 = 0\\\\6(t- \frac{5}{2} )^2- \frac{9}{2} = 0\\\\t = 1.63\ s \ \ or \ 3.36 \ s[/tex]
The velocity is positive at when the time of motion is as follows;
[tex]0<t<1.63 \ s \ \ or \ \ t> 3.36 \ s[/tex].
The total distance traveled in the first 10 seconds is calculated as follows;
[tex]2(10)^3 - 15(10)^2 + 33(10) + 17 = 847 \ m[/tex]
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