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Let $v(t)$ the velocity of an object in the direction of a forze defined by: $$v(t) = \left\{ \begin{array}{ll} 4t & 0 \leq t\leq 4\\ 16+(4-t)^2 & 4 \leq t\leq 14 \\ \end{array} \right.$$ i) Find the Work if apply $200N$ for any $t$ (Use Simpson's Rule). ii) Make the velocity graph in function of time $(h=2)$ ii)Make the Displacement graph in function of time

i) I suppose that he need the total Work using Simpson's Rule on $v(t)$ using $h=2$ and then multiply the 200N to the result.

ii) i suppose that only i need graph $v(t)$, maybe the $h=2$ was a mistake writting the document

iii)I cant understand this point. how i can graph the Displacement in function of time using "numerical analysis" tools?

sango
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  • Have you covered splines yet in your class? – user5713492 Feb 09 '20 at 02:54
  • @user5713492 as interpolations? – sango Feb 09 '20 at 03:10
  • Yeah, you would have data points for $t\in{0,2,4,6,8,10,12,14}$ from part ii) and then you could use Simpson's $1/3$ rule and one application of Simpson's $3/8$ rule to get displacement for $t\in{0,4,8,14}$. Then a natural spline for $t\in[0,4]$ and a spline where the first (or second) derivative is given at the endpoints for the rest of the domain. Just a thought... – user5713492 Feb 09 '20 at 05:51

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