Answer
$$v_{avg}=\frac{4.5(12)^{2}-4.5(0)^{2}}{12-0}=54$$
$$v_{inst}=9t=9\cdot 6=54$$
Work Step by Step
The average velocity is:
$$v_{avg}=\frac{s(12)-s(0)}{12-0}$$
$$v_{avg}=\frac{4.5(12)^{2}-4.5(0)^{2}}{12-0}=54$$
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$$v_{inst}=\lim\limits_{h \to 0}\frac{s(t+h)-s(t)}{h}$$
$$v_{inst}=\lim\limits_{h \to 0}\frac{4.5(t+h)^{2}-4.5t^{2}}{h}$$
$$v_{inst}=\lim\limits_{h \to 0}\frac{4.5t^{2}+9th+4.5h^{2}-4.5t^{2}}{h}$$
$$v_{inst}=\lim\limits_{h \to 0}\frac{+9th+4.5h^{2}}{h}$$
$$v_{inst}=\lim\limits_{h \to 0}(9t+4.5h)$$
$$v_{inst}=9t=9\cdot 6=54$$
