First we have to calculate the distance x at each t.

\(\displaystyle{x}{\left({0}\right)}={Z}{e}{r}{o}\ {m}\)

\(\displaystyle{x}{\left({2}\right)}={1.50}{\left({2}\right)}^{{{2}}}-{0.0500}{\left({2}\right)}^{{{3}}}={5.6}{m}\)

\(\displaystyle{x}{\left({4}\right)}={1.50}{\left({4}\right)}^{{{2}}}-{0.0500}{\left({4}\right)}^{{{3}}}={20.8}{m}\)

The average velocity is the displacement divided by the time interval at which this displacement happened.

\(\displaystyle{v}_{{{x},{a}{v}{g}}}={\frac{{\triangle{x}}}{{\triangle{t}}}}\)

\(\displaystyle\triangle{x}={x}_{{{f}}}-{x}_{{{i}}}\)

\(\displaystyle\triangle{t}={t}_{{{f}}}-{t}_{{{i}}}\)

Step 2

(a) \(\displaystyle{v}_{{{x},{a}{v}{g}}}={\frac{{{x}_{{{f}}}-{x}_{{{i}}}}}{{{t}_{{{f}}}-{t}_{{{i}}}}}}\)

\(\displaystyle{x}{\left({0}\right)}={Z}{e}{r}{o}\ {m}\)

\(\displaystyle{x}{\left({2}\right)}={1.50}{\left({2}\right)}^{{{2}}}-{0.0500}{\left({2}\right)}^{{{3}}}={5.6}{m}\)

\(\displaystyle{v}_{{{x},{a}{v}{g}}}={\frac{{{5.6}-{0}}}{{{2}-{0}}}}\)

\(\displaystyle={2.8}\frac{{m}}{{s}}\)

Step 3

(b) \(\displaystyle{x}{\left({0}\right)}={Z}{e}{r}{o}\ {m}\)

\(\displaystyle{x}{\left({4}\right)}={1.50}{\left({4}\right)}^{{{2}}}-{0.0500}{\left({4}\right)}^{{{3}}}={20.8}{m}\)

\(\displaystyle{v}_{{{x},{a}{v}{g}}}={\frac{{{20.8}-{0}}}{{{4}-{0}}}}\)

\(\displaystyle={5.2}\frac{{m}}{{s}}\)

Step 4

(c) \(\displaystyle{x}{\left({2}\right)}={1.50}{\left({2}\right)}^{{{2}}}-{0.0500}{\left({2}\right)}^{{{3}}}={5.6}{m}\)

\(\displaystyle{x}{\left({4}\right)}={1.50}{\left({4}\right)}^{{{2}}}-{0.0500}{\left({4}\right)}^{{{3}}}={20.8}{m}\)

\(\displaystyle{v}_{{{x},{a}{v}{g}}}={\frac{{{20.8}-{5.6}}}{{{4}-{2}}}}\)

\(\displaystyle={7.6}\frac{{m}}{{s}}\)