c) Consider that the average velocity is determine by the slope of the curve. You can notice that the slope of the curve is greater in magnitude for times in between 0 and 4 seconds.
d) Calculate the first derivative of the given function, as follow:
[tex]\begin{gathered} s(t)=100\cos (0.75t)e^{-0.2t}+100 \\ s^{\prime}(t)=100\lbrack-0.75\sin (0.75t)\cdot e^{-0.2t}+\cos (0.75t)(-0.2)e^{-0.2t}\rbrack \end{gathered}[/tex]
s'(t) is the instantaneous velocity. Then, for t = 5.
[tex]\begin{gathered} s^{\prime}(5)=100\lbrack0.75\sin (0.75(5))\cdot e^{-0.2(5)}+\cos (0.75(5))(-0.2)e^{-0.2(5)}\rbrack \\ s=100\lbrack0.21+0.06\rbrack=\frac{27.0m}{s} \end{gathered}[/tex]
Hence, the intantaneous velocity is approximately 27m/s
