Question

Need help on c, d , and e. Thank you!

Answer 1

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:

`\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}`

s'(t) is the instantaneous velocity. Then, for t = 5.

`\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=(27.0m)/(s) \end{gathered}`

Hence, the intantaneous velocity is approximately 27m/s