1.
A particle moves in a straight line with the velocity
\begin{equation*}
v(t) = \cos(t) \qquad \text {in m/s}
\end{equation*}
Find the displacement and the total distance traveled over the time interval \([0,3\pi]\text{.}\)
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Worksheet Some Exercises for this section
I included some practice problems that cover some main concepts in this section. You don’t need to turn it in, but I highly encourage you to work on this with your classmates. I may take problems here to be your in-class practice problems, homework problems, and/or exam problems. Reach out to Richard for help if you get stuck or have any questions.
I will only include the final answer to some of the problems for you to check your result. If you want to check your work, talk to Richard and he is happy to discuss the process with you.
2.
Find the net change in velocity over \([1,4]\) of an object with \(a(t) = 8t - t^2\,\, \text{m/s}^2\)
3.
Show that a particle, located at the origin at \(t = 1\) and moving along the \(x\)-axis with velocity \(v(t) = t^{-2}\) will never pass the point \(x = 2\text{.}\)
4.
A population of insects increases at a rate of \(200 + 10t + 0.25t^2\) insects per day. Find the insect population after \(3\) days, assuming that there are \(35\) insects at \(t = 0\text{.}\)
