Question

Find the velocity of the object as a function of t.

s(t) = tcos(pi-4t)    I have no idea where to start with this, I know it uses the product rule and the chain rule I having trying to figure this out for a while, basically where to start.

Answer 1

`\bf s(t)=tcos(\pi -4t)\\\\ -----------------------------\\\\ \cfrac{ds}{dt}[tcos(\pi -4t)] \\\\\\ \begin{array}{llll} \left[ 1\cdot cos(\pi -4t) \right]\quad +\quad &\left[t\cdot \underline{[-sin(\pi -4t)]\cdot (0-4)} \right]\\ &\qquad \qquad \uparrow \\ &\textit{the chain-rule applies}\\ &\textit{when taking the derivative}\\ &\textit{to the second term}\\ &\textit{in the product rule} \end{array} \\\\\\ \left[ cos(\pi -4t) \right]+\left[ 4tsin(\pi -4t) \right]\impliedby s'(t)\iff velocity`