Acceleration on a Road
- Page ID
- 91934
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Finding the Components of Acceleration of a Truck on a Road
A self driving truck will be driving on a remote dirt road and it's possible position functions have already been determined and validated in several tests. Your job will be to validate the code that will determine the components of acceleration once it is written. You will be given the position function below and you must determine \(a_{\vecs T}\) and \(a_{\vecs N}\) at the given value of \(t\) rounded to four decimal places.
\(\vecs{r}(t)=(t+1)\hat{i}+(1-t^2)\hat{j}+e^{-t}\hat{k}\) at \(t=1\)
\(\vecs{r}(t)=\cos(t)\hat{i}+\sin(t)\hat{j}+\sqrt{t}\hat{k}\) at \(t=4\)
\(\vecs{r}(t)=(2t-1)\hat{i}+\cos(t)\hat{j}+\sin(2t)\hat{k}\) at \(t=2\)
\(\vecs{r}(t)=\frac{1}{t+1}\hat{i}+\frac{1}{t+1}\hat{j}+\frac{1}{t+3}\hat{k}\) at \(t=1\)
\(\vecs{r}(t)=\sin(t)\hat{i}+\sin(2t)\hat{j}+\sin(3t)\hat{k}\) at \(t=2\)
\(\vecs{r}(t)=\frac{1}{t+1}\hat{i}+\frac{1}{(t+1)^2}\hat{j}+\frac{1}{(t+1)^3}\hat{k}\) at \(t=1\)
\(\vecs{r}(t)=e^{-t}\hat{i}+e^{-2t}\hat{j}+e^{-3t}\hat{k}\) at \(t=0.5\)
\(\vecs{r}(t)=(t+\sin(t))\hat{i}+t^2\hat{j}+e^t\hat{k}\) at \(t=0.8\)
\(\vecs{r}(t)=(t+\frac{1}{t+2})\hat{i}+(t^2-t-1)\hat{j}+(t^3-3t^2)\hat{k}\) at \(t=3\)
\(\vecs{r}(t)=e^{-t}\hat{i}+\cos(2t)\hat{j}+\ln(t+1)\hat{k}\) at \(t=2\)
\(a_{\vecs T}(t)\) = \(a_{\vecs N}(t)\) =
Click on the Start button to begin.