Solution 8.5a
From Mechanics
We assume the origin is att the point of tacke off which means \displaystyle \ \ \mathbf{ r}_{0}=0.
Also we have \displaystyle \mathbf{a}=\mathbf{i}+4\mathbf{j},\ \ \displaystyle \mathbf{u}=80\mathbf{i}\ \.
Using \displaystyle \mathbf{v}=\mathbf{u}+\mathbf{a}t\ \ gives at time \displaystyle t,
\displaystyle \mathbf{v}=80\mathbf{i}+(\mathbf{i}+4\mathbf{j})t\ \ or
\displaystyle \mathbf{v}=(80+t\ )\mathbf{i}+4t\ \mathbf{j}
Using \displaystyle \mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+{{\mathbf{r}}_{0}} gives at time \displaystyle t,
\displaystyle \mathbf{r}=80\mathbf{i}t+\frac{1}{2}(\mathbf{i}+4\mathbf{j}){t}^{\ 2}
\displaystyle \mathbf{r}=(80t+\frac{1}{2}{t}^{\ 2}\ )\mathbf{i}+2{t}^{\ 2}\ \mathbf{j}