Solution 8.3

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(New page: In this case we have <math>\mathbf{u}=0</math> , <math>\mathbf{a}=2\mathbf{i}+3\mathbf{j}</math> and <math>{{\mathbf{r}}_{0}}=0</math>. Substituting these into the equation <math>\math...)
Current revision (15:25, 13 April 2010) (edit) (undo)
 
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Substituting these into the equation
Substituting these into the equation
<math>\mathbf{v}=\mathbf{u}+\mathbf{a}t \ \</math>
<math>\mathbf{v}=\mathbf{u}+\mathbf{a}t \ \</math>
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gives the velocity of the ball at time <math>t=4 \text{ s }</math> as:
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gives the velocity of the body at time <math>t=4 \text{ s }</math> as:
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<math>\mathbf{v}=8\mathbf{i}+12\mathbf{j} \ \text{ m}{{\text{s}}^{\text{-1}}}</math>
<math>\mathbf{v}=8\mathbf{i}+12\mathbf{j} \ \text{ m}{{\text{s}}^{\text{-1}}}</math>
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 +
Then substituting the above into the equation
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<math>\mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+{{\mathbf{r}}_{0}}</math>
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gives the position vector of the body at time <math>t=4 \text{ s }</math> as:
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 +
<math>\begin{align}
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& \mathbf{r}=0\times 4+\frac{1}{2}(2\mathbf{i}+3\mathbf{j})\times {{4}^{\ 2}}+0 \\
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& =16\mathbf{i}+24\mathbf{j} \ \text{m}
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\end{align}</math>

Current revision

In this case we have \displaystyle \mathbf{u}=0 , \displaystyle \mathbf{a}=2\mathbf{i}+3\mathbf{j} and \displaystyle {{\mathbf{r}}_{0}}=0.

Substituting these into the equation \displaystyle \mathbf{v}=\mathbf{u}+\mathbf{a}t \ \ gives the velocity of the body at time \displaystyle t=4 \text{ s } as:


\displaystyle \mathbf{v}=0+(2\mathbf{i}+3\mathbf{j})\times 4

which gives

\displaystyle \mathbf{v}=8\mathbf{i}+12\mathbf{j} \ \text{ m}{{\text{s}}^{\text{-1}}}

Then substituting the above into the equation \displaystyle \mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+{{\mathbf{r}}_{0}} gives the position vector of the body at time \displaystyle t=4 \text{ s } as:

\displaystyle \begin{align} & \mathbf{r}=0\times 4+\frac{1}{2}(2\mathbf{i}+3\mathbf{j})\times {{4}^{\ 2}}+0 \\ & =16\mathbf{i}+24\mathbf{j} \ \text{m} \end{align}

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