The position vector of a moving particle at ‘t’ sec is given by $\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}$ . Its displacement during an interval of t = 1s to 3 sec is

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9 \hat{i} + 36 \hat{j} - 27 \hat{k}

\hat{j} - \hat{k}

32 \hat{j} - 26 \hat{k}

3 i + 4 \hat{j} - \hat{k}

answer is D.

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Detailed Solution

\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}

$t = 1 s to 3 s$

$\vec{S_{1}} = 3 \hat{i} + 4 \hat{j} - \hat{k}$

$\vec{S_{2}} = 3 \hat{i} + 36 \hat{j} - 27 \hat{k}$

$S_{2} - S_{1} = 3 \hat{i} + 36 \hat{j} - 27 \hat{k} - 3 \hat{i} + 4 \hat{j} - \hat{k}$

$= 32 \hat{j} - 26 \hat{k}$

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