The position vector of a moving particle at ‘t’ sec is given by r→=3i^+4t2j^−t3k^. Its displacement during an interval of t = 1s to 3 sec is

t=1s⇒r¯1=3i^+4j^−k^t=3s⇒r¯2=3i^+36j^−27k^s¯=r¯2−r¯1=32j^−26k^

The position vector of a moving particle at ‘t’ sec is given by r→=3i^+4t2j^−t3k^. Its displacement during an interval of t = 1s to 3 sec is

t=1s⇒r¯1=3i^+4j^−k^t=3s⇒r¯2=3i^+36j^−27k^s¯=r¯2−r¯1=32j^−26k^

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

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

$\hat{j} - \hat{k}$

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

answer is D.

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$\begin{array}{l} t = 1 s \Rightarrow {\bar{r}}_{1} = 3 \hat{i} + 4 \hat{j} - \hat{k} \\ t = 3 s \Rightarrow {\bar{r}}_{2} = 3 \hat{i} + 36 \hat{j} - 27 \hat{k} \\ \bar{s} = {\bar{r}}_{2} - {\bar{r}}_{1} = 32 \hat{j} - 26 \hat{k} \end{array}$

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The position vector of a moving particle at ‘t’ sec is given by r→=3i^+4t2j^−t3k^. Its displacement during an interval of t = 1s to 3 sec is

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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