# The position vector of a moving particle at time t is r=3i+4t^2j-t^3k .. Its displacement during the time interval t=1 s to t=3 s is

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The position vector of a moving particle at time t is $$r=3i+4t^2j-t^3k$$  .. Its displacement during the time interval t=1 s to t=3 s is

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

b) $$3\hat{i}+4\hat{j}-\hat{k}$$

c) $$9\hat{i}+36\hat{j}-27\hat{k}$$

d) $$32\hat{j}-26\hat{k}$$

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Correct answer is $$32\hat{j}-26\hat{k}$$

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

$$\vec{r}_{t=1s}=3\hat{i}+4\hat{j}-\hat{k}$$

$$\vec{r}_{t=3s}=3\hat{i}+36\hat{j}-27\hat{k}$$

Displacement = $$(\vec{r}_{t=3s})-(\vec{r}_{t=1s})$$

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