Question

The position vector of a moving particle at time t is $r=3i+4t^{2}j-t^{3}k$  .. 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) $32\hat{j}-26\hat{k}$

Answer 1

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

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

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

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

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

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