Question

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) \(32\hat{j}-26\hat{k}\)

Answer 1

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

                        =\(32\hat{j}-26\hat{k}\)