Question

A particle moves from the point $(2.0 \hat{i} + 4.0 \hat{j}) m, $ at $t = 0$, with an initial velocity $(5.0 \hat{i} + 4.0 \hat{j}) ms^{-1}$ . It is acted upon by a constant force which produces a constant acceleration $(4.0 \hat{i} + 4.0 \hat{j}) ms^{-2}$. What is the distance of the particle from the origin at time $2 \,s$ ?

• A. $20 \sqrt{2} m$
• B. $10 \sqrt{2} m$
• C. $5\, m$
• D. $15\, m$

Answer 1

Answer: (A)

$\vec{S} = \left(5\hat{i} +4\hat{j}\right)2+ \frac{1}{2} \left(4\hat{i} +4\hat{j}\right)4 $
$ = 10\hat{i} + 8\hat{j} +8\hat{i} + 8\hat{j}$
$ \vec{r}_{f} - \vec{r}_{i} = 18\hat{i}+16\hat{j} $
$ \vec{r}_{f} = 20\hat{i} + 20\hat{j} $
$ \left|\vec{r}_{f}\right| = 20 \sqrt{2} $