Question

A particle of mass $2\text{kg}$ moves with an initial velocity of $(4\hat{i}+2\hat{j}){\text{ms}}^{-1}$ on the x - y plane. A force $\overrightarrow{F}=(2\hat{i}-8\hat{j})\text{N}$ acts on the particle. The initial position of the particle is $(2,3)\text{m}$. Then when particle reaches $y=3\text{m},$

• A. Possible value of $x$ is only $x=2\text{m}$
• B. Possible value of $x$ is not only $x=2\text{m}$, but there exists some other value of $x$ also
• C. Time taken is $2\text{s}$
• D. All of the above

Answer 1

The correct option is B Possible value of $x$ is not only $x=2\text{m}$, but there exists some other value of $x$ also

$\overrightarrow{u}=4\hat{i}+2\hat{j}\overrightarrow{a}=\frac{\overrightarrow{F}}{m}=\hat{i}-4\hat{j}$
Let at any time, the coordinates be $(x,y)$
$x-2=u_{x}t+\frac{1}{2}{a}_x{t}^2$
$\Rightarrow x-2=4t+\frac{1}{2}{t}^{2}y-3=2t-\frac{1}{2}4t^2$
$\Rightarrow y-3=2t-2t^2$
When $y=3\text{m},t=0\text{s}\text{and}1\text{s}$;
When $t=0,x=2\text{m}$
When $t=1\text{s},x=6.5\text{m}$