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

A particle of mass $m$ is at rest at the origin at time $t=0.$ It is subjected to a force $F\left(t\right)=F_0{e}^{-bt}$ in the $x$ direction. Its speed $v\left(t\right)$ is depicted by which of the following curves?

Hint $:$ Acceleration $\mathrm{=}\frac{\text{ Force} }{\text{ Mass }}$

A particle starts from origin at time $t=0$ and moves along the positive $x-$axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t=5 \mathrm{s}$?