The force on a body of mass 1 kg is~(20 ^ i + 10 ^ j )N . If it...

F = 20\overset{^}{i} + 10\overset{^}{j}

$∴ {F}_{x} = 20N$ and ${F}_{y} = 10N$

$∴$ Acceleration,

${a}_{x} = \dfrac{Fx}{m} = \dfrac{20}{1}$
${a}_{x} = 20ms^{- 2}$

and ${a}_{y} = \dfrac{Fy}{m} = \dfrac{10}{1} = 10ms^{- 2}$

$∴$ Displacement of body in $x$ -direction in $2s$.

$x = {u}_{x}t + \dfrac{1}{2}{a}_{x}t^{2}$

$= 0 + \dfrac{1}{2} \times 20 \times {2}^{2}$
$= 40m$

Displacement of body in $y$-direction in $2s$.

$y = {u}_{y}t + \dfrac{1}{2}{a}_{y}t^{2}$

$= 0 + \dfrac{1}{2} \times 10 \times {2}^{2}$

$= 20m$

$∴$ Position of the body at $t = 2s$

r = x\overset{^}{i} + y\overset{^}{j}
r = 40\overset{^}{i} + 20\overset{^}{j}