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Starting from the origin at time $t=0,$ with initial velocity $5 \hat{ j }\, ms ^{-1},$ a particle moves in the $x-y$ plane with a constant acceleration of $(10 \hat{ i }+4 \hat{ j })\, ms ^{-2}$. At time $t$, its coordinates are $\left(20\, m , y _{0}\, m \right) .$ The values of $t$ and $y _{0},$ are respectively
$4\, s$ and $52\, m$
$2\, s$ and $24\, m$
$2\,s$ and $18\, m$
$5\, s$ and $25\, m$
Solution
Given $\quad \overrightarrow{ u }=5 \hat{ j } m / s , \overrightarrow{ a }=10 \hat{ i }+4 \hat{ j }, \quad$ final coordinate $\left(20, y_{0}\right)$ in time $t$
$S_{x}=4 u_x \times {t}+\frac{1}{2} a_{x} t^{2}$
$\frac{1}{2} \times 10 \times t^{2}$
$t=2 \sec$
$S_{y}=u_{y} \times t+\frac{1}{2} a_{y} t^{2}$
$y_{0}=5 \times 2+\frac{1}{2} 4 \times 2^{2}=18 m$
$2 \sec$ and $18\, m$
