Starting from the origin at time $t = 0$ , with initial velocity $5^j {ms}^{- 1},$ a particle moves in the $x y -$ plane with a constant acceleration of $10^i + 4^j {ms}^{- 2} .$ At time $t$ , its coordinates are $20 m, y_{0} m .$ The values of $t$ and $y_{0}$ are, respectively-

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Solution

Given, $u = 5^j {ms}^{- 1}$
Acceleration, $a = 10^i + 4^j {ms}^{- 1}$ and
Final position coordinates are $(20 m, y_{0} m)$ at time $t$

$S_{x} = u_{x} t + \frac{1}{2} a_{x} t^{2} [∵ u_{x} = 0]$
$\Rightarrow 20 = 0 + \frac{1}{2} \times 10 \times t^{2}$
$\Rightarrow t = 2 s$
$S_{y} = u_{y} t + \frac{1}{2} a_{y} t^{2}$
$y_{0} = 5 \times 2 + \frac{1}{2} \times 4 \times 2^{2} = 18 m$

 Hence, $(A)$ is the correct answer.

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Starting from the origin at time $t = 0$ , with an initial velocity $5 \hat{j} m / s$ , a particle moves in the $xy$ plane with a constant acceleration of $(10 \hat{i} + 4 \hat{j}) m / s^{2}$ .At time t, its coordinates are $(20, y_{\circ})$ .The values of $t$ and $y_{\circ}$ are, respectively: