Starting from the origin at time $t = 0$ , with initial velocity $5^j {ms}^{- 1}$ , the particle moves in the $x - y$ plane with a constant acceleration of $(10^i + 4^j) {m/s}^{2}$ . 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: $\to u = 5^j m/s$
Acceleration, $\to a = 10^i + 4^j$ and final coordinates $(20, y_{0})$ in time $t$ .

Using equation of motion along $x-axis$ ,

$x = u_{x} t + \frac{1}{2} a_{x} t^{2}$

$[∵ u_{x} = 0]$
$\Rightarrow 20 = 0 + \frac{1}{2} \times 10 \times t^{2}$

$\Rightarrow t = 2 s$

Using equation of motion along $y-axis$ ,

$y = u_{y} \times t + \frac{1}{2} a_{y} t^{2}$

$y = y_{0} = 5 \times 2 + \frac{1}{2} \times 4 \times 2^{2} = 18 m$

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

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