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

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$2 s and 18 m$

$4 s and 52 m$

$2 s and 24 m$

$5 s and 25 m$

answer is A.

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Detailed Solution

Given : $\vec{u} = 5 \overset{Λ}{j} m / s$
Acceleration, $\vec{a} = 10 \overset{Λ}{i} + 4 \overset{Λ}{j}$ and final coordinate $(20, y_{0})$ in time t.
$S_{x} = u_{x} t + \frac{1}{2} a_{x} t^{2} \Rightarrow 20 = 0 + \frac{1}{2} \times 10 \times t^{2} \Rightarrow t = 2 s S_{y} = u_{y} \times t + \frac{1}{2} a_{y} t^{2} y_{0} = 5 \times 2 + \frac{1}{2} \times 4 \times 2^{2} = 18 m$