Q. A particle starts from origin at t = 0 with constant velocity $ \displaystyle 5\hat{i} $ m/s and moves in xy plane under action of a force which produces a constant acceleration of $\displaystyle (3 \hat{i} + 2\hat{j} )$ ms^{-2} . The y – coordinate of the particle at the instant its x co-ordinate is 84 m in m is

(a) 6

(b) 36

(c) 18

(d) 9

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Sol:By applying $ \displaystyle S = u t + \frac{1}{2}a t^2$

here , a_{x} = 3 ms^{-2}

a_{y} = 2 ms^{-2}

$ \displaystyle x = 5 t + \frac{1}{2}3 t^2$

$ \displaystyle 84 = 5 t + \frac{1}{2}3 t^2$

$ \displaystyle 3t^2 + 10t = 168 $

$ \displaystyle 3t^2 + 10t – 168 = 0 $

$ \displaystyle 3t^2 – 18t + 28 t – 168 = 0 $

Hence , t = 6 sec

$\displaystyle y = 0 + \frac{1}{2}2 t^2$

y = 36 m