Kinematics

JEE Main level, single correct, medium

59 of 308

Question 59 of 308

Starting from the origin at time t=0\text{t}=0, with initial velocity 5j⏜ms−15j^{⏜}{\text{ms}}^{-1}, a particle moves in the xx -yy plane with a constant acceleration of (10i⏜+4j⏜)ms−2\left(10i^{⏜}+4j^{⏜}\right){\text{ms}}^{-2}. At time t\text{t}, its coordinates are (20m, y0m)\left(20{\text{m, y}}_{0}\text{m}\right). The values of t\text{t} and y0{\text{y}}_{0} are, respectively:

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Answer: (A) 2s2\text{s} and 18m18\text{m}

Equation (1)\left(1\right)
Sx=12axt2{S}_{x}=\dfrac{1}{2}{a}_{x}{t}^{2}
20=12×10×t220=\dfrac{1}{2}\times 10\times {t}^{2}
t=2t=2
Equation (2)\left(2\right)
Sy=uyt+12ayt2{S}_{y}={u}_{y}t+\dfrac{1}{2}{a}_{y}{t}^{2}
y=5(2)+12(4)(2)2y=5\left(2\right)+\dfrac{1}{2}\left(4\right){\left(2\right)}^{2}
y=18y=18

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