Motion In One Dimension Question 4
Question 4 - 2024 (27 Jan Shift 1)
A particle starts from origin at $t=0$ with a velocity $5 \hat{i} m / s$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3 \hat{i}+2 \hat{j}) m / s^{2}$. If the $x$-coordinate of the particle at that instant is $84 m$, then the speed of the particle at this time is $\sqrt{\alpha} m / s$. The value of $\alpha$ is
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Answer: (673)
Solution:
$u _x=5 m / s \quad a _x=3 m / s^{2} h x=84 m$
$v _x^{2}-u _x^{2}=2 ax$
$v _x^{2}-25=2(3)(84)$
$V _x=23 m / s$
$v _x-u _x=a _x t$
$t=\frac{23-5}{3}=6 s$
$v _y=0+a _y t=0+2 \times(6)=12 m / s$
$v^{2}=v _x^{2}+v _y^{2}=23^{2}+12^{2}=673$
$v=\sqrt{673} m / s$
