Variables of Motion in Two Dimensions questions | Variables of Motion in Two Dimensions jee questions

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Topic Question Set

Q 1 :
The co-ordinates of a particle moving in $x - y$ plane is given by $x = 2 + 4 t, y = 3 t + 8 t^{2}$

The motion of the particle is [2024]

uniform motion along a straight line
uniformly accelerated having motion along a parabolic path
non-uniformly accelerated
uniformly accelerated having motion along a straight line

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(B) Given, $x = 2 + 4 t$ and $y = 3 t + 8 t^{2}$

$v_{x} = \frac{d x}{d t} = 4 =$ constant, hence $a_{x} = 0$

and $v_{y} = 3 + 16 t$ also, $\frac{d v_{y}}{d t} = a_{y} = 16$

the motion will be uniformly accelerated motion.

Also, $t = \frac{x - 2}{4}$

$∴ y = 3 (\frac{x - 2}{4}) + 8 {(\frac{x - 2}{4})}^{2}$

This is a quadratic equation so path will be parabola, parabolic path.

Q 2 :
Position of an ant (S in metres) moving in Y-Z plane is given by $S = 2 t^{2} \hat{j} + 5 \hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t = 1$ s will be [2024]

16 m/s in $y$ -direction
4 m/s in $x$ -direction
9 m/s in $z$ -direction
4 m/s in $y$ -direction

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(D)

Q 3 :
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 $\sqrt{α} m / s .$ The value of $α$ is ____________ . [2024]

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(673) Given, $u_{x} = 5$ $m / s, a_{x} = 3$ $m / s^{2}$ and $x = 84$ $m$

$Using, v_{x}^{2} - u_{x}^{2} = 2 a x$

$v_{x}^{2} - 25 = 2 (3) (84) \Rightarrow v_{x} = 23 m / s$

$v_{x} - u_{x} = a_{x} t \Rightarrow t = \frac{23 - 5}{3} = 6 s$

$v_{y} = 0 + a_{y} t = 0 + 2 \times (6) = 12 m / s$

$v^{2} = v_{x}^{2} + v_{y}^{2} = 23^{2} + 12^{2} = 673$

$\Rightarrow v = \sqrt{673} m / s$

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