Starting from the origin at time <math><mi>t</mi><mo>=</mo><mn>0</mn></math> , with initial velocity <math><mn>5</mn><mover accent="true"><mrow><mrow><mi>j</mi></mrow></mrow><mi>&circ;</mi></mover><msup><mrow><mrow><mtext></mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">s</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>1</mn></mrow></mrow></msup></math> , a particle moves in the <math><mi>x </mi></math><math><mo>-</mo><mi>y</mi></math> plane with a constant acceleration of <math><mo>(</mo><mn>10</mn><mover accent="true"><mrow><mrow><mi>i</mi></mrow></mrow><mi>&circ;</mi></mover><mo>+</mo><mn>4</mn><mover accent="true"><mrow><mrow><mi>j</mi></mrow></mrow><mi>&circ;</mi></mover><mo>)</mo><msup><mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">s</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup></math> . At time <math><mi>t</mi></math> , its coordinates are <math><mo>(</mo><mn>20</mn></math> <math><mfenced open="" separators="|"><mrow><mrow><mi>m</mi><mo>,</mo><msub><mrow><mrow><mi>y</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><mi>m</mi></mrow></mrow></mfenced></math> . The values of <math><mi>t</mi></math> and <math><msub><mrow><mrow><mi>y</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math> are, respectively:

U? =5jˆa? =10iˆ+4jˆ⇒S? =U? t+12 (a? )t2⇒20iˆ+y0jˆ=5t2iˆ+5t+2t2jˆ20=5t2y0=5t+2t2t=2⇒18m.

Starting from the origin at time&nbsp;<math><mi>t</mi><mo>=</mo><mn>0</mn></math>&nbsp;, with initial velocity&nbsp;<math><mn>5</mn><mover accent="true"><mrow><mrow><mi>j</mi></mrow></mrow><mi>&circ;</mi></mover><msup><mrow><mrow><mtext></mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">s</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>1</mn></mrow></mrow></msup></math>&nbsp;, a particle moves in the&nbsp;<math><mi>x </mi></math><math><mo>-</mo><mi>y</mi></math>&nbsp;plane with a constant acceleration of&nbsp;<math><mo>(</mo><mn>10</mn><mover accent="true"><mrow><mrow><mi>i</mi></mrow></mrow><mi>&circ;</mi></mover><mo>+</mo><mn>4</mn><mover accent="true"><mrow><mrow><mi>j</mi></mrow></mrow><mi>&circ;</mi></mover><mo>)</mo><msup><mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">s</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup></math>&nbsp;. At time&nbsp;<math><mi>t</mi></math>&nbsp;, its coordinates are&nbsp;<math><mo>(</mo><mn>20</mn></math>&nbsp;<math><mfenced open="" separators="|"><mrow><mrow><mi>m</mi><mo>,</mo><msub><mrow><mrow><mi>y</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><mi>m</mi></mrow></mrow></mfenced></math>&nbsp;. The values of&nbsp;<math><mi>t</mi></math>&nbsp;and&nbsp;<math><msub><mrow><mrow><mi>y</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math>&nbsp;are, respectively:

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Physics Class 12th Motion in a Plane Physics NCERT Exemplar Solutions Class 12th Chapter Four

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

Option 1 -

$2 s$ and $24 m$

Option 2 -

$4 s$ and $52 m$

Option 3 -

$5 s$ and $25 m$

Option 4 -

$2 s$ and $18 m$

4 Views | Posted 2 months ago

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

$\overset{?}{U} = 5 \hat{j}$

$\overset{?}{a} = 10 \hat{i} + 4 \hat{j}$

$\Rightarrow \overset{?}{S} = \overset{?}{U} t + \frac{1}{2} (\overset{?}{a}) t^{2}$

$\Rightarrow 20 \hat{i} + y_{0} \hat{j} = (5 t^{2}) \hat{i} + (5 t + 2 t^{2}) \hat{j}$

$\begin{array}{r} 20 = 5 t^{2} y_{0} = 5 t + 2 t^{2} \\ t = 2 \Rightarrow 18 m . \end{array}$

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Starting from the origin at time t=0 , with initial velocity 5jˆms-1 , a particle moves in the x -y plane with a constant acceleration of (10iˆ+4jˆ)ms-2 . At time t , its coordinates are (20 m,y0m . The values of t and y0 are, respectively:

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