A particle is moving along the <math> <mi>x</mi> </math> <math></math> -axis with its coordinate with time ' <math> <mi>t</mi> </math> <math></math> ' given by <math> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <mn>10</mn> <mo>+</mo> <mn>8</mn> <mi>t</mi> <mo>-</mo> <mn>3</mn> <msup> <mrow> <mrow> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> . Another particle is moving along the <math></math> <math> <mi>y</mi> </math> -axis with its coordinate a function of time given by <math> <mi>y</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <mn>5</mn> <mo>-</mo> <mn>8</mn> <msup> <mrow> <mrow> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> . At <math> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">s</mi> </math> <math><mtext></mtext></math> , the speed of the second particle as measured in the frame of the first particle is given as <math> <mroot> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow></mrow> </mroot> </math> <math><mroot><mrow><mrow></mrow></mrow></mroot></math> . Then <math> <mi>v</mi> </math> <math></math> (in <math></math> ) <math> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </math> is

580 X 1 = - 3 t 2 + 8 t + 10 v ? 1 = ( - 6 t + 8 ) i ˆ = 2 i ˆ Y 2 = 5 - 8 t 3 v ? 2 = - 24 t 2 j ˆ v = v ? 2 - v ? 1 = | - 24 j ˆ - 2 i ˆ | v = 24 2 + 2 2 v = 580

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Physics NCERT Exemplar Solutions Class 12th Chapter Fifteen Physics Class 11th Physics Motion in Plane

A particle is moving along the $x$ -axis with its coordinate with time ' $t$ ' given by $x (t) = 10 + 8 t - 3 t^{2}$ $^{}$ . Another particle is moving along the $y$ -axis with its coordinate a function of time given by $y (t) = 5 - 8 t^{3}$ $^{}$ . At $t = 1 s$ , the speed of the second particle as measured in the frame of the first particle is given as $\sqrt[]{v}$ . Then $v$ (in ) $m / s$ is

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Raj Pandey | Contributor-Level 9

a month ago

$580$

$X_{1} = - 3 t^{2} + 8 t + 10$

${\overset{?}{v}}_{1} = (- 6 t + 8) \hat{i} = 2 \hat{i}$

$Y_{2} = 5 - 8 t^{3}$

${\overset{?}{v}}_{2} = - 24 t^{2} \hat{j}$

$\sqrt[]{v} = |{\overset{?}{v}}_{2} - {\overset{?}{v}}_{1}| = | - 24 \hat{j} - 2 \hat{i} |$

$\sqrt[]{v} = \sqrt[]{24^{2} + 2^{2}}$

$v = 580$

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