If a particle starting from rest having constant acceleration covers distance S1 in first (p – 1) seconds and S2 in first p seconds, then determine time for which displacement is S1 + S2

S1 = 1 2 <!- [if gte mso 9]><xml> </xml><! [endif]->a (p – 1)2S2 = 1 2 <!- [if gte mso 9]><xml> </xml><! [endif]->ap2S1 + S2 = 1 2 <!- [if gte mso 9]><xml> </xml><! [endif]->a [ (p – 1)2 + p2] = 1 2 <!- [if gte mso 9]><xml> </xml><! [endif]->at2 t = 2 p 2 + 1 − 2 p <!- [if gte mso 9]><xml> </xml><! [endif]->

If a particle starting from rest having constant acceleration covers distance S1 in first&nbsp;(p – 1) seconds and S2 in first p seconds, then determine time for which displacement is S1 + S2

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Physics Class 11th Physics Motion in Straight Line

If a particle starting from rest having constant acceleration covers distance S₁ in first (p – 1) seconds and S₂ in first p seconds, then determine time for which displacement is S₁ + S₂

Option 1 -

$\sqrt[]{2 p^{2} + 1 - 2 p}$

Option 2 -

$\sqrt[]{2 p^{2} + 1 + 2 p}$

Option 3 -

$\sqrt[]{{(p + 1)}^{2} - p}$

Option 4 -

2 Views | Posted a month ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

S₁ = $\frac{1}{2}$ a (p – 1)²

S₂ = $\frac{1}{2}$ ap²

S₁ + S₂ = $\frac{1}{2}$ a [ (p – 1)² + p²] = $\frac{1}{2}$ at²

$t = \sqrt[]{2 p^{2} + 1 - 2 p}$

S1 = <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820655146"> </o:OLEObject></xml><! [endif]->a (p – 1)2S2 = <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820655147"> </o:OLEObject></xml><! [endif]->ap2S1 + S2 = <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1820655148"> </o:OLEObject></xml><! [endif]->a [ (p – 1)2 + p2] = <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1820655149"> </o:OLEObject></xml><! [endif]->at2 <math> <mrow> <mi>t</mi> <mo>=</mo> <mroot> <mrow> <mn>2</mn> <msup> <mrow> <mi>p</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo>−</mo> <mn>2</mn> <mi>p</mi> </mrow> <mrow></mrow> </mroot> </mrow> </math>             <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1820655150"> </o:OLEObject></xml><! [endif]->

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If a particle starting from rest having constant acceleration covers distance S₁ in first (p – 1) seconds and S₂ in first p seconds, then determine time for which displacement is S₁ + S₂

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