Class 11th Physics Motion in Straight Line Physics

Two buses P AN Q start form a point at the same time and move in a straight line and their positions are represented by X_p (t) = at + bt² and X_Q (t) = ft – t². At what time, both the buses have same velocity?

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>α</mi> <mo>−</mo> <mi>f</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>β</mi> </mrow> </mfrac> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>f</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mi>β</mi> <mo>−</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>f</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>β</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>f</mi> <mo>−</mo> <mi>α</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>β</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math> </span></p>

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Answered by

Raj Pandey | Contributor-Level 9

6 months ago

Correct Option - 4

Detailed Solution:

$X_{P} (t) = α t + β t^{2}$

$V_{P} (t) = α + 2 β t$ - (i)

$X_{Q} (t) = f t - t^{2}$

$V_{Q} (t) = f - 2 t$ - (ii)
(i) = (ii)

$α + 2 β t = f - 2 t \Rightarrow t (2 β + 2) = f - α$

$t = \frac{f - α}{2 (β + 1)}$

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