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 Xp (t) = at + bt2 and XQ (t) = ft – t2. At what time, both the buses have same velocity?

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 ⇒ t ( 2 β + 2 ) = f − α  t = f − α 2 ( β + 1 )

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 Xp (t) = at + bt2 and XQ (t) = ft – t2. At what time, both the buses have same velocity?

Ask & Answer Question

Physics Motion in Straight Line Physics Class 11th Motion in a Straight Line

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 -

$\frac{α - f}{1 + β}$

Option 2 -

$\frac{α + f}{2 (β - f)}$

Option 3 -

$\frac{α + f}{2 (1 + β)}$

Option 4 -

^{$\frac{f - α}{2 (1 + β)}$}

2 Views | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

3 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)

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

$t = \frac{f - α}{2 (β + 1)}$ &

...more

$X_{P} (t) = α t + β t^{2}$

$V_{P} (t) = α + 2 β t$ -(i)

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

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

(i) = (ii)

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

$t = \frac{f - α}{2 (β + 1)}$

less

<math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>α</mi> <mi>t</mi> <mo>+</mo> <mi>β</mi> <msup> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math>    <math> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>α</mi> <mo>+</mo> <mn>2</mn> <mi>β</mi> <mi>t</mi> </mrow> </math>                            -(i) <math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>Q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mi>t</mi> <mo>−</mo> <msup> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math>                <math> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi>Q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mo>−</mo> <mn>2</mn> <mi>t</mi> </mrow> </math>                                 -(ii)                             (i) = (ii) <math> <mrow> <mi>α</mi> <mo>+</mo> <mn>2</mn> <mi>β</mi> <mi>t</mi> <mo>=</mo> <mi>f</mi> <mo>−</mo> <mn>2</mn> <mi>t</mi> <mo>⇒</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>β</mi> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mo>−</mo> <mi>α</mi> </mrow> </math>               <math> <mrow> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <mi>f</mi> <mo>−</mo> <mi>α</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mi>β</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math>

0 Upvotes 0 Downvotes

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?

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question