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QJEEM23Ph1797: JEE Main 2023 Physics - Class 11 JEEM23Ph1797 Solution: An object moves with speed and along a line segment AB, BC and…

An object moves with speed v1,v2v_1,v_2 and v3v_3 along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

JEE Main 2023 (Online) 1st February Morning Shift Physics - Motion in a Straight Line Question 37 English

Multiple Choice Options

  • A v1v2v33(v1v2+v2v3+v3v1){{{v_1}{v_2}{v_3}} \over {3({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}
  • B (v1+v2+v3)3{{({v_1} + {v_2} + {v_3})} \over 3}
  • C (v1+v2+v3)3v1v2v3{{({v_1} + {v_2} + {v_3})} \over {3{v_1}{v_2}{v_3}}}
  • D 3v1v2v3(v1v2+v2v3+v3v1){{3{v_1}{v_2}{v_3}} \over {({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}

Step-by-Step Verified Solution

AB=BC=CDA B=B C=C D

⇒ Average speed amp;= Distance  Time amp;=ADABV1+ABV2+ABV3amp;=3V1V2V3V1V2+V2V3+V1V3\begin{aligned}\Rightarrow \text { Average speed } & =\frac{\text { Distance }}{\text { Time }} \\\\& =\frac{A D}{\frac{A B}{V_{1}}+\frac{A B}{V_{2}}+\frac{A B}{V_{3}}} \\\\& =\frac{3 V_{1} V_{2} V_{3}}{V_{1} V_{2}+V_{2} V_{3}+V_{1} V_{3}}\end{aligned}

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