A person travelling in a straight line moves with a constant velocity v1 for certain distance 'x' and with a constant velocity v2 for next equal distance. The average velocity v is given by the relation

Question

A person travelling in a straight line moves with a constant velocity v1 for certain distance 'x' and with a constant velocity v2 for next equal distance. The average velocity v is given by the relation (A) (1/v)=(1/v1)+(1/v2) (B) (2/v)=(1/v1)+(1/v2) (C) (v/2)=(v1+v2/2) (D) v=√v1v2

Tardigrade Admin · Accepted Answer

Average velocity = ( textTotal distance/ textTotal time) = (X + X/ (X)V1 + (X)V2 ⇒ v = (2/(1)v1 + (1)v2 ⇒ (2/v) = (1/v1) + (1/v2)

Q. A person travelling in a straight line moves with a constant velocity v1 for certain distance 'x' and with a constant velocity $v_{2}$ for next equal distance. The average velocity v is given by the relation

$\frac{1}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$

$\frac{2}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$

$\frac{v}{2} = \frac{v _{1} + v _{2}}{2}$

$v = v_{1} v_{2}$

Average velocity $= \frac{Total distance}{Total time}$
$= \frac{X + X}{\frac{X}{V _{1}} + \frac{X}{V _{2}}}$
$\Rightarrow v = \frac{2}{\frac{1}{v _{1}} + \frac{1}{v _{2}}}$
$\Rightarrow \frac{2}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$

Q. A person travelling in a straight line moves with a constant velocity v1 for certain distance 'x' and with a constant velocity v2​ for next equal distance. The average velocity v is given by the relation

v1​=v1​1​+v2​1​

v2​=v1​1​+v2​1​

2v​=2v1​+v2​​

v=v1​v2​​