A person travels along a straight road for the first (t/3) time with a speed v1 and for next (2 t/3) time with a speed v2. Then the mean speed v is given by

Question

A person travels along a straight road for the first (t/3) time with a speed v1 and for next (2 t/3) time with a speed v2. Then the mean speed v is given by (A) v=(v1+2 v2/3) (B) (1/v)=(1/3 v1)+(2/3 v2) (C) v=(1/3) √2 v1 v2 (D) v=√(3 v2/2 v1)

Tardigrade Admin · Accepted Answer

v av =( text Distance / text Time)=( text Speed × text Time / text Time ) =(v1 × (t/3)+v2 × (2 t/3)/(t)3+(2 t)3 ⇒ v/ av )=((v1/3)+(2 v2/3)/1)=(v1+2 v2/3) ⇒ v av =(v1+2 v2/3)

Q. A person travels along a straight road for the first $\frac{t}{3}$ time with a speed $v_{1}$ and for next $\frac{2 t}{3}$ time with a speed $v_{2}$ . Then the mean speed $v$ is given by

$v = \frac{v _{1} + 2 v _{2}}{3}$

$\frac{1}{v} = \frac{1}{3 v _{1}} + \frac{2}{3 v _{2}}$

$v = \frac{1}{3} 2 v_{1} v_{2}$

$v = \frac{3 v _{2}}{2 v _{1}}$

Q. A person travels along a straight road for the first 3t​ time with a speed v1​ and for next 32t​ time with a speed v2​. Then the mean speed v is given by

v=3v1​+2v2​​

v1​=3v1​1​+3v2​2​

v=31​2v1​v2​​

v=2v1​3v2​​​

vav​= Time Distance ​= Time Speed × Time ​ =3t​+32t​v1​×3t​+v2​×32t​​ ⇒vav​=13v1​​+32v2​​​=3v1​+2v2​​ ⇒vav​=3v1​+2v2​​

Q. A person travels along a straight road for the first $\frac{t}{3}$ time with a speed $v_{1}$ and for next $\frac{2 t}{3}$ time with a speed $v_{2}$ . Then the mean speed $v$ is given by

$v = \frac{v _{1} + 2 v _{2}}{3}$

$\frac{1}{v} = \frac{1}{3 v _{1}} + \frac{2}{3 v _{2}}$

$v = \frac{1}{3} 2 v_{1} v_{2}$

$v = \frac{3 v _{2}}{2 v _{1}}$