If a school bus, on it's way to school, covers half the distance with velocity v1 and other half with velocity v2. The average velocity of the school bus would be:

Question

If a school bus, on it's way to school, covers half the distance with velocity v1 and other half with velocity v2. The average velocity of the school bus would be: (A) (v1+v2/v1 v2) (B) (2(v1+v2)/v1 v2) (C) (v1 v2/v1+v2) (D) (2 v1 v2/v1+v2)

Tardigrade Admin · Accepted Answer

Time taken for first half of the distance

= t_{1}

= \frac{d}{v _{1}}

Time taken for second half of the distance

= t_{2} = \frac{d}{v _{2}}

Hence,

V_{average} = (\frac{Total distance}{Total time})

= (\frac{d + d}{t _{1} + t _{2}})

= \frac{2 d}{( \frac{d}{v _{1}} ) + ( \frac{d}{v _{2}} )}

= \frac{2}{( \frac{1}{v _{1}} ) + ( \frac{1}{v _{2}} )}

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

∴ v_{average} = \frac{2 v _{1} v _{2}}{v _{1} + v _{2}}

Q. If a school bus, on it's way to school, covers half the distance with velocity $v_{1}$ and other half with velocity $v_{2}$ . The average velocity of the school bus would be:

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

$\frac{2 ( v _{1} + v _{2} )}{v _{1} v _{2}}$

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

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

Q. If a school bus, on it's way to school, covers half the distance with velocity v1​ and other half with velocity v2​. The average velocity of the school bus would be:

v1​v2​v1​+v2​​

v1​v2​2(v1​+v2​)​

v1​+v2​v1​v2​​

v1​+v2​2v1​v2​​

Q. If a school bus, on it's way to school, covers half the distance with velocity $v_{1}$ and other half with velocity $v_{2}$ . The average velocity of the school bus would be:

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

$\frac{2 ( v _{1} + v _{2} )}{v _{1} v _{2}}$

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

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