A body moves in a straight line with speed v1 and v2 for distance which are in ratio 1: 2. Find average speed.

Question

A body moves in a straight line with speed v1 and v2 for distance which are in ratio 1: 2. Find average speed. (A) 3 v1+v2 (B) v2+2 v1 (C) (3 v1 v2/v2+2 v1) (D) (3 v1 v2/v2-2 v1)

Tardigrade Admin · Accepted Answer

Given that, the distances travelled by the body are in ratio

1 : 2

.
Let us suppose that

s

is the distance, the body travels with speed

v_{1}

.
Then,

2 s

will be the distance travelled by the body with speed

v_{2} .

This scenario is shown in the line-diagram below

For

A

to

C

,
Average speed

= \frac{Total distance travelled}{Total time taken}

v_{avg} = \frac{s _{1} + s _{2}}{t _{1} + t _{2}} = \frac{s + 2 s}{\frac{s}{v _{1}} + \frac{2 s}{v _{2}}}

= \frac{3 s}{s [ \frac{1}{v _{1}} + \frac{2}{v _{2}} ]} = \frac{3}{[ \frac{v _{2} + 2 v _{1}}{v _{1} v _{2}} ]} = \frac{3 v _{1} v _{2}}{v _{2} + 2 v _{1}}

Q. A body moves in a straight line with speed $v_{1}$ and $v_{2}$ for distance which are in ratio $1 : 2$ . Find average speed.

$3 v_{1} + v_{2}$

$v_{2} + 2 v_{1}$

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

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

Q. A body moves in a straight line with speed v1​ and v2​ for distance which are in ratio 1:2. Find average speed.

3v1​+v2​

v2​+2v1​

v2​+2v1​3v1​v2​​

v2​−2v1​3v1​v2​​

Q. A body moves in a straight line with speed $v_{1}$ and $v_{2}$ for distance which are in ratio $1 : 2$ . Find average speed.

$3 v_{1} + v_{2}$

$v_{2} + 2 v_{1}$

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

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