Question

A person travels along a straight road for half
the distance with velocity V, and the remaining
half distance with velocity V, the average
velocity is given by
V2
V1 + V2
2v, V2
2)
4)
V1
2 V + V2
2.
1) V, V2
3)​

Answer 1

Explanation:

2v1v2/(v1+v2) is the correct answer.

Answer 2

Solution :-

Let us consider that the person travels from point A to B with velocity V1 and point B to C with velocity be V2

Let, the total distance traveled by the person be d

From A to B

• Velocity = V 1

• Distance = d / 2

we know that ,

$\implies\mathtt{V_1 = \dfrac{d }{ 2 t_1 }}$

On rearranging ,

$\implies\mathtt{t_ 1 = \dfrac{d }{ 2 V_1 }}$

From B to C

• Velocity = V 2

• Distance = d / 2

we know that ,

$\implies\mathtt{V_ 2 = \dfrac{d }{ 2 t_2 }}$

On rearranging ,

$\implies\mathtt{t_ 2 = \dfrac{d }{ 2 V_2 }}$

----------------------------------

As per the formula ,

$\implies\mathtt{Avg.velocity = \dfrac{total \:distance }{ total \:time}}$

$\implies\mathtt{Avg.velocity = \dfrac{d}{ t_1 + t_2}}$

$\implies\mathtt{Avg.velocity = \dfrac{d}{ \dfrac{d }{ 2 V_1 } + \dfrac{d }{ 2 V_2 }}}$

$\implies\mathtt{Avg.velocity = \dfrac{d}{ \dfrac{d}{2}(\dfrac{1}{ V_1 } + \dfrac{1 }{ V_2 })}}$

$\implies\mathtt{Avg.velocity = \dfrac{2}{ \dfrac{V_1+V_2}{ V_1V_2 } }}$

$\implies\boxed{\mathtt{Avg.velocity = \dfrac{2 V_1V_2}{ V_1+V_2 }}}$