Question

A person travelling along a straight Road for half the distance with the velocity V1 and the remaining half distance with velocity V2 the average velocity is given by

Answer 1

SoLuTiOn :

➡ Given:

✏ A person covers half of total distance with velocity 'V1' and the remaining half distance with velocity 'V2'.

➡ To Find:

✏ Average velocity ?

➡ Formula:

✏ Formula of average velocity is given by

$\star \: \underline{ \boxed{ \bold{ \rm{ \pink{V_{av} = \frac{total \: distance}{total \: time}}}}}} \: \star$

➡ Calculation :

✏ Let body covers first d/2 distance in time t1 and the remaining d/2 distance in time t2.

✏ Total distance covered by body = d

$\mapsto \rm \: V_{av} = \frac{ d }{t_1 + t_2} \\ \\ \mapsto \rm \: V_{av} = \frac{d}{ \frac{d}{2V_1} + \frac{d}{2V_2} } = \frac{ \cancel{d}}{ \cancel{d}( \frac{V_1 + V_2}{2V_1V_2} )} \\ \\ \mapsto \: \red{ \rm{V_{av} = \frac{2V_1V_2}{V_1 + V_2}}}$

Answer 2

$\large{\underline{\underline{\mathfrak{Answer :}}}}$

$\sf{V_{avg} \: = \: \dfrac{2 v_1 v_2}{v_1 \: + \: v_2}}$

$\rule{200}{0.5}$

$\underline{\underline{\mathfrak{Step-By-Step-Explanation :}}}$

As we know that :

$\large{\boxed{\sf{V_{avg} \: = \: \dfrac{Distance}{Time}}}} \\ \\ \implies {\sf{V_{avg} \: = \: \dfrac{d}{t_1 \: + \: t_2}}} \\ \\ \implies {\sf{V_{avg} \: = \: \dfrac{d}{\dfrac{d}{2v_1} \: + \: \dfrac{d}{2v_2}}}} \\ \\ \implies {\sf{V_{avg} \: = \: \dfrac{2 v_1 v_2}{v_1 \: + \: v_2}}}$