Question

A Particale Covers half of its total distance with
Speed V¹ and the rest half distance with speed v²
its average speed during
the complete Journey is
​

Answer 1

★Solution :-

• Let us consider the particle moves with speed V1 as it travels from point A to point B and speed V 2 when it's when it travels from point B to C

• Let the total distance covered by the particle be d

➽ From A to B :-

• Speed of the particle = V 1
• Distance covered by the particle = d /2

we know that

➥ Speed = Distance / time

➥ Time =. Distance / Speed

➥ Time =. d / 2 V 1

➥ t = d / 2 V 1

➽ From B to C :-

Speed of the particle = V 2

Distance covered by the particle = d /2

we know that

➥ Speed = Distance / time

➥ Time =. Distance / Speed

➥ Time =. d / 2 V 2

➥ t ’ = d / 2 V 2

Average speed is given by the formula ,

$\bigstar\boxed{\mathtt{ Avg. speed =\dfrac{ total \: distance}{ time \: taken }}}$

$\implies \mathtt{ Avg. speed =\dfrac{ d}{ t + t'}}$

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

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

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

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