Question

a car travels with a constant speed V1 from A to B and return back to A with a speed of V2 what will be the average speed of car?​

Answer 1

Need to FinD :-

• The average velocity of the car .

$\red{\frak{Given}}\begin{cases}\textsf{ A car travels with a constant speed v _1 from A to B .}\\\\\textsf {It returns back to A with a speed of v _2 .}\end{cases}$

We need to find the average velocity of the car . Let us take that the car travelled x distance while going from A to B , therefore the total distance covered in the journey will be 2x.

• We note that the average speed is defined as total distance travelled by total time taken .

$\sf \longrightarrow V_{avg}= \dfrac{ Total \ distance \ travelled }{Total \ time \ taken }$

• Also we know the relation between speed velocity and time as ( for uniform motion ) s = vt . So that ,

$\sf \longrightarrow t_1 = \dfrac{ x}{v_1}$

$\sf \longrightarrow t_2= \dfrac{ x}{v_2}$

• Put on the respective values in formula find average speed ,

$\sf \longrightarrow v_{avg}= \dfrac{ x + x }{ t_1+ t_2} \\\\\\ \sf \longrightarrow v_{avg}=\dfrac{ 2x}{ \dfrac{ x}{v_1}+\dfrac{ x}{v_2}} \\\\\\ \sf \longrightarrow v_{avg}= \dfrac{ 2x}{ \dfrac{ x ( v_1 + v_2)}{v_1v_2} } \\\\\\ \sf \longrightarrow\underline{\underline{\red{ v_{avg}= \dfrac{2v_1v_2}{v_1+v_2} }}}$