If a car covers $2 / 5^{\text {th }}$ of the total distance with $v_{1}$ speed and $3 / 5^{\text {th }}$…

If a car covers $2 / 5^{\text {th }}$ of the total distance with $v_{1}$ speed and $3 / 5^{\text {th }}$ distance with $v_{2}$ then average speed is
  1. $\frac{1}{2} \sqrt{v_{1} v_{2}}$
  2. $\frac{v_{1}+v_{2}}{2}$
  3. $\frac{2 v_{1} v_{2}}{v_{1}+v_{2}}$
  4. $\frac{5 v_{1} v_{2}}{3 v_{1}+2 v_{2}}$

Solution

Average speed $=\frac{\text { Total distance travelled }}{\text { Total time taken }}$
$=\frac{x}{\frac{2 x / 5}{v_{1}}+\frac{3 x / 5}{v_{2}}}=\frac{5 v_{1} v_{2}}{3 v_{1}+2 v_{2}}$ *

Asked in: JEE Mains - Motion In One Dimension - Test 1

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