A person moving along a straight line travels with a uniform velocity v₁ for a distance x , and then with a uniform velocity v₂ for the next equal distance. The average velocity v is given by

Step-by-step solution

Time taken to travel the first distance x is t₁ = x v₁ Time taken to travel the next distance x is t₂ = x v₂ Total distance traveled is x + x = 2x Total time taken is t = t₁ + t₂ = x v₁ + x v₂ Average velocity v = Total distance Total time = 2x x v₁ + x v₂ v = 2 1 v₁ + 1 v₂ 2 v = 1 v₁ + 1 v₂