A person travelling along a straight line moves with a uniform velocity v₁ for a certain duration and with a uniform velocity v₂ for the next equal duration. The average velocity v is given by

Step-by-step solution

Let the equal time intervals be t . Distance travelled in the first interval is d₁ = v₁ t . Distance travelled in the second interval is d₂ = v₂ t . Total distance travelled is d = d₁ + d₂ = v₁ t + v₂ t = (v₁ + v₂) t . Total time taken is T = t + t = 2t . Average velocity v = Total distance Total time = (v₁ + v₂) t 2t = v₁ + v₂ 2 .