A person travelling along a straight line moves with uniform velocity v₁ for a distance x and with uniform velocity v₂ for the next 3x/2 distance. The average velocity for the complete motion is 50/7 m/s. If v₁ = 5 m/s, find v₂ in m/s.
Physics · Kinematics Part-1 (one dimension) · Distance,Displacement ,Avg speed and Avg velocity
JEE Mains 2025 2 April Morning Shift

Question

A person travelling along a straight line moves with uniform velocity v₁ for a distance x and with uniform velocity v₂ for the next 3x/2 distance. The average velocity for the complete motion is 50/7 m/s. If v₁ = 5 m/s, find v₂ in m/s.

Physics · Kinematics Part-1 (one dimension) · Distance,Displacement ,Avg speed and Avg velocity

JEE Mains 2025 2 April Morning Shift

G1 Physics · Accepted Answer

Total distance: D = x + 3x/2 = 5x/2. Total time: t = x/v₁ + (3x/2)/v₂. Given v₁=5 m/s and average velocity 50/7 m/s: 50/7 = (5x/2) / [x/5 + 3x/(2v₂)]. Cancel x: 50/7 = (5/2) / [1/5 + 3/(2v₂)]. Therefore 1/5 + 3/(2v₂) = (5/2)(7/50) = 7/20. So 3/(2v₂) = 7/20 - 4/20 = 3/20. Hence 1/(2v₂) = 1/20 ⇒ v₂ = 10 m/s. Answer: 10.