A particle moves along the positive x -axis. It travels from x = 0 to x = L at a constant speed v , and then from x = L to x = 3L at a constant speed 3v . The average speed of the particle for the entire journey is:

Step-by-step solution

Total distance travelled by the particle is x = 3L - 0 = 3L . Time taken for the first part of the journey (from x = 0 to x = L ) is: t₁ = L v Time taken for the second part of the journey (from x = L to x = 3L ) is: t₂ = 3L - L 3v = 2L 3v Total time taken is: t = t₁ + t₂ = L v + 2L 3v = 5L 3v Average speed is given by: v_ avg = Total distance Total time = 3L 5L 3v = 9v 5 Answer: 9v 5