A particle travels along a straight line. It covers the first one-third of the total distance at a constant speed of 10 m/s . The remaining two-thirds of the distance is covered such that half of the time is spent travelling at 20 m/s and the other half of the time is spent travelling at an unknown constant speed v . If the overall average speed for the complete journey is 18 m/s , the value of v (in m/s ) is _______

Step-by-step solution

Let the total distance be 3d . The first part of the journey covers a distance d at 10 m/s . Time taken for the first part, t₁ = d 10 . The remaining distance is 2d . Let the total time taken to cover this remaining distance be t₂ . For this part, half the time is spent at 20 m/s and the other half at v . Distance covered in the second part = 20 ( t₂ 2 ) + v ( t₂ 2 ) = 2d t₂ (10 + v 2 ) = 2d t₂ = 4d 20 + v The overall average speed is given by: v_ avg = Total Distance t₁ + t₂ = 18 3d d 10 + 4d 20 + v = 18 Cancellin