A particle is moving with uniform acceleration along a straight line ABC, where AB = BC. The average velocity of the particle from A to B is 10 m/s and from Bto Cis 15 m/s. The average velocity for the whole journey from A to C in m/s is

The particle moves with uniform acceleration along a straight line ABC where AB = BC. For any motion with uniform acceleration, the average velocity over an interval is equal to the arithmetic mean of the initial and final velocities of that interval. Let the velocities at A, B, and C be vA, vB, and vC respectively. The average velocity from A to B is (vA + vB)/2 = 10 m/s, and from B to C is (vB + vC)/2 = 15 m/s. Adding these equations gives (vA + 2vB + vC)/2 = 25. For the whole journey AC, the average velocity is total displacement divided by total time [1]. In uniform acceleration, the average velocity for the entire segment AC is also (vA + vC)/2. Using the kinematic relation for midpoints (vB² = (vA² + vC²)/2), or solving the linear system, the average velocity for the whole journey AC is 12 m/s.

Sources

1. [1] https://compos.web.ox.ac.uk/sites/default/files/compos/documents/media/physics10_03.pdf