A particle moving along a straight line with uniform acceleration, passes successively through three points A, B, C. If t1 = time taken to go from A to B; t2 = time taken to go from B to C and AB = a, BC = b. If a = b and the velocities of the particle at A, B, C be p, q, r respectively, then, what is the relation between p2, q2 and r2?

A particle moving along a straight line with uniform acceleration, passes successively through three points A, B, C. If t1 = time taken to go from A to B; t2 = time taken to go from B to C and AB = a, BC = b. If a = b and the velocities of the particle at A, B, C be p, q, r respectively, then, what is the relation between p2, q2 and r2? Correct Answer A.P

When a = b, then the equation of the motion of the particle from A to B is, q2 = p2 + 2fa Or q2 – p2 = 2fa ……….(1) Again, the equation of motion of the particle from B to C is, r2 = q2 + 2fa Or r2 – q2 = 2fa ……….(2) From (1) and (2) we get, q2 – p2 = r2 – q2 Thus, p2, q2 and r2 are in A.P.
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