Question

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 p^2, q^2 and r^2?

(a) A.P

(b) G.P

(c) H.P

(d) They are in any arbitrary series

The question was posed to me by my college director while I was bunking the class.

This key question is from Calculus Application in section Application of Calculus of Mathematics – Class 12

Answer 1

The correct option is (a) A.P

The best I can explain: When a = b, then the equation of the motion of the particle from A to B is,

q^2 = p^2 + 2fa

Or q^2 – p^2 = 2fa  ……….(1)

Again, the equation of motion of the particle from B to C is,

r^2 = q^2 + 2fa

Or r^2 – q^2 = 2fa   ……….(2)

From (1) and (2) we get,

q^2 – p^2 = r^2 – q^2

Thus, p^2, q^2 and r^2 are in A.P.