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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 seriesThe 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»

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.


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