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, then what is the value of acceleration?

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, then what is the value of acceleration? Correct Answer 2(bt1 – at2)/t1t2(t1 + t2)

Let the particle beam moving with uniform acceleration f and its velocity at A be u. Then, the equation of the motion of the particle from A to B is, ut1 + ft12/2 = a   ……….(1) Again, the equation of motion of the particle from A to C is, u(t1 + t2) + f(t1 + t2)2/2 = a + b  ……….(2) Multiplying (1) by (t1 + t2) and (2) by t1 we get, ut1 (t1 + t2) + ft12(t1 + t2)/2 = a(t1 + t2) ……….(3) And ut1(t1 + t2) + f(t1 + t2)2/2 = (a + b)t1 ……….(4) Subtracting (3) and (4) we get, 1/2(ft1)(t1 + t2)(t1 – t1 – t2) = at2 – bt1 Solving the above equation, we get, f = 2(bt1 – at2)/t1t2(t1 + t2)
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