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One motor car A stands 24m in front of a motorcycle B. Both starts from rest along a straight road in the same direction. If A moves with uniform acceleration of 2 m/sec2, B runs at a uniform velocity of 11 m/sec how many times will they meet?

One motor car A stands 24m in front of a motorcycle B. Both starts from rest along a straight road in the same direction. If A moves with uniform acceleration of 2 m/sec2, B runs at a uniform velocity of 11 m/sec how many times will they meet? Correct Answer 2

Let P and Q be the initial positions of the motor car and motorcycle B respectively, where PQ = 24m. If possible, let us assume that B overtakes A after point R on the straight road after time t seconds from the start. Then, considering the motion of motor car A, we get PR = 1/2 (2) (t2) = t2 In this case when B runs at a uniform velocity 11 m/sec, we shall have, QR = 11t. Therefore, in this case, QP + PR = QR gives, Or 24 + t2 = 11t Or t2 – 11t + 24 = 0 Or (t – 3)(t – 8) = 0 Or t = 3 or t = 8 Clearly, we are getting two real positive values of t. Therefore, A and B will meet twice during the motion.

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