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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 and B runs with a uniform velocity of 9 m/sec, is it possible for B to overtake A?

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 and B runs with a uniform velocity of 9 m/sec, is it possible for B to overtake A? Correct Answer No

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 Again, considering the motion of motorcycle B we get QR = 9t. Now,QP+PR = QR Or 24 + t2 = 9t Or t2 – 9t + 24 = 0 Or t = /2 Or t = (9 ± √-15)/2 Clearly, the values of t are imaginary. Therefore, there is no real positive time when B overtake A. Hence, the in this case B will never overtake A.

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