Question

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/sec^2 and B runs with a uniform velocity of 9 m/sec, is it possible for B to overtake A?

(a) No

(b) Yes

(c) Data not sufficient

(d) Answer cannot be determined

The question was posed to me in unit test.

The above asked question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12

Answer 1

The correct answer is (a) No

To explain I would say: 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) (t^2) = t^2

Again, considering the motion of motorcycle B we get QR = 9t.

Now,QP+PR = QR

Or 24 + t^2 = 9t

Or t^2 – 9t + 24 = 0

Or t = [9 ± √(81 – 4*24)]/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.