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?

Category: QuestionsOne 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?
Editor">Editor Staff asked 11 months ago

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
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1 Answers
Editor">Editor Staff answered 11 months ago

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.