Two particles start from rest from the same point and move along the same straight path; the first starts with a uniform velocity of 20 m/minute and the second with a uniform acceleration of 5 m/ min2. Before they meet again, then what will be the maximum distance?

Two particles start from rest from the same point and move along the same straight path; the first starts with a uniform velocity of 20 m/minute and the second with a uniform acceleration of 5 m/ min2. Before they meet again, then what will be the maximum distance? Correct Answer 40m

Suppose, the two particle starts from rest at and move along the straight path OA. Further assume that the distance between the particle is maximum after t minutes from start (before they meet again). If we be the position of the particle after 30 minutes from the start which moves with uniform acceleration 5 m/min2 and C that of the particle moving with uniform velocity 20 m/min, then we shall have, OB = 1/2(5t2) and OC = 20t If the distance between the particle after t minutes from start be x m, then, x = BC = OC – OB = 20t – (5/2)t2 ……….(1) Now, dx/dt = 20 – 5t and d2x/dt2 = -5 For maximum or minimum values of x, we have, dx/dt = 0 Or 20 – 5t = 0 Or t = 4 And = -5 < 0 Thus, x is maximum at t = 4. Therefore, the maximum value is, = 20*4 – (5/2)(42) = 40 m
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