A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct^2 (a, b > 0). What is the meaning of the constant b?

(a) Final velocity

(b) Initial velocity

(c) Mid velocity

(d) Arbitrary velocity

This question was posed to me in examination.

My doubt is from Calculus Application topic in section Application of Calculus of Mathematics – Class 12

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Correct answer is (b) Initial velocity

Best explanation: We have, x = a + bt + ct^2 ……….(1)

Let, v and f be the velocity and acceleration of a particle at time t seconds.

Then, v = dx/dt = d(a + bt + ct^2)/dt = b + ct ……….(2)

Now from (2) we get v = b, when t = 0.

Hence b represents the initial velocity of the particle.