Question

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 a?

(a) Initial position

(b) Final position

(c) Mid position

(d) Any arbitrary position

The question was posed to me in an online quiz.

The origin of the question is Calculus Application in portion Application of Calculus of Mathematics – Class 12

Answer 1

The correct choice is (a) Initial position

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

Now from (1) we get x = a, when t = 0.

This means that the distance of the particle from O at time t = 0 is a ft.

Thus, a represents the initial position of the particle.