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 will be the nature of motion of the particle when c = 0?

(a) Uniform retardation

(b) Uniform speed

(c) Uniform acceleration

(d) Uniform velocity

This question was posed to me at a job interview.

I would like to ask this question from Calculus Application in section Application of Calculus of Mathematics – Class 12

Answer 1

Right choice is (d) Uniform velocity

For explanation I would say: 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)

And f = dv/dt = d(b + ct)/dt = c   ……….(3)

Clearly, when c = 0, then f = 0 that is, acceleration of the particle is zero.

Hence in this case the particle moves with an uniform velocity.