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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 velocityThis 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»

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.


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