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
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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.