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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I’d like to ask this question from Calculus Application topic in division Application of Calculus of Mathematics – Class 12
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The correct option is (a) Uniform retardation
Easy 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)
And f = dv/dt = d(b + ct)/dt = c ……….(3)
Clearly, when c < 0,implies f < 0.
Hence in this case the particle moves withan uniform retardation.