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 + ct2 (a, b > 0). What will be the nature of motion of the particle when c < 0?
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 + ct2 (a, b > 0). What will be the nature of motion of the particle when c < 0? Correct Answer Uniform retardation
We have, x = a + bt + ct2 ……….(1) Let, v and f be the velocity and acceleration of a particle at time t seconds. Then, v = dx/dt = d(a + bt + ct2)/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.
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Feb 20, 2025