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?

Category: QuestionsA 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?
Editor">Editor Staff asked 11 months ago

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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1 Answers
Editor">Editor Staff answered 11 months ago

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.