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
 
The question was asked in an internship interview.
 
I’d like to ask this question from Calculus Application topic in division Application of Calculus of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.