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 is the meaning of the constant b?

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 is the meaning of the constant b?
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 is the meaning of the constant b?
 
(a) Final velocity
 
(b) Initial velocity
 
(c) Mid velocity
 
(d) Arbitrary velocity
 
This question was posed to me in examination.
 
My doubt is from Calculus Application topic in section 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

Correct answer is (b) Initial velocity
 
Best 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)
 
Now from (2) we get v = b, when t = 0.
 
Hence b represents the initial velocity of the particle.