A particle is moving in a straight line and its distance s cm from a fixed point in the line after t seconds is given by s = 12t – 15t^2 + 4t^3. What is the velocity of the particle after 3 seconds?

Category: QuestionsA particle is moving in a straight line and its distance s cm from a fixed point in the line after t seconds is given by s = 12t – 15t^2 + 4t^3. What is the velocity of the particle after 3 seconds?
Editor">Editor Staff asked 11 months ago

A particle is moving in a straight line and its distance s cm from a fixed point in the line after t seconds is given by s = 12t – 15t^2 + 4t^3. What is the velocity of the particle after 3 seconds?
 
(a) 10 cm/sec
 
(b) 20 cm/sec
 
(c) 30 cm/sec
 
(d) 40 cm/sec
 
The question was asked in class test.
 
I want to ask this question 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 option is (c) 30 cm/sec
 
To elaborate: We have, s = 12t – 15t^2 + 4t^3 ……….(1)
 
Differentiating both side of (1) with respect to t we get,
 
(ds/dt) = 12 – 30t + 12t^2
 
So, velocity of the particle after 3 seconds is,
 
[ds/dt]t = 3 = 12 – 30(3) + 12(3)^2
 
= 30 cm/sec.