A particle is moving in a straight line is at a distance x from a fixed point in the straight line at time t seconds, where x = 2t^3 – 12t + 11. What is the velocity of the particle at the end of 2 seconds?(a) 10 cm/sec(b) 12 cm/sec(c) 14 cm/sec(d) 16 cm/secThe question was posed to me during an interview.The doubt is from Calculus Application topic in division Application of Calculus of Mathematics – Class 12

A particle is moving in a straight line is at a distance x from a fixe

1.	A particle is moving in a straight line is at a distance x from a fixed point in the straight line at time t seconds, where x = 2t^3 – 12t + 11. What is the velocity of the particle at the end of 2 seconds?(a) 10 cm/sec(b) 12 cm/sec(c) 14 cm/sec(d) 16 cm/secThe question was posed to me during an interview.The doubt is from Calculus Application topic in division Application of Calculus of Mathematics – Class 12
Answer» RIGHT choice is (b) 12 cm/sec The best I can explain: We have, x = 2t^3 – 12t + 11 ……….(1) Let v and F be the VELOCITY and acceleration RESPECTIVELY of the particle at time t seconds. Then, v = dx/dt = d(2t^3 – 12t + 11)/dt = 6t^2 – 12 ……….(2) Putting the value of t = 2 in (2), Therefore, the displacement of the particle at the end of 2 seconds, 6t^2 – 12 = 6(2)^2 – 12 = 12 cm/sec.

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