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 = 2t3 – 12t + 11. What is the velocity of the particle at the end of 2 seconds?

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 = 2t3 – 12t + 11. What is the velocity of the particle at the end of 2 seconds? Correct Answer 12 cm/sec

We have, x = 2t3 – 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(2t3 – 12t + 11)/dt = 6t2 – 12 ……….(2) Putting the value of t = 2 in (2), Therefore, the displacement of the particle at the end of 2 seconds, 6t2 – 12 = 6(2)2 – 12 = 12 cm/sec.
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