A particle starts from rest and moves in a straight line whose equation of motion is given by S = 2t³ - t² - 1. The acceleration of the particle after one second will be-

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NPCIL SA/ST ME GJ held on 07/11/2019 Shift-1

Answer 1

Concept:

If s = f(t)

Then, First derivative with respect to time represents the velocity

\(v=\frac{ds}{dt}\)

Acceleration is given by

\(a=\left( \frac{{{d}^{2}}S}{d{{t}^{2}}} \right)\)

Where s is the displacement

Calculation:

Given:

s = 2t3 – t2 - 1 and t = 1 sec.

\(\frac{ds}{dt}=6{{t}^{2}}-2t\)

\(\frac{{{d}^{2}}s}{d{{t}^{2}}}=12t-2\)

\({{\left( \frac{{{d}^{2}}s}{d{{t}^{2}}} \right)}_{t=1s}}=12-2=10 \;m/s^2\)