A force acts on a 30 gm particle in such a way that the

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A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t² + t³, where x is in metres and t is in seconds. The work done during the first 4 seconds is

1. 576 mJ
2. 450 mJ
3. 490 mJ
4. 530 mJ

Correct Option: A

x = 3t –4t² + t³

	dx	= 3 - 8t + 3t²
	dt

Acceleration =	d²x	= - 8 + 6t
	dt²

Acceleration after 4 sec = –8 + 6 × 4 = 16 ms^–2
Displacement in 4 sec = 3 × 4 – 4 × 4² + 4³ = 12 m
∴ Work = Force × displacement = Mass × acc. × disp.
= 3 × 10^–3 × 16 × 12 = 576 mJ