First slide

Numericals based on work energy theorem

Question

A particle of mass 2 kg starts moving from the origin along x-axis under the action of a force which is varying according to the graph shown in figure. Initial velocity of the particle is 2 m/s. Then work done by the force on the particle at t = 6 s is

Difficult

A

10 J
B

8 J
C

12 J
D

16 J

Solution

Change is momentum = Area under F - t graph
$∴ 2 \times v - 2 \times 2 = 8 \times 2 + \frac{1}{2} \times (6 - 2) \times (- 6)$
$\Rightarrow v = 4 m / s$
By work energy theorem, $W = {(K E)}_{f} - {(K E)}_{i} = \frac{1}{2} \times 2 \times 4^{2} - \frac{1}{2} \times 2 \times 2^{2}$
$\Rightarrow w = 12 joule$

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