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A particle which is experiencing a force, given by $\vec{F} = 3 \vec{i} - 12 \vec{j},$ undergoes a displacement of $\vec{d} = 4 \vec{i} .$ If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?

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15 J

9 J

10 J

12 J

answer is A.

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Detailed Solution

Given,

$\vec{F} = 3 \hat{i} - 12 \hat{j} \vec{d} = 4 \hat{i}$

We know that work done,

$W = \vec{F .} \vec{d} W = 12 J$

by work energy theorem,

$W_{n e t} = ∆ K E 12 = K_{f} - 3 K_{f} = 15 J$

Hence the correct answer is 15J.

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