Question

A work done by a force f= -6x^3 i^in displacing a particle from x=4m to x=-2m

Answer 1

Explanation:

please inform if the explanation is helpful

Answer 2

The work done by the force is 360 Joules.

Explanation:

It is given that,

Force acting on the particle, $F=-6x^3\ N$

We need to find the work done by a force displacing a particle from x = 4 m to x = 2 m

The integral form of work done is given by :

$W=\int\limits {F{\cdot}dx}$

Position of particle from x = 4 m to x = 2 m

So, $W=\int\limits^{-2}_{4} {-6x^3{\cdot}dx}$

$W=-\dfrac{6x^4}{4}|_4^{-2}$

$W=-\dfrac{3x^4}{2}|_4^{-2}$

$W=\dfrac{-3}{2}[(-2)^4-4^4]$

W = 360 Joules

So, the work done by the force is 360 Joules. Hence, this is the required solution.

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