A particle moves in one dimension under the influence of a variable force given by function: $F (x) = F_{0} (\frac{x}{x _{0}})^{3}$ Here, $F_{0}$ and $x_{0}$ are positive constants. Find an expression for the work done by the force as the particle moves from $x = 0$ (the origin) to $x = x_{0}$ in terms of these constants.

Question

A particle moves in one dimension under the influence of a variable force given by function:

F (x) = F_{0} (\frac{x}{x _{0}})^{3}

Here,

F_{0}

and

x_{0}

are positive constants. Find an expression for the work done by the force as the particle moves from

x = 0

(the origin) to

x = x_{0}

in terms of these constants.

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