A force F → = 2 + 3 x i ^ acts on a particle in the x direction where F is in Newton and x is in meter. The work done by this force during a displacement from x = 0 to x = 4 m is _____ J .

Question

TestHub · Accepted Answer

The formula to calculate the work done by a variable force is given by

$W = \int_{x_{1}}^{x_{2}} F d x . . . (1)$

Substitute the values of the known parameters into equation (1) to calculate the required work done.

$\begin{array}{rcl} W & = & \int_{0}^{4} (2 + 3 x) d x \\ = & {[2 x + \frac{3}{2} x^{2}]}_{0}^{4} \\ = & [8 + 24] J \\ = & 32 J \end{array}$

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