A force → F = (2 + 3x) ^ 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 = 4m is _____ J .

Question

Quantrex Academy · Accepted Answer

Correct answer: 0

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

$W = {∫}_{{x}_{1}}^{{x}_{2}}Fdx . . . \left(1\right)$

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

$\begin{cases}W & = & {∫}_{0}^{4} ( 2 + 3x ) dx \\ & = & {\left[2x + \dfrac{3}{2}{x}^{2}\right]}_{0}^{4} \\ & = & [ 8 + 24 ] J \\ & = & 32J\end{cases}$

A force → F = (2 + 3x) ^ i acts on a particle in the x direction...

Correct answer

Step-by-step solution

More from Work, Power and Energy