A variable force of the form F=3x² + 2x + 5 N acts on a 2 kg object as it moves from x = 2 m to x = 3 m.How much work is done by this force?

Question

Quizplus · Accepted Answer

To find the work done, we need to integrate the force with respect to displacement:
W = ∫Fdx
W = ∫(3xS1U1P12S1S1P0 + 2x + 5)dx from x=2 to x=3
W = [3/2(xS1U1P22S1S1P0) + xS1U1P2 + 5x] from x=2 to x=3
W = [3/2(3S1U1P22S1S1P0) + 3S1U1P2 + 15] - [3/2(2S1U1P22S1S1P0) + 2S1U1P2 + 10]
W = 29 J
The work done by the force is 29 J. Therefore, the best choice is B.

A Variable Force of the Form F=3x2 + 2x

A Variable Force of the Form F=3x² + 2x