The force applied against an object moving horizontally on a linear path is described by F(x)= cospix+3x . By how much does the object's kinetic energy change as the object moves from x in [ 1, 2 ]?

1 Answer
Feb 9, 2016

\Delta K = W = \int_1^2 F(x) dx = 9/2 Joules

Explanation:

Work-Energy Theorem: The total work done by all the forces acting on a body must be equal to the change in its kinetic energy.

\Delta K = K_f-K_i = W

W \equiv \int_{1}^{2} F(x) dx = \int_1^2 (cos\pix+3x) dx,

\qquad = 1/\pi\int_1^2 \frac{d}{dx}(sin\pi x) dx + [3/2 x^2]_1^2

\qquad =\frac{1}{pi} [sin \pix]_1^{2} + 9/2=0+9/2=4.5 J