The force applied against an object moving horizontally on a linear path is described by #F(x)=8-x#. By how much does the object's kinetic energy change as the object moves from # x in [ 0, 4]#?

1 Answer
Apr 24, 2017


The kinetic energy of the object will decrease by 24J.


Change in #E_k#
= Work done on object
= Area under the F-x graph

#int_0^4 F(x) dx = int_0^4 (8-x) dx = [8x-0.5x^2]_0^4 = 32-8 = 24#