The force applied against an object moving horizontally on a linear path is described by #F(x)=2x +4 #. By how much does the object's kinetic energy change as the object moves from # x in [ 3, 5 ]#?

1 Answer
Feb 12, 2016

Answer:

#Delta E_k=-16 J#

Explanation:

#W:" work doing"#
#E_k:" changing of the kinetic energy"#
#W=Delta E_k=int_a^b F(x) d x#
#W=Delta E_k=int _3^5(2x+4)*d x#
#Delta E_k=[2*1/2*x^2+4*x]_3^5#
#Delta E_k=[x^2+4x]_3^5#
#Delta E_k=(5^2+4*5)-(3^2+4*3)#
#Delta E_k=5-21#
#Delta E_k=-16 J#