The force applied against an object moving horizontally on a linear path is described by #F(x)= cospix+1 #. By how much does the object's kinetic energy change as the object moves from # x in [ 2, 5 ]#?

1 Answer
Feb 12, 2016

Answer:

#Delta E_k=3J#

Explanation:

#"Work done by Force is equal to changing kinetic energy in interval(2,5)"#
#Delta E_k=W=int _2^5 (cos pi x+1)d x#
#Delta E_k= int_2^5(cos pi x)d x+int_2^5d x#
#Delta E_k=[-1/pi sin pix]_2^5+[x]_2^5#
#Delta E_k=[-1/pi sin 5 pi-(-1/pi sin 2 pi)]+(5-2)#
#Delta E_k=[-1/pi 0-(-1/pi 0)]+3#
#Delta E_k=3J#