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 [ 0, 3 ]#?

1 Answer
Mar 31, 2018

Answer:

The change in kinetic energy will be #3# joules.

Explanation:

Recall that #"Work" = F * d = Delta KE#

Therefore, if we find #F * d# one #[0, 3]#, we'll have our change in kinetic energy. Therefore, we will have to integrate the force function on #[0, 3]#.

#I = int_0^3 cos(pix) + 1#

#I = [1/pi sin(pix) + x]_0^3#

#I = 1/pisin(3pi) + 3 - 1/pisin(0) - 0#

#I = 3#

Therefore the change in kinetic energy will be #3# Joules.

Hopefully this helps!