The force applied against a moving object travelling on a linear path is given by #F(x)= 4x + 4#. How much work would it take to move the object over #x in [ 1, 5] #?

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Answer 1 · 2016-03-24T16:42:28

#64# units.

Work done = force x distance moved in the direction of the force.

Since the force #F# is a function of the displacement #x# we need to use integration:

#W=intF.dx#

#:.W=int_1^5(4x+4).dx#

#:.W=[(4x^2)/2+4x]_1^5#

#W=[2x^2+4x]_1^5#

#W=[50+20]-[2+4]=70-6=64#