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:

$W=intF.dx$

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

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

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

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

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