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

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Answer 1 · 2016-03-09T19:58:34

Use Work Energy Theorem:
$W_F = DeltaKE = [(x(x^3-12))/4]_3^5 = 130J$
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Use Work Energy Theorem:
$W_F = DeltaKE = 1/2mDeltav^2$
Now $W_F = intF*dr = int_3^5 F*dx = int_3^5 x^3+3*dx$
$W_F = [(x(x^3-12))/4]_3^5 = 130J$

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