The work done by a variable force $F ( x ) = ( 4 x - 1 ) ^ { 2 }$ Newtons that moves an object along a straight line in the direction of F from x = 2 meters to x = 4 meters, in Newton-meters, is

A) $\frac { 50 } { 3 }$
B) $\frac { 758 } { 3 }$
C) $\frac { 825 } { 2 }$
D) $\frac { 782 } { 27 }$
E) $\frac { 302 } { 3 }$

Question

The work done by a variable force $F ( x ) = ( 4 x - 1 ) ^ { 2 }$ Newtons that moves an object along a straight line in the direction of F from x = 2 meters to x = 4 meters, in Newton-meters, is

A) $\frac { 50 } { 3 }$
B) $\frac { 758 } { 3 }$
C) $\frac { 825 } { 2 }$
D) $\frac { 782 } { 27 }$
E) $\frac { 302 } { 3 }$

Quizplus · Accepted Answer

The work done by a variable force is calculated by integrating the force function over the distance. For $F(x) = (4x - 1)^2$, the work done from $x = 2$ to $x = 4$ is $\int_{2}^{4} (4x - 1)^2 dx$. Solving this integral gives $\frac{758}{3}$ Newton-meters.

The Work Done by a Variable Force F(x)=(4x−1)2F ( x ) = ( 4 x - 1 ) ^ { 2 }F(x)=(4x−1)2

The Work Done by a Variable Force $F ( x ) = ( 4 x - 1 ) ^ { 2 }$