The force applied against an object moving horizontally on a linear path is described by $F (x) = 4 x^{2} + 5 x$ $F(x)= 4x^2+5x$ . By how much does the object's kinetic energy change as the object moves from $x \in [1, 2]$ $x in [ 1, 2 ]$ ?

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The force applied against an object moving horizontally on a linear path is described by $F (x) = 4 x^{2} + 5 x$ $F(x)= 4x^2+5x$ . By how much does the object's kinetic energy change as the object moves from $x \in [1, 2]$ $x in [ 1, 2 ]$ ?

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Answer 1 · 2016-05-08T07:54:20

$\frac{35}{3}$ $35/3$ unit

Explanation:

Kinetic energy gained by the object is equlal to the work done by the aplied foce .So KE= $\int_{1}^{2} F (x) d x = \int_{1}^{2} (4 x^{2} + 5 x) d x$ $int_1^2F(x)dx=int_1^2(4x^2+5x)dx$
$= {[4 \frac{x^{3}}{3} + 5 \frac{x^{2}}{2}]}_{1}^{2} = 4 \cdot \frac{2^{3}}{3} + 5 \cdot \frac{2^{2}}{2} - 4 \cdot \frac{1^{3}}{1} - 5 \cdot \frac{1^{2}}{1} = \frac{35}{3}$ $=[4x^3/3+5x^2/2]_1^2=4*2^3/3+5*2^2/2-4*1^3/1-5*1^2/1=35/3$

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The force applied against an object moving horizontally on a linear path is described by $F (x) = 4 x^{2} + 5 x$ $F(x)= 4x^2+5x$ . By how much does the object's kinetic energy change as the object moves from $x \in [1, 2]$ $x in [ 1, 2 ]$ ?

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The force applied against an object moving horizontally on a linear path is described by F(x)=4x2+5xF(x)= 4x^2+5x . By how much does the object's kinetic energy change as the object moves from x∈[1,2] x in [ 1, 2 ]?

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Explanation:

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The force applied against an object moving horizontally on a linear path is described by $F (x) = 4 x^{2} + 5 x$ $F(x)= 4x^2+5x$ . By how much does the object's kinetic energy change as the object moves from $x \in [1, 2]$ $x in [ 1, 2 ]$ ?