The force applied against an object moving horizontally on a linear path is described by F(x)= 4x+3 N . By how much does the object's kinetic energy change as the object moves from  x in [ 1 , 2 ]?

May 17, 2016

$\Delta {E}_{k} = 9 J$

Explanation:

$\text{Work done is equal to changing of the Kinetic Energy}$

$\text{Work="int _"x1"^"x2} F \left(x\right) \cdot d x = \Delta {E}_{k}$

$\text{Work=} {\int}_{1}^{2} \left(4 x + 3\right) d x = \Delta {E}_{k}$

$\Delta {E}_{k} = | 4 \cdot {x}^{2} / 2 + 3 x {|}_{1}^{2}$

$\Delta {E}_{k} = | 2 {x}^{2} + 3 x {|}_{1}^{2}$

$\Delta {E}_{k} = \left(2 \cdot {2}^{2} + 3 \cdot 2\right) - \left(2 \cdot {1}^{2} + 3 \cdot 1\right)$

$\Delta {E}_{k} = \left(8 + 6\right) - \left(2 + 3\right)$

$\Delta {E}_{k} = 14 - 5$

$\Delta {E}_{k} = 9 J$