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 , 3 ]?

1 Answer
Apr 18, 2017

Given force applied against an object moving horizontally on a linear path
F(x)=4x+3 ......(1)
where it is assumed x is in meters

Since the object moves horizontally on a linear path, we can assume that potential energy of the object does not change. As such only change is in its kinetic energy due to work done against the force.

We know that work done dW by force while moving through distance dx is
dW=vecFcdot dvecx
Since both force and direction of motion are co-linear angle between the two is =0^@and :. cos0^@=1
:.dW=Fdx

As the force moves through distance x in[1,3], total work done against the object or change in its kinetic energy
W=int_1^3Fdx
Inserting value of force from (1) we have
W=int_1^3(4x+3)dx
=>W=[4x^2/2+3x]_1^3
=>W=[(2xx3^2+3xx3)-(2xx1^2+3xx1)]
=>W=[(18+9)-(2+3)]
=>W=22J