The force applied against an object moving horizontally on a linear path is described by #F(x)= 4x^2+x #. By how much does the object's kinetic energy change as the object moves from # x in [ 1, 2 ]#?
We begin by writing the acceleration in terms of the force,
Multiply both sides by
then integrate both sides
We know that the kinetic energy is given by
The change in kinetic energy will be the difference at the two point in
I've decided that this is actually much easier than the previous answer. Let's use the concept of work which is the force integrated over the distance that is applied.
The work that we do ends up increasing the kinetic energy of the object, so