The kinetic energy KE of an object of mass m moving with a velocity v is defined as
. If a force
acts on the object, moving it along the x-axis from
to
, the Work-Energy Theorem states that the net work done is equal to the change in the kinetic energy: 
, where
is the velocity atand 
is the velocity at.
Let
be the position function of the object at time t and
,
the velocity and acceleration function. Prove the Work-Energy Theorem by first using substitution rule for Definite integrals (4.5.5) to show that
Then use Newton’s Second law of Motion (
) and the substitution 
to evaluate the integral.
How much work (in ft-lb) is required to hurl a 12-lb bowling ball at 20 mi/h (Note: Divide the weights in pounds by 32
, the acceleration due to gravity, to find the mass, measured in slugs.)
The kinetic energy KE of an object of mass m moving with a velocity v is defined as. If a forceacts on the object, moving it along the x-axis fromto, the Work-Energy Theorem states that the net work done is equal to the change in the kinetic energy: , whereis the velocity atand is the velocity at.
Let
be the position function of the object at time t and,the velocity and acceleration function. Prove the Work-Energy Theorem by first using substitution rule for Definite integrals (4.5.5) to show that
Then use Newton’s Second law of Motion (
How much work (in ft-lb) is required to hurl a 12-lb bowling ball at 20 mi/h (Note: Divide the weights in pounds by 32
, the acceleration due to gravity, to find the mass, measured in slugs.)
