Question

A 1.0-kg object moving in a certain direction has a kinetic energy of 2.0 J. It hits a wall and comes back with half its original speed. What is the kinetic energy of this object at this point?

Answer 1

Lets calculate the initial speed of the block. We know that kinetic energy is given by:

$K_0 =\dfrac{mv_0^2}{2}$

Solving for v₀:

$v_0 = \sqrt{ \dfrac{2K_0}{m}} = \sqrt{ \dfrac{2(2\;J)}{1\;kg}} = 2\;m/s$

If the speed after it hits a wall is half its original speed then:

v = v₀/2 = 2 m/s / 2 = 1 m/s

Then the kinetic energy at this point is:

$K =\dfrac{mv^2}{2} = \dfrac{(1\;kg)(1\;m/s)^2}{2} = \dfrac{1}{2}\;J = 0.5\;J$

The inetic energy of this object at this point is 0.5 J.