Reducing your speed by half before crashing into a concrete post will result in how much reduction in kinetic energy?

When considering the kinetic energy of an object, it is important to understand the formula for kinetic energy, which is given by:

[ KE = \frac{1}{2} mv^2 ]

where ( KE ) represents kinetic energy, ( m ) is mass, and ( v ) is velocity.

If you reduce your speed by half, the new speed will be ( \frac{v}{2} ). Plugging this reduced velocity into the kinetic energy formula, we have:

[ KE_{new} = \frac{1}{2} m \left(\frac{v}{2}\right)^2 ]

[ KE_{new} = \frac{1}{2} m \left(\frac{v^2}{4}\right) ]

[ KE_{new} = \frac{1}{8} mv^2 ]

Now, the original kinetic energy can be described as:

[ KE_{original} = \frac{1}{2} mv^2 ]

Comparing the original kinetic energy to the new kinetic energy, we can see that:

[ \frac{KE_{original}}{KE_{new}} = \frac{\frac{1}{2} mv^2}{