Why does kinetic energy Ek=½mv2?
Students and non-specialist teachers alike wonder: whence the half?
This post is intended to be a diagrammatic answer to this question using a Singapore Bar Model approach: so pedants, please avert your eyes.
I am indebted to Ben Rogers’ recent excellent post on showing momentum using the Bar Model approach for starting me thinking along these lines.
Part the First: How to get the *wrong* answer
Imagine pushing an object with a mass m with a constant force Fso that it accelerates with a constant acceleration aso that covers a distance s in a time t. The object was initially at rest and ends up moving at velocity v.
(On the diagram, I’ve used the SUVAT dual coding conventions that I suggested in a previous post.)
So let’s consider the work done on the…
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