(Phew! Houston, we no longer have a problem.) It doesn’t because it is accelerating: it starts off moving slowly and ends up moving at the maximum, final velocity v when it has travelled the total distance s.īut remember that s = (average velocity) x t.īecause the object is accelerating at a constant rate, the average velocity is ( v + u) / 2 and since u = 0 then average velocity is v / 2. We wrongly assumed that the object has a constant velocity over the whole of the distance s. Part the Second: how to get the *right* answer That’s just wrong: where did the half go? The kinetic energy is represented by the volume of the bar. On a Singapore Bar Model diagram this can be represented as follows: In other words, it is the energy the object has gained because it is moving - its kinetic energy, no less: E k = mv 2. Since this is the work done on the object by the force, it is equal to the energy transferred to the kinetic energy store of the object. Step 1: work done = force x distance moved in the direction of the forceĪlso remember that a = change in velocity / time, so a = ( v – 0) / t = v / t. So let’s consider the work done on the object by the force: (On the diagram, I’ve used the SUVAT dual coding conventions that I suggested in a previous post.) The object was initially at rest and ends up moving at velocity v. ![]() ![]() Imagine pushing an object with a mass m with a constant force F so that it accelerates with a constant acceleration a so that covers a distance s in a time t. ![]() Part the First: How to get the * wrong* answer I am indebted to Ben Rogers’ recent excellent post on showing momentum using the Bar Model approach for starting me thinking along these lines. This post is intended to be a diagrammatic answer to this question using a Singapore Bar Model approach: so pedants, please avert your eyes. Students and non-specialist teachers alike wonder: whence the half?
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