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# Tricky physics question watch

1. This is something I've been thinking bout for a while, but have made zero progress in. Why is kinetic energy proportional to the speed squared?

In other terms, why does it take so much more energy to accelerate an object form 10ms-20ms, than it does to accelerate it from 0ms-10ms?

I think I missing a basic concept here, any help?
2. Ok, there's an amazing walter lewin video that derives the formula for kinetic energy.
I think my explanation would be worse than this amazing teacher's one.
3. (Original post by Kota Dagnino)
Ok, there's an amazing walter lewin video that derives the formula for kinetic energy.
I think my explanation would be worse than this amazing teacher's one.
That's a really great vid that explains the mathematics behind it, but I want to think about it more intuitively. It doesn't really answer my question about why you need more and more energy to accelrate an object to higher speeds
4. Well, if you think about it, as an apple accelerates downwards, it gains velocity, but at the same time also converts potential energy into kinetic energy. However, this velocity isn't constant, and indeed that's why as time passes more more kinetic energy is converted. Because the apple has less time to accelerate as its velocity is increasing. This example can be applied to your car.
5. A decent way to think about force and kinetic energy is to consider a falling weight. Gravity applies a constant force and thus a constant acceleration. Every meter it’s lowered it provides the same amount of energy, so lowering it 2 meters provides twice the energy as lowering it 1 meter.
Now imagine the weight free-falling that distance (instead of being slowly lowered). After the first meter it’ll already be moving, so it’ll fall through the second meter faster and in less time. The velocity gained is acceleration times time, so since it spends less time falling through that second meter, the falling weight spends less time accelerating and gains less speed.
But it still has to gain the same amount of energy every meter it falls. That means that at higher speeds you gain the same amount of energy from a smaller increase in speed. Or (equivalently) once you’re moving faster, the same increase in speed produces a greater increase in energy.
6. It is much harder to keep an object moving than to make it start moving. That is an application of static and kinetic friction.
7. (Original post by Kota Dagnino)
It is much harder to keep an object moving than to make it start moving. That is an application of static and kinetic friction.
No friction is involved. No drag either.
8. I know it's just a way of saying. Look at the posts before though, those may be more useful

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