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Old 04-08-2014, 08:58 AM   #5 (permalink)
RedDevil
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Red Devil - '11 Honda Insight Elegance
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Forget that last post. I goofed up right from the start.

It takes one Newton to speed up one kilo from a standstill to one meter per second, or 3.6 km/h, in one second.
It will travel half a meter doing that, so one Newton over half a meter means just half a Joule was spent.

We need to go 60 miles per hour, that is 96.56 km/h or 26.8222 m/s.
The relation between speed and energy is quadratic, so we need that squared times half a Joule to find how many joules we need to speed up one kilo to 60 mph: 359.72 Joules

The Tesla S weighs 1999 kg, so it needs 719,072 joules to reach 60 mph from a standing start.
It produces 225,000 Watt (Joules per second).
So according to this formula it needs 3.19 seconds to reach 60 mph.

That's a lot less than the 5.9 it actually needs.
Of course the driver adds extra weight. Say 5%. That would slow it down to 3.24 seconds.

It cannot use all its power when it is still moving below a certain speed; the wheels would spin.
Say it would accelerate at 6 m/sē until it can use full power, from where the acceleration slows down. At 225 kW and 2100 kg (add driver) that would be at 17,8 meters per second, say after 3 seconds.
It would have spent, on average, half the power it has during those 3 seconds so that adds 1.5 seconds to the time we calculated earlier, so 4.74 seconds.
Still more than a second faster than the actual acceleration time.

There are additional factors.
Maybe the traction control jumps in, there is friction in the tires from deforming while accelerating, there is wind resistance, rolling resistance, rotational mass to speed up.
If that all combines to 20-25% of the whole then we've done it! Accuracy
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