# How to calculate distance travelled while car is rolling, given start and end speed?

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There is deceleration caused by friction and drag, which is complicated as far as computing is concerned (as someone noted above). It can be determined empirically with help of some controlled experiments and curve fitting.

The simplest is off course to assume that it is constant deceleration. Depending on the application, it may suffice. If so, the formula for distance traveled in terms of starting speed $u$, final speed $v$ and time $t$ is $$s = \frac{v+u}{2t}$$

Note that this is simply the area under the speed - time graph. You can get better accuracy if you are able to note down speed at multiple time points in this graph.

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### Raresh Gosman

Updated on June 26, 2020

• Raresh Gosman almost 3 years

I'm trying to calculate the distance travelled by my Formula Student racecar if it starts at a certain speed, goes into Neutral (no acceleration, no brakes, just rolling on its wheels), and ends at another speed.

This obviously needs to take into account drag coefficients, friction (not too in-depth), losses through the drivetrain (not too in-depth), and rotational inertia from the flywheel.

I know I must be missing some other key figures, so any help would be appreciated.

The big question is, what formulas can I use to find my required distance?

• Kyle Kanos almost 8 years
If it "goes into neutral" as you describe it, isn't that the same thing as moving at constant speed? Or are you assuming that a deceleration is possible due to friction in the axle/wheels? (which would somewhat contradict the "no acceleration" bit because a negative acceleration is a deceleration).
• John Rennie almost 8 years
Calculating all this from first principles would be a formidable task. I suspect the best you can do is measure the deceleration under some controlled conditions and use that to calculate the drag. Note that the drag will be a function of speed.
• Raresh Gosman almost 8 years
When it goes into Neutral, this disengages the engine. The car is left to roll on the bearings that support the week. It becomes an oversized Hot Wheels car, which slows down because there is no more locomotive power pushing it forwards. Wind resistance and friction are primarily what will slow it down. To clarify, there WILL indeed be deceleration. Sorry for any confusion.
• CuriousOne almost 8 years
In cases like these one wouldn't try to calculate from first principles but do measurements on the real thing and then fit a number of parameters to the data.